The Liouville Space Extension of Quantum Mechanics

  1. I. Prigogine3,4 and
  2. Stuart A. Rice5
  1. T. Petrosky1,2 and
  2. I. Prigogine1,2

Published Online: 14 MAR 2007

DOI: 10.1002/9780470141588.ch1

Advances in Chemical Physics: Resonances, Instability, and Irreversibility, Volume 99

Advances in Chemical Physics: Resonances, Instability, and Irreversibility, Volume 99

How to Cite

Petrosky, T. and Prