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.

Shuji Nakamura discovered *p*-type doping in Gallium Nitride (GaN) and developed blue, green, and white InGaN based light emitting diodes (LEDs) and blue laser diodes (LDs). His inventions made possible energy efficient, solid-state lighting systems and enabled the next generation of optical storage. Together with Isamu Akasaki and Hiroshi Amano, he is one of the three recipients of the 2014 Nobel Prize in Physics. In his Nobel lecture, Shuji Nakamura gives an overview of this research and the story of his inventions***.

Shuji Nakamura discovered p-type doping in Gallium Nitride (GaN) and developed blue, green, and white light emitting diodes (LEDs) and blue laser diodes (LDs). His inventions made possible energy efficient, solid-state lighting systems and enabled the next generation of optical storage. Together with Isamu Akasaki and Hiroshi Amano, he is one of the three recipients of the 2014 Nobel Prize for Physics. In his Nobel lecture, Shuji Nakamura gives an overview of this research and the story of his inventions.

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.

A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field is present the phenomenon of vacuum birefringence takes place. The indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field are calculated. The electric field of a point-like charge is not singular at the origin and the static electric energy is finite. We have calculated the static electric energy of point-like particles for different parameters of the model. The canonical and symmetrical Belinfante energy-momentum tensors and dilatation current are obtained. We demonstrate that the dilatation symmetry and dual symmetry are broken in the model suggested.

A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field is present the phenomenon of vacuum birefringence takes place. The indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field are calculated. The electric field of a point-like charge is not singular at the origin and the static electric energy is finite. The static electric energy of point-like particles for different parameters of the model is calculated. The canonical and symmetrical Belinfante energy-momentum tensors and dilatation current are obtained. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the model suggested.

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.

An ideal way to design a material with a specific property would be to solve an inverse problem: use a physical property to predict structure. In his review, **Vladan Mlinar** proposes strategies of utilizing an inverse approach to design materials over nano- to macro-scales are discussed. Risks and limitations of the approach are analyzed and its dependence on factors such as structure parametrization, approximations in theoretical models, feedback from structural characterization is addressed.

Picture: V. Mlinar, pp. 187-204 in this issue

A new type of photonic crystal (PC) named graded index 2 (GRIN) PC was proposed by E. Centeno in 2005. It is obtained by appropriately modifying the parameters of a regular PC, thus resulting in gradual index variation. In their review, **Qingyi Zhu, Lei Jin, and Yongqi Fu** introduce different ways of designing GRIN PCs from both theoretical and experimental point of views. They proposed a GRIN PC with radial index variation (pp. 205–218). Some typical applications based on GRIN PCs are presented, followed by the focusing mechanism of GRIN PC.

Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process in order to account for the impossibility of instantaneous measurement of physical fields. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. In particular, we analyze how an uniformly accelerated observer perceives a homogeneous and isotropic black body radiation. We show that all nonlocal effects are transient and most relevant in the first period of acceleration.

]]>In the light of recent developments in computer technology, a promising and efficient way to design a material with a desired property would be to solve the inverse problem: use a physical property to predict structure. Here, we discuss the basic idea and mathematical foundation of the inverse approach, and proposed strategies for its utilization in the design of materials over nano- to macro-scales. At the nano-scale, analyzed strategies include scanning of a high-dimensional space of chemical compounds for those compounds that have a targeted property, and identification of correlations in large databases of materials. However, unlike utilization of inverse approach at nano-scale where full structural information - atoms and their positions- is linked to targeted properties, at the meso- and macro-scale, only partial structural information, manifested via structural motifs or representative volume elements, is available. We discuss the role of partial structural information in the inverse approach to the design of materials at those scales. Risks and limitations of the inverse approach are analyzed and dependence of the approach on factors such as structure parametrization, approximations in theoretical models, and feedback from structural characterization, is addressed.

An ideal way to design a material with a specific property would be to solve an inverse problem: use a physical property to predict structure. Here, proposed strategies of utilizing an inverse approach to design materials over nano- to macro-scales are discussed. Risks and limitations of the approach are analyzed and its dependence on factors such as structure parametrization, approximations in theoretical models, feedback from structural characterization is addressed.

A new type of photonic crystal (PC) named graded index (GRIN) PC was proposed by E. Centeno in 2005. It is obtained by appropriately modifying the parameters of a regular PC, thus resulting in gradual index variation. Many applications are inspired by this notion. This review will introduce different ways of designing GRIN PCs from both theoretical and experimental point of views. Some typical applications based on GRIN PCs are presented, followed by the focusing mechanism of GRIN PC.

