Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system are obtained through a variation-induced exact diagonalization procedure. The information entropy-based uncertainty relation is shown to be a better measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in this case. Additionally, the phase-space description provides a semi-classical explanation for this feature. Total information entropy and phase-space area show similar behavior with increasing barrier height.

Information-based uncertainty quantities like Fisher information, Shannon entropy, Onicescu energy and Onicescu-Shannon entropy are shown to be better a measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in a symmetric doublewell potential of the form,

These studies show appearences of extrema at certain characteristic β values explaining the interplay of localisation and delocalisation of the particle.

Electromagnetic theories have reproduced the scattering properties of differently shaped particles and successfully been used to characterize numerous systems. However, certain anomalous features remain unexplained that include enhanced extinction when particles are much smaller than the wavelength. Here we explain these features exploiting recent research in electromagnetic scattering theories that suggests incorporating the effect of particle charge results in new physical outcomes that deviate appreciably from what is predicted by electromagnetic interaction from uncharged systems. For electrically charged particles, the resonant excitation of surface modes is governed by excess charges deposited on the particle surface. Charge effects become large when particles are small compared to the incident wavelength, and we show that the electrostatic approximation is not valid for modelling the electromagnetic interaction from such particles. Charge-induced resonances appear in such systems that can reproduce previously unexplained phenomena, for instance, amplified microwave attenuation observed in sandstorms.

We report new developments in electromagnetic scattering theory in which charge-induced resonances in nanoparticles result from interaction with electromagnetic radiation. The net surface charge can be a significant factor in many systems, for instance, colloids of metallic particles. Among colloidal particles at liquid interfaces, charged nanoparticles are a fertile subject of new technological concepts and can be decisive in the development of new devices and novel technologies in the nanosciences, such as optical attenuators, modulators, and switches that can be turned on or off through the application of charge. For electrically charged particles, the resonant excitation of surface modes is governed by exc ess charges deposited on the particle surface. Charge-induced resonances appear in such systems that can reproduce previously unexplained phenomena, for instance, amplified microwave attenuation observed in sandstorms.

One way to look for complex behaviours in many-body quantum systems is to let the number *N* of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as tend to commute, whence complexity at the quantum level can only be inherited from complexity at the classical level. Instead, fluctuations of microscopic observables scale as and exhibit collective Bosonic features, typical of a mesoscopic regime half-way between the quantum one at the microscopic level and the classical one at the level of macroscopic averages. Here, we consider the mesoscopic behaviour emerging from an infinite quantum spin chain undergoing a microscopic dissipative, irreversible dynamics and from global states without long-range correlations and invariant under lattice translations and dynamics. We show that, from the fluctuations of one site spin observables whose linear span is mapped into itself by the dynamics, there emerge bosonic operators obeying a mesoscopic dissipative dynamics mapping Gaussian states into Gaussian states. Instead of just depleting quantum correlations because of decoherence effects, these maps can generate entanglement at the collective, mesoscopic level, a phenomenon with no classical analogue that embodies a peculiar complex behaviour at the interface between micro and macro regimes.

Here, it is considered the mesoscopic behaviour emerging from an infinite quantum spin chain undergoing a microscopic dissipative, irreversible dynamics and from global states without long-range correlations and invariant under lattice translations and dynamics. It is shown that, from the fluctuations of one site spin observables whose linear span is mapped into itself by the dynamics, there emerge bosonic operators obeying a mesoscopic dissipative dynamics mapping Gaussian states into Gaussian states.

This brief review describes a class of uniquely crafted particle physics experiments that typically each tackle just one investigation—and they do that very well. The aim of these experiments is to both establish Standard Model parameters and also to provide unique tests in search of new physics. I provide a brief snapshot of many of the current activities, selected with a bias toward low-energy and high precision. These include searches for permanent electric dipole moments, charged lepton flavor violation, tests of the weak interaction, and other broad searches for deviations from very precise Standard Model predictions, such as the muon's anomalous magnetic moment. I highlight what drives these efforts and how they might impact a new Standard Model.

The deserved world's attention on the re-energized atom-smashing power of the Large Hadron Collider anticipates the discovery of new physics beyond the Standard Model. However, there is a quieter, alternative and complementary approach, which does not rely on Earth-shattering high energy collisions, but instead uses exquisite precision to hunt for deviations from Standard Model expectations. In this review, we describe a series of these unique experiments that may have far reaching implications.

We present a feasible protocol of continuous variable quadripartite entanglement from the coupled type I second harmonic generation (SHG) below threshold. According to the sufficient inseparability criteria for multipartite continuous variable (CV) entanglement, the four output fields are proved to be multicolored entangled beams in separable locations with four-mode amplitude quadratures correlation and relative phase quadratures correlation. It shows that the coupled system can produce a compact tunable multimode entangled source that can be applied into the quantum communication.

The continuous variable quadripartite entanglement generated by the coupled type I second harmonic generation are investigated below threshold. The entanglement degree versus normalized frequency, pump parameter, and coupling parameter are analyzed. The four output fields are proved to be entangled beams in separable locations. The result shows that the coupled system can be used to produce compact multimode entangled resource for quantum communication.

One of the major challenges of modern physics is to decipher the nature of dark matter. Astrophysical observations provide ample evidence for the existence of an invisible and dominant mass component in the observable universe, from the scales of galaxies up to the largest cosmological scales. The dark matter could be made of new, yet undiscovered elementary particles, with allowed masses and interaction strengths with normal matter spanning an enormous range. Axions, produced non-thermally in the early universe, and weakly interacting massive particles (WIMPs), which froze out of thermal equilibrium with a relic density matching the observations, represent two well-motivated, generic classes of dark matter candidates. Dark matter axions could be detected by exploiting their predicted coupling to two photons, where the highest sensitivity is reached by experiments using a microwave cavity permeated by a strong magnetic field. WIMPs could be directly observed via scatters off atomic nuclei in underground, ultra low-background detectors, or indirectly, via secondary radiation produced when they pair annihilate. They could also be generated at particle colliders such as the LHC, where associated particles produced in the same process are to be detected. After a brief motivation and an introduction to the phenomenology of particle dark matter detection, I will discuss the most promising experimental techniques to search for axions and WIMPs, addressing their current and future science reach, as well as their complementarity.

There is overwhelming evidence for dark matter in our Universe. So far, it is based on indirect observations, where its influence on visible matter is studied. A large programme of experiments aiming to directly detect this new form of matter in the laboratory, in space or to produce it at particles colliders is underway. These approaches are complementary to one another and exciting new results are expected within the current decade.

We study the quantum exciton dynamics in light-harvesting complexes under the influence of underdamped vibrational molecular modes. We observe prolonged coherent population oscillations between different pigments due to an underdamped mode connected to the originally excited pigment. At the same time, an underdamped vibration at the exit site of the complex provides additional channels for the excitation energy transfer towards the reaction center which shortens the transfer times.

The article studies the influence of coherent vibrational quantum modes on energy transfer dynamics in light-harvesting complexes. Coherent vibrational quantum modes coupled to the energy entrance pigment prolong coherent population oscilations between the entrance and neighbouring pigments. Modes coupled to the energy exit pigments enhance energy transfer speeds.

We discuss the impact the observation of the Higgs Boson has had on models of Dark Energy.

Perhaps the most perplexing fact about our Universe is that it is accelerating today due to some unknown form of Dark Energy which makes up 65% of the total energy density pie. In this brief article we discuss possible links between the Higgs field and the nature of Dark Energy and ask how might we test for the latter now that we know something about the former.

We investigate in detail a recently introduced “coherent averaging scheme” in terms of its usefulness for achieving Heisenberg limited sensitivity in the measurement of different parameters. In the scheme, *N* quantum probes in a product state interact with a quantum bus. Instead of measuring the probes directly and then averaging as in classical averaging, one measures the quantum bus or the entire system and tries to estimate the parameters from these measurement results. Combining analytical results from perturbation theory and an exactly solvable dephasing model with numerical simulations, we draw a detailed picture of the scaling of the best achievable sensitivity with *N*, the dependence on the initial state, the interaction strength, the part of the system measured, and the parameter under investigation. In particular, we identify the situations allowing one to reach Heisenberg-limited scaling of the sensitivity.

Quantum enhanced measurements are usually associated with highly entangled states. They allow one to achieve Heisenberg-limited scaling of the sensitivity of measurements. The coherent averaging scheme achieves the same without entanglement by modifying the basic information flow: instead of classically averaging measurement results from independent probes, the information is assembled in the quantum realm by means of an interaction of the probes with a common quantum bus.

Vibrational relaxation is a key issue in chemical reaction dynamics in condensed phase and at the gas-surface interface, where the environment is typically highly structured and cannot be expressed in terms of a simple friction coefficient. Rather, full knowledge of the coupling of the molecular oscillator to the environment is required, as typically subsumed in the spectral density of the environmental coupling. Here, we focus on harmonic Brownian motion and investigate the effectiveness of classical, canonical position autocorrelation functions to compute the spectral density of the coupling needed to describe vibrational relaxation in complex environments. Classical dynamics is performed on model systems, and several effects are investigated in detail, notably the presence of anharmonicity, the role of a high-frequency “Debye” cutoff in the environment and the influence of the detailed structure of the latter. The spectral densities are then used in standard independent oscillator Hamiltonian models which are numerically solved at T = 0 K to investigate quantum relaxation and decoherence.

This article investigates the effectiveness of classical, canonical position autocorrelation functions to compute the spectral density of the coupling needed to describe vibrational relaxation and decoherence in complex environments. The effect of anharmonicity and of a high-frequency “Debye” cutoff are addressed in detail, and the high-dimensional quantum dynamics of the associated independent oscillator models is investigated at T = 0 K with a numerically exact method.

The apparent dominance of matter over antimatter in our universe is an obvious and puzzling fact which cannot be adequately explained in present physical frameworks that assume matter-antimatter symmetry at the big bang. However, our present knowledge of starting conditions and of known sources of CP violation are both insufficient to explain the observed asymmetry. Therefore ongoing research on matter-antimatter differences is strongly motivated as well as attempts to identify viable new mechanisms that could create the present asymmetry. Here we concentrate on possible precision experiments at low energies towards a resolution of this puzzle.

The dominance of matter over antimatter in our universe today is an obvious and puzzling fact. It cannot be sufficiently explained in present physical frameworks built on symmetric conditions at the big bang. Known sources of CP violation are insufficient to explain the matter-antimatter asymmetry. CPT violation could alternatively provide an explanation and is therefore being searched for as well as are differences in the properties of particles and their antiparticles. New precision experiments at low energies provide for a promising way towards resolving this puzzle.

The quantum efficiency in the transfer of an initial excitation in disordered finite networks, modeled by the *k*-body embedded Gaussian ensembles of random matrices, is studied for bosons and fermions. The influence of the presence or absence of time-reversal symmetry and centrosymmetry/centrohermiticity are addressed. For bosons and fermions, the best efficiencies of the realizations of the ensemble are dramatically enhanced when centrosymmetry (centrohermiticity) is imposed. For few bosons distributed in two single-particle levels this permits perfect state transfer for almost all realizations when one-particle interactions are considered. For fermionic systems the enhancement is found to be maximal for cases when all but one single particle levels are occupied.

Disordered centrosymmetric networks of fermionic or bosonic many-body systems with few-body interactions display remarkable statistical properties of the best transport efficiencies attained, with non-zero probability for perfect state transfer.

We report on dissipative exciton dynamics calculations performed with the hierarchy equations of motion method for a molecular heterodimer coupled to a multi-mode Brownian oscillator bath. Coherent oscillations in the population dynamics after initial excitation of the highest exciton state are analysed in terms of a Fourier spectrum and compared to the exciton-vibronic structure of the dimer eigenstates obtained by means of direct diagonalization. The signatures of Coulomb coupling induced quantum state mixing between elementary excitonic and vibronic excitations are systematically discussed for various Coulomb coupling strengths and Huang-Rhys factors.

The issue of quantum state mixing between excitonic and vibronic excitations in a molecular heterodimer coupled to a bath is addressed, combining dissipative exciton dynamics calculations and with calculations of the vibronic level structure. Coherent oscillations in the population dynamics, which are systematically discussed in terms of Fourier spectra for various Coulomb and vibronic coupling strengths, indicate a significant influence of quantum state mixing on the dynamics.

Cosmic rays (charged particles), γ-rays and neutrinos offer unique opportunities to extend the search for dark matter, to test quantum gravity phenomenology through the study of the invariance of the group of Lorentz transformations, and to probe the existence of sterile neutrinos. We discuss here these tests of beyond the Standard Model particle physics with present and planned future missions including the Pierre Auger Observatory, the space-borne mission Alpha Magnetic Spectrometer (AMS-02), *Fermi*-LAT, the High Altitude Water Cherenkov (HAWC), the IceCube South Pole Neutrino Observatory as presently operating experiments, and the Cherenkov Telescope Array (CTA) and the IceCube-Gen2 as future large scale infrastructures.

The Standard Model of particle physics is extremely successful in describing the properties of matter and forces, although it leaves fundamental questions unanswered, like the existence of dark matter, the asymmetry of matter anti-matter in the universe, and the neutrino masses. Cosmic particles offer unique opportunities to address these many fundamental questions. Tests done with present and planned future missions are reviewed.

We review the Pyramid Scheme, the only class of models known to be consistent with phenomenology, coupling unification, and the Cosmological SUSY Breaking (CSB) relation between the gravitino mass and the cosmological constant (c.c.). These models are Terascale effective field theories, which have a super-Poincare invariant, discrete R symmetric limit. R breaking terms come from diagrams in which a gravitino is exchanged with the horizon, and satisfy peculiar selection rules, which solve the μ problem, the strong CP problem, and the problem of low dimension operators in the theory, which violate *B* and *L*. The model predicts large Dirac and Majorana masses for gauginos, which make these states heavier than corresponding squarks and sleptons by a factor of roughly . Gluinos are too heavy to be seen at the 14 TeV LHC, and the NLSP is a right handed slepton (the three sleptons are quite degenerate), which decays promptly into a gravitino and a lepton.

This article gives a brief summary of the Pyramid Schemes, a class of supersymmetric models of particle physics below the 100 TeV scale, which is compatible both with existing experimental constraints and the very low scale of supersymmetry breaking implied by the idea of Cosmological Supersymmetry Breaking. This idea leads to novel solutions to some of the fine tuning problems of the conventional approach to particle phenomenology based in effective quantum field theory. Most notable is the novel resolution of the absence of CP violation in strong interaction physics. The Pyramid Schemes, in a certain range of parameters predict that squarks are much lighter than gluinos and that the lightest supersymmetric particle, apart from the gravitino, is a supersymmetric partner of one of the right handed leptons.

The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically by the nonequilibrium Green's function method. In the case of specular reflections at the boundary, the Hall resistance shows equidistant peaks, which are due to classical cyclotron motion. When the strength of the magnetic field is increased, anomalous resistance oscillations are observed, similar to those found in a nonrelativistic 2D electron gas [New. J. Phys. 15:113047 (2013)]. Using a simplified model, which allows to solve the Dirac equation analytically, the oscillations are explained by the interference between the occupied edge states causing beatings in the Hall resistance. A rule of thumb is given for the experimental observability. Furthermore, the local current flow in graphene is affected significantly by the boundary geometry. A finite edge current flows on armchair edges, while the current on zigzag edges vanishes completely. The quantum Hall staircase can be observed in the case of diffusive boundary scattering. The number of spatially separated edge channels in the local current equals the number of occupied Landau levels. The edge channels in the local density of states are smeared out but can be made visible if only a subset of the carbon atoms is taken into account.

The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically. In the case of specular boundary reflections, the Hall resistance shows equidistant peaks due to classical cyclotron motion. When the magnetic field strength is increased, anomalous resistance oscillations appear. Solving the Dirac equation analytically within a simplified model, the oscillations are explained by the interference between the occupied edge states.

The complexity of a quantum state may be closely related to the usefulness of the state for quantum computation. We discuss this link using the tree size of a multiqubit state, a complexity measure that has two noticeable (and, so far, unique) features: it is in principle computable, and non-trivial lower bounds can be obtained, hence identifying truly complex states. In this paper, we first review the definition of tree size, together with known results on the most complex three and four qubits states. Moving to the multiqubit case, we revisit a mathematical theorem for proving a lower bound on tree size that scales superpolynomially in the number of qubits. Next, states with superpolynomial tree size, the Immanant states, the Deutsch-Jozsa states, the Shor's states and the subgroup states, are described. We showed that the universal resource state for measurement based quantum computation, the 2D cluster state, has superpolynomial tree size. Moreover, we showed how the complexity of subgroup states and the 2D cluster state can be verified efficiently. The question of how tree size is related to the speed up achieved in quantum computation is also addressed. We show that superpolynomial tree size of the resource state is essential for measurement based quantum computation. The necessary role of large tree size in the circuit model of quantum computation is still a conjecture; and we prove a weaker version of the conjecture.

The complexity of a quantum state may be closely related to the usefulness of the state for quantum computation. This link is discussed using the tree size of a multiqubit state, a complexity measure that has two noticeable features: it is in principle computable, and non-trivial lower bounds can be obtained, hence identifying truly complex states. The 2D cluster states are shown to have verifiable superpolynomial tree size.

The discovery of a light Higgs boson at the LHC opens a broad program of studies and measurements to understand the role of this particle in connection with New Physics and Cosmology. Supersymmetry is the best motivated and most thoroughly formulated and investigated model of New Physics which predicts a light Higgs boson and can explain dark matter. This paper discusses how the study of the Higgs boson connects with the search for supersymmetry and for dark matter at the LHC and at a future collider and with dedicated underground dark matter experiments.

The Higgs boson discovery at LHC starts an exciting program to understand the role of this particle in connection with New Physics and Cosmology. Supersymmetry is the best motivated and thoroughly formulated model of New Physics predicting a light Higgs and able to explain dark matter. This paper connects the study of the Higgs boson with the search for supersymmetry and dark matter at colliders and underground experiments.

The state of supersymmetry after RUN I of the LHC is discussed. Several scenarios with signatures of supersymmetry more hidden than it is suggested by the simplest models are reviewed.

There are many good reasons to favor supersymmetry as an extension of the Standard Model. But it may be more hidden than often expected and one should pursue experimental search for it, keeping in mind several different scenarios.

In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schrödinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics.

In the context of the exact factorization of the electron-nuclear wave function, the time-dependent potential energy surface is calculated to propagate semiclassically frozen gaussians. The nuclear wave function, from the factorization, is reconstructed as the superposition of coherent states, the complex-valued frozen gaussians. This approximation is used to study the electron-nuclear coupling term in the electronic equation from the factorization, representing the nuclear effect on electronic dynamics.

The discovery of non-zero neutrino mass and mixing has opened a portal to physics beyond the Standard Model whose implications are only beginning to be understood. The next decade promises critical developments with a program of ambitious experiments that will probe the fundamental nature of neutrino mass and mixing, and provide important clues on the primordial matter-dominance of the universe.

The discovery of non-zero neutrino mass and mixing has opened a portal to physics beyond the Standard Model. The next decade promises critical developments with a program of ambitious experiments that will probe the fundamental nature of neutrino mass and mixing, and provide important clues on the primordial matter-dominance of the universe. The image shows an electron-like Cherenkov ring in the Super-Kamiokande detector arising from the conversion of a muon neutrino produced in the T2K neutrino beam to an electron neutrino through the neutrino oscillation process (image: courtesy of the T2K collabortion and the Kamioka Observatory, ICRR, University of Tokyo).

We investigate electron transport in two quantum circuits with mutual Coulomb interaction. The first circuit is a double quantum dot connected to two electron reservoirs, while the second one is a quantum point contact in the weak tunneling limit. The coupling is such that an electron in the first circuit enhances the barrier of the point contact and, thus, reduces its conductivity. While such setups are frequently used as charge monitors, we focus on two different aspects. First, we derive transport coefficients which have recently been employed for testing generalized equilibrium conditions known as exchange fluctuation relations. These formally exact relations allow us to test the consistency of our master equation approach. Second, a biased point contact entails noise on the DQD and induces non-equilibrium phenomena such as a ratchet current.

Quantum dots are often coupled to a point contact that measures the dot occupation. This setup can be employed beyond that purpose. For example, if a double quantum dot is strongly detuned, the shot noise of the point contact can induce a pump or ratchet current. Moreover, it allows testing the compliance of a master equation formalism with exact generalized equilibrium relations known as exchange fluctuation theorems.

Scattering theory is complemented by recent results on full counting statistics, the multivariate fluctuation relation for currents, and time asymmetry in temporal disorder characterized by the Connes-Narnhofer-Thirring entropy per unit time, in order to establish relationships with the thermodynamics of quantum transport. Fluctuations in the bosonic or fermionic currents flowing across an open system in contact with particle reservoirs are described by their cumulant generating function, which obeys the multivariate fluctuation relation as the consequence of microreversibility. Time asymmetry in temporal disorder is shown to manifest itself out of equilibrium in the difference between a time-reversed coentropy and the Connes-Narnhofer-Thirring entropy per unit time. This difference is shown to be equal to the thermodynamic entropy production for ideal quantum gases of bosons and fermions. The results are illustrated for a two-terminal circuit.

Thermodynamic entropy is produced during the quantum transport of bosons or fermions through a small hole in a thin wall separating two reservoirs at different temperatures or densities. Yet, the Hamiltonian microdynamics is symmetric under time reversal. Time asymmetry arises at the statistical level of description after the paths of the scattering process are weighted by probabilities associated with the reservoirs where the particles are coming from.

The pattern of quark flavour violation predicted by the Standard Model agrees within theoretical and experimental uncertainties with the available data except for a number of intriguing anomalies that require further investigation. In the coming flavour precision era a multitude of new observables will be measured and the accuracy of the measurements of quark flavour violating rare processes and of the relevant lattice QCD calculations will be significantly improved. This will allow us not only to clarify these anomalies but also hopefully to discover new physics (NP). On the other hand a discovery of charged lepton flavour violation and of non-vanishing electric dipole moments (EDMs) of particles would be a clear signal of NP. Most importantly the unique role of quark and lepton flavour physics and of EDMs in the coming years will be to allow us to get insight into the dynamics well beyond the reach of high energy processes at the LHC. In fact scales as short as 10^{−21} m (*Zeptouniverse*) corresponding to energy scale of 200 TeV or even shorter distance scales can be explored in this manner. We discuss the requirements that have to be met for such a flavour expedition to the Zeptouniverse to be successful. In particular we emphasize the power of correlations between flavour observables in the search for NP. In this context the proposed DNA charts allow for a clear distinction between various alternatives for the new dynamics at the LHC scales and at much shorter distance scales.

In the coming flavour precision era a multitude of new quark and lepton flavour observables will be measured with high precision and theoretical calculations will improve. This will hopefully bring the discovery of new physics beyond the Standard Model. Most importantly the unique role of quark and lepton flavour physics in the coming years will be to allow us with the help of quantum fluctuations to get insight into the dynamics at length scales as short as ). The requirements that have to be met for such a flavour expedition to the Zeptouniverse to be successful are summarized.

A brief review is given of the implications of a 126 GeV Higgs boson for the discovery of supersymmetry. Thus a 126 GeV Higgs boson is problematic within the Standard Model because of vacuum instability pointing to new physics beyond the Standard Model. The problem of vacuum stability is overcome in the SUGRA GUT model but the 126 GeV Higgs mass implies that the average SUSY scale lies in the several TeV region. The largeness of the SUSY scale relieves the tension on SUGRA models since it helps suppress flavor changing neutral currents and CP violating effects and also helps in extending the proton life time arising from baryon and lepton number violating dimension five operators. The geometry of radiative breaking of the electroweak symmetry and fine tuning in view of the large SUSY scale are analyzed.Consistency with the Brookhaven result is discussed. It is also shown that a large SUSY scale implied by the 126 GeV Higgs boson mass allows for light gauginos (gluino, charginos, neutralinos) and sleptons. These along with the lighter third generation squarks are the prime candidates for discovery at RUN II of the LHC. Implication of the 126 GeV Higgs boson for the direct search for dark matter is discussed. Also discussed are the sparticles mass hierarchies and their relationship with the simplified models under the Higgs boson mass constraint.

A brief review is given of the implications of a 126 GeV Higgs boson for the discovery of supersymmetry. The 126 GeV Higgs mass implies a large SUSY scale which explains the non-observation of sparticles thus far. The large scale also helps suppression of FCNC, CP violation effects and helps stabilize the proton against B&L violating dimension five operators. It is shown that the gluino, charginos, neutralinos, sleptons and a stop can be light and are the prime candidates for discovery at the LHC.

Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi–one-dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer-matrix scheme, for strips of different widths. These results are described accurately by analytical formulas based on a weak-disorder expansion of backscattering mean free paths.

The interplay of disorder and interaction is studied via the Anderson localization of Bogoliubov quasiparticles, the elementary excitations of disordered lattice Bose gases in quasi-one-dimensional geometries. The localization length is computed by a numerical transfer-matrix scheme. These results are described accurately by analytical formulas based on a weak-disorder expansion of backscattering mean free paths. This approach provides a framework for the description of transport and localization in mesoscopic systems of interacting bosons.

Quantum mechanical effects can enable energy to flow more efficiently in one direction along a molecule than in others. Ultrafast spectroscopic experiments on substituted benzenes [J. Phys. Chem. B 117, 10898 (2013)] reveal such an asymmetry in the flow of vibrational energy between the two chemical groups of the molecule, i.e., between the phenyl and the substituent. We examine theoretically energy flow in toluene, one of the substituted benzenes probed in the recent experiments, and show that quantum mechanical bottlenecks give rise to a preferred direction of energy flow in this molecule.

There is currently much interest in designing nanoscale thermal diodes, in which vibrational energy transport in one direction is more favorable than in the other. This paper presents a theoretical analysis of a molecular vibrational energy diode. It is shown that quantum mechanical bottlenecks to vibrational energy transfer in specific chemical groups give rise to a preferred direction of energy flow in the molecule.

We introduce a number of random matrix models describing the Google matrix *G* of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and a broad distribution of eigenvalues in the complex plain. The eigenstates of *G* are characterized by the Anderson transition from localized to delocalized states and a mobility edge curve in the complex plane of eigenvalues.

Anderson transition, awarded by Nobel prize, appears in disordered solids separating insulator (localized) and metallic (delocalized) phases of electron transport. It exists also in random matrix ensembles of Hermitian matrices. Here, random matrix models of Markov chains and Google matrix Gare considered. The eigenvectors of G, and especially PageRank vector, are at the basis of Google search engine of World Wide Web and other directed networks. The results for random matrix models of G show that the Anderson transition, from localized (blue) to delocalized (rose) states, appears in a domain of complex eigenvalues λ of G at certain conditions (see Fig.).

A two-band Bose-Hubbard model is presented which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many-body problem is studied by sweeping the system across an avoided level crossing. The linear sweep generalizes Landau-Zener transitions from single-particle to many-body realizations. The temporal evolution of single- and two-body observables along the sweeps is investigated in order to characterize the non-equilibrium dynamics in our complex quantum system.

The standard problem of Bloch bands is extended to a situation with many-body correlations. This gives a rich and experimentally accessible scenario for tests of quantum chaos and the study of a coherent sequence of Landau-Zener transitions and quantum thermalization. Since the time scales of strong interband mixing can be controlled at will, a fast thermalization and an engineering of the interband dynamics is promising for future experiments.

Open many-body quantum systems have recently gained renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. A series of results in diverse setups is presented, based on a Master equation approach to describe the dissipative dynamics of ultracold bosons in a one-dimensional lattice. The creation of mesoscopic stable many-body structures in the lattice is predicted and the non-equilibrium transport of neutral atoms in the regime of strong and weak interactions is studied.

Recent advances in the fields of quantum information, quantum transport (also with biological clusters) and ultracold atoms have renewed the interest in open many-body quantum systems. Different setups are studied describing the dissipative dynamics of ultracold bosons in a one-dimensional lattice. The creation of mesoscopic superpositions of stable solitons are predicted and the impact of interactions and reservoir couplings on the non-equilibrium transport of the atoms is studied.

Stefan W. Hell received the Nobel Prize in Chemistry in 2014 “for the development of super-resolved fluorescence microscopy”, together with Eric Betzig and William Moerner. With the invention of STED (Stimulated Emission Depletion) microscopy experimentally realized in 1999, he has revolutionized light microscopy, overcoming the resolution limit of conventional optical microscopes - a breakthrough that has enabled new ground-breaking discoveries in biological and medical research.