Graded index photonic crystal is a new type of photonic crystals. This review firstly introduces different ways of designing graded index photonic crystals. Then the emphasis is put on typical applications of graded index photonics crystals. Calculating the effective refractive index and the focusing mechanism of the graded index photonic crystals is also discussed in the review.

Defects and frequently used defect models of solids are reviewed. Signatures for identifying the disorder from x-ray and neutron scattering data are given. To give illustrative examples how technologically important defects contribute to x-ray and neutron scattering numerical method able to treat non-periodical solids possessing several simultaneous defect types is given for simulating scattering in nanosize disordered clusters. The approach takes particle size, shape, and defects into account and isolates element specific signals. As a case study a statistical approximation model for lead-zirconate titanate [Pb(Zr_{x}Ti)O_{3}, PZT] is introduced. PZT is a material possessing several defect types, including substitutional, displacement and surface defects. Spatial composition variation is taken into account by introducing a model in which the edge lengths of each cell depend on the distribution of Zr and Ti ions in the cluster. Spatially varying edge lengths and angles is referred to as microstrain. The model is applied to compute the scattering from ellipsoid shaped PZT clusters and to simulate the structural changes as a function of average composition. Two-phase co-existence range, the so called morphotropic phase boundary composition is given correctly. The composition at which the rhombohedral and tetragonal cells are equally abundant was . Selected x-ray and neutron Bragg reflection intensities and line shapes were simulated. Examples of the effect of size and shape of the scattering clusters on diffraction patterns are given and the particle dimensions, computed through Scherrer equation, are compared with the exact cluster dimensions. Scattering from two types of 180° domains in spherical particles, one type assigned to Ti-rich PZT and the second to the MPB and Zr-rich PZT, is computed. We show how the method can be used for modelling polarization reversal.

Methods for modelling technologically important defects are reviewed. A numerical approach for simulating scattering intensities from clusters of different size and shape, possessing co-existing defects, is given. As an example material lead-zirconate- titanate is used, a classical and probably the most widely used ferro- and piezoelectric material. It is demonstrated how complex disorder cases can be modeled and pinpoint the signatures in x-ray and neutron scattering intensity evidencing crystalline disorder.

In this paper, an implementation of energetic damping for fermionic transport simulations which respects particle conservation is presented. For this, nonhermitian terms in the Hamiltonian of the system are used. After an explanation of the method, it is demonstrated studying the current over time and I/V characteristics in the noninteracting resonant level model for spinless fermions.

In this paper, an implementation of energetic damping for fermionic transport simulations which respects particle conservation is presented. For this, nonhermitian terms in the Hamiltonian of the system are used. After an explanation of the method, it is demonstrated studying the current over time and I/V characteristics in the noninteracting resonant level model for spinless fermions.

The diffusion of gallium in liquid Ga-Sn alloy embedded into different porous silica matrices was studied by NMR. Spin relaxation was measured for two gallium isotopes, ^{71}Ga and ^{69}Ga, at two magnetic fields. Pronounced rise of quadrupole contribution to relaxation was observed for the nanostructured alloy which increased with decreasing the pore size. The correlation time of atomic mobility was evaluated and found to be much larger than in the relevant bulk melt which evidenced a pronounced diffusion slowdown in the Ga-Sn alloy under nanoconfinement. It is shown that the diffusion was slower by a factor of 30 for the alloy within 7 nm pores. The spectral densities of electric field gradients at zero frequency were found to double for the finest pores. The Knight shift was found to decrease but slightly for the nanostructured alloy.

Nuclear spin relaxation of gallium isotopes in melted Ga-Sn alloy under nanoconfinement is much faster than in bulk, depends on field and isotope, and is dominated by quadrupole coupling. The evaluated time of atomic mobility increases gradually with decreasing pore size. Knight shift decreases under nanoconfinement depending on pore sizes.

Presuming that CMB photons are described by the deconfining phase of an SU(2) Yang-Mills theory with the critical temperature for the deconfining-preconfining phase transition matching the present CMB temperature K (SU(2)_{CMB}), we investigate how CMB temperature *T* connects with the cosmological scale factor *a* in a Friedmann-Lemaître-Robertson-Walker Universe. Owing to a violation of conformal scaling at late times, the tension between the (instantaneous) redshift of reionisation from CMB observation () and quasar spectra () is repealed. Also, we find that the redshift of CMB decoupling moves from to which questions ΛCDM cosmology at high redshifts. Adapting this model to the conventional physics of three flavours of massless cosmic neutrinos, we demonstrate inconsistency with the value N_{eff} ∼ 3.36 extracted from Planck data. Interactions between cosmic neutrinos and the CMB implies a *common* temperature *T* of (no longer separately conserved) CMB and neutrino fluids. N_{eff} ∼ 3.36 then entails a universal, temperature induced cosmic neutrino mass with . Our above results on *z*_{re} and *z*_{dec}, derived from SU(2)_{CMB} alone, are essentially unaffected when including such a neutrino sector.