Picture: Stefan W. Hell, pp. 423–445 in this issue (© Andriy Chmyrov, Stefan Hell, Max Planck Institute for Biophysical Chemistry)

Stefan W. Hell received the Nobel Prize in Chemistry in 2014 “for the development of super-resolved fluorescence microscopy”, together with Eric Betzig and William Moerner. With the invention of STED (Stimulated Emission Depletion) microscopy experimentally realized in 1999, he has revolutionized light microscopy, overcoming the resolution limit of conventional optical microscopes – a breakthrough that has enabled new ground-breaking discoveries in biological and medical research.

Stefan W. Hell received the Nobel Prize in Chemistry in 2014 “for the development of super-resolved fluorescence microscopy”, together with Eric Betzig and William Moerner. With the invention of the STED (Stimulated Emission Depletion) microscopy he has revolutionized light microscopy, overcoming the resolution limit of conventional optical microscopes – a breakthrough that has enabled new ground-breaking discoveries in biological and medical research. Image: Live-cell imaging with parallelized RESOLFT nanoscopy. The image shows the protein keratin in cancer cells. The image is based on recording 144 frames, the total image acquisition time was on the order of a second. Scale bar: 10 μm. (© Andriy Chmyrov, Stefan Hell, Max Planck Institute for Biophysical Chemistry).

A digital micromirror device (DMD) is a product of micromechanics. The DMD employs numerous micromirrors as the actuating components to switch small portions of light on and off. During the past few decades, such devices have been widely applied in digital light processing technology. The expanding range of applications makes the DMD increasingly important in various research aspects. Recent advances demonstrate that the DMD is potentially better than the traditional liquid crystal spatial light modulator in speed, spectrum sensitivity, and polarization modulation. These characteristics have been verified in a series of recently reported experiments. This review summarizes the related theory, experimental techniques, and applications for wavefront shaping with DMDs in both statically shaping various spatial modes and dynamically compensating for wavefront distortion caused by the scattering medium.

A digital micromirror device (DMD) employs numerous micromirrors as the actuating components to switch small portions of light. The expanding range of applications makes the DMD increasingly important in various research aspects. A series of recent reports have verified that such a device has better perfomance than the liquid crystal counterparts. The review summarizes the related theory, experimental techniques, and applications for both static and dynamic wavefront shaping systems.

Nonlinear optical microscopy (NLOM) relies on nonlinear light–matter interactions to provide images from larger depths within biological structures compared to conventional confocal fluorescence microscopy. These nonlinear light–matter interactions include multiphoton excitation fluorescence (MPEF), second-harmonic generation (SHG), coherent anti-Stokes Raman scattering (CARS), and stimulated Raman scattering (SRS). This review discusses the theories of and instrumentation for various NLOM techniques, with a particular focus on endogenous signals and exogenous probes. These signals and probes expand the breadth of information that optical imaging can provide. We also discuss the application of NLOM in biomedical research, including tissue engineering, drug delivery and clinical diagnostics. Current technological limitations are also discussed.

Nonlinear optical microscopy (NLOM) relies on nonlinear light–matter interactions to provide images from larger depths within biological structures compared to conventional confocal fluorescence microscopy. These nonlinear light–matter interactions include multiphoton excitation fluorescence (MPEF), second-harmonic generation (SHG), coherent anti-Stokes Raman scattering (CARS), and stimulated Raman scattering (SRS). This review discusses the theories of and instrumentation for various NLOM techniques, with a particular focus on endogenous signals and exogenous probes.

The interest to mesoscale dielectric objects, whose effective dimensions are comparable with the incident radiation wavelength, is caused by their unique ability to modify the spatial structure of the incident wave in the specific manner and to produce a highly localized intensive optical flux (“photonic jet”) with the subwavelength spatial resolution. In the current paper we brief review the modern state-of-the-art of main principles of the photonic jet formation by non-spherical and non-symmetrical dielectric mesoscale particles both in transmitting and reflection mode. A deeper understanding of the photonic jet is nevertheless needed to fully exploit the potential performance of nano- and micro- dielectric mesoscale objects as diffractive components at different wavebands.

So far, the bulk of theoretical studies of so-called photonic jets are devoted to the light jets originated from microparticles with high degree of spatial symmetry like spheres, spheroids, cylinders, disks because of their unique capability to produce extreme spatial field localization.

In this paper we intend to fill this gap and brief review of investigations on EM-jet formation by the 3D mesoscale particles with more complicated non-spherical spatial shapes and even by non-symmetric bodies both in transmitting and reflection modes.

We determine the regularized van der Waals contribution to pressure within a spherical cavity of vapor in a homogeneous, isotropic, infinite medium. The spherical Hamaker function, , has been defined, for the first time, in contrast to the conventional Hamaker function for planar surfaces, . For the materials under consideration, the pressure inside the cavity varies as , where *a* is the radius of the cavity. For radii below a transition radius, the surface energy (or surface tension) becomes size dependent and could have important implications for homogeneous nucleation of nanosized bubbles in liquids, as well as cavitation of bubbles.

How does the Casimir effect affect surface energy of a nanocavity in a homogeneous, isotropic, infinite medium? A transition radius has been determined by calculating the newly defined spherical Hamaker function in comparison to the conventional Hamaker function for planar surface. For radii below the transition radius, surface energy or surface tension becomes size dependent and could have important implications for homogeneous nucleation of nanosized bubbles in liquids, as well as cavitation of bubbles.

Repulsive gravity is not very popular in physics. However, one comes across it in at least two main occurrences in general relativity: in the negative-*r* region of Kerr spacetime, and as the result of the gravitational interaction between matter and antimatter, when the latter is assumed to be CPT-transformed matter. Here we show how these two independent developments of general relativity are perfectly consistent in predicting gravitational repulsion and how the above Kerr negative-*r* region can be interpreted as the habitat of antimatter. As a consequence, matter particles traveling along vortical geodesics can pass through the throat of a rotating black hole and emerge as antimatter particles (and vice versa). An experimental definitive answer on the gravitational behavior of antimatter is awaited in the next few years.

One comes across repulsive gravity in two main occurrences in general relativity: in the negative-*r* region of Kerr spacetime, and as the result of the matter-antimatter gravitational interaction, when the latter is assumed to be CPT-transformed matter. Here it is shown how these two independent developments of general relativity are perfectly consistent in predicting gravitational repulsion and how the Kerr negative-*r* region can be interpreted as the habitat of antimatter.

Microsphere-assisted imaging has emerged as an extraordinary simple technique of obtaining optical super-resolution. This work addresses two central problems in developing this technology: i) methodology of the resolution measurements and ii) limited field-of-view provided by each sphere. It is suggested that a standard method of resolution analysis in far-field microscopy based on convolution with the point-spread function can be extended into the super-resolution area. This allows developing a unified approach to resolution measurements, which can be used for comparing results obtained by different techniques. To develop the surface scanning functionality, the high-index (*n* ∼ 2) barium titanate glass microspheres were embedded in polydimethylsiloxane (PDMS) thin-films. It is shown that such films adhere to the surface of nanoplasmonic structures so that the tips of embedded spheres experience the objects’ optical near-fields. Based on rigorous criteria, the resolution ∼*λ*/6-*λ*/7 (where *λ* is the illumination wavelength) is demonstrated for arrays of Au dimers and bowties. Such films can be translated along the surface of investigated samples after liquid lubrication. It is shown that just after lubrication the resolution is diffraction limited, however the super-resolution gradually recovers as the lubricant evaporates.

Microsphere-assisted imaging has emerged as an extraordinary simple technique of obtaining optical super-resolution. This work addresses two central problems in developing this technology: i) methodology of the resolution measurements and ii) limited field-of-view provided by each sphere. It is suggested that a standard method of resolution analysis in far-field microscopy based on convolution with the point-spread function can be transferred into the super-resolution area. It is shown that this allows developing unified approach to resolution measurements which can be used for comparing results obtained by different techniques. To develop the surface scanning functionality, the high-index (*n*∼2) barium titanate glass microspheres were embedded in polydimethylsiloxane (PDMS) thin films. It is shown that such films adhere to the surface of nanoplasmonic structures so that the tips of embedded spheres experience the objects’ optical near-fields. Based on rigorous criteria, the resolution ∼*λ*/6-*λ*/7 (where *λ* is the illumination wavelength) is demonstrated for arrays of Au dimers and bowties. Such films can be translated along the surface of investigated samples after liquid lubrication. It is shown that just after lubrication the resolution is diffraction limited, however the super-resolution gradually recovers as the lubricant evaporates.

Single crystalline LiAlO is known as a very poor ion conductor. Thus, in its crystalline form it unequivocally disqualifies itself from being a powerful solid electrolyte in modern energy storage systems. On the other hand, its interesting crystal structure proves beneficial to sharpen our understanding of Li ion dynamics in solids which in return might influence application-oriented research. LiAlO allows us to apply and test techniques that are sensitive to extremely slow Li ion dynamics. This helps us clarifying their diffusion behaviour from a fundamental point of view. Here, we combined two techniques to follow Li ion translational hopping in LiAlO that can be described by the same physical formalism: dynamic *mechanical* relaxation and *electrical* relaxation, *i.e*., ionic conductivity measurements. Via both methods we were able to track the same transport mechanism in LiAlO. Moreover, this enabled us to directly probe extremely slow Li exchange rates at temperatures slightly above 430 K. The results were compared with recent insights from nuclear magnetic resonance spectroscopy. Altogether, an Arrhenius-type Li diffusion process with an activation energy of ca. 1.12 eV was revealed over a large dynamic range covering 10 orders of magnitude, *i.e*., spanning a dynamic range from the nano-second time scale down to the second time scale.

LiAlO_{2} serves as a suitable model system to study extremely slow Li ion transport properties in an oxide that is composed of corner-shared LiO_{4}-polyhedra. The study represents one of the rare cases where both *electrical* and *mechanical* relaxation have been applied to monitor the same Li ion transport process in single crystals. Our results point to Debye-like translational ion dynamics with an activation energy of ca. 1.12 eV.