A late-time modification of the (conformal) relation between the FLRW scale factor and the temperature of the cosmic microwave background is derived based on the postulate that fundamentally an SU(2) gauge principle underlies photon propagation. Consequences constructively address early re-ionisation, dark matter in the early universe, and the physics of cosmic neutrinos.

Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process in order to account for the impossibility of instantaneous measurement of physical fields. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. In particular, we analyze how an uniformly accelerated observer perceives a homogeneous and isotropic black body radiation. We show that all nonlocal effects are transient and most relevant in the first period of acceleration.

Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process in order to account for the impossibility of instantaneous measurement of physical fields. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. It is analyzed how a uniformly accelerated observer perceives a homogeneous and isotropic black body radiation.

Analytical solutions of the Schrödinger equation for the one-dimensional quantum well with all possible permutations of the Dirichlet and Neumann boundary conditions (BCs) in perpendicular to the interfaces uniform electric field are used for the comparative investigation of their interaction and its influence on the properties of the system. Limiting cases of the weak and strong voltages allow an easy mathematical treatment and its clear physical explanation; in particular, for the small , the perturbation theory derives for all geometries a linear dependence of the polarization on the field with the BC-dependent proportionality coefficient being positive (negative) for the ground (excited) states. Simple two-level approximation elementary explains the negative polarizations as a result of the field-induced destructive interference of the unperturbed modes and shows that in this case the admixture of only the neighboring states plays a dominant role. Different magnitudes of the polarization for different BCs in this regime are explained physically and confirmed numerically. Hellmann-Feynman theorem reveals a fundamental relation between the polarization and the speed of the energy change with the field. It is proved that zero-voltage position entropies are BC independent and for all states but the ground Neumann level (which has ) are equal to while the momentum entropies depend on the edge requirements and the level. Varying electric field changes position and momentum entropies in the opposite directions such that the entropic uncertainty relation is satisfied. Other physical quantities such as the BC-dependent zero-energy and zero-polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

Qualitative – and to the large degree of precision, quantitative – explanation of the negative polarization of the excited states of the quantum well with arbitrary permutation of the Dirichlet and Neumann boundary conditions is based on the perturbation analysis of the evolution of the wave function under applied electric fields that also lead to the modification of the space and momentum quantum information entropies, which, however, always satisfy entropic uncertainty relation.

Thermodynamic properties of the one-dimensional (1D) quantum well (QW) with miscellaneous permutations of the Dirichlet (D) and Neumann (N) boundary conditions (BCs) at its edges in the perpendicular to the surfaces electric field are calculated. For the canonical ensemble, analytical expressions involving theta functions are found for the mean energy and heat capacity for the box with no applied voltage. Pronounced maximum accompanied by the adjacent minimum of the specific heat dependence on the temperature *T* for the pure Neumann QW and their absence for other BCs are predicted and explained by the structure of the corresponding energy spectrum. Applied field leads to the increase of the heat capacity and formation of the new or modification of the existing extrema what is qualitatively described by the influence of the associated electric potential. A remarkable feature of the Fermi grand canonical ensemble is, at any BC combination in zero fields, a salient maximum of observed on the *T* axis for one particle and its absence for any other number *N* of corpuscles. Qualitative and quantitative explanation of this phenomenon employs the analysis of the chemical potential and its temperature dependence for different *N*. It is proved that critical temperature of the Bose-Einstein (BE) condensation increases with the applied voltage for any number of particles and for any BC permutation except the ND case at small intensities what is explained again by the modification by the field of the interrelated energies. It is shown that even for the temperatures smaller than the total dipole moment may become negative for the quite moderate . For either Fermi or BE system, the influence of the electric field on the heat capacity is shown to be suppressed with *N* growing. Different asymptotic cases of, e.g., the small and large temperatures and low and high voltages are derived analytically and explained physically. Parallels are drawn to the similar properties of the 1D harmonic oscillator, and similarities and differences between them are discussed.

Heat capacity for one fermion, contrary to the many-particle case, in the flat quantum well exhibits a pronounced maximum whose location on the temperature axis depends on the type of the boundary conditions and which is qualitatively and quantitatively explained by the interplay between the two lowest states. Electric field smoothes out and widens these extrema leading also to the evolution of other thermodynamic properties considered in canonical and two grand canonical ensembles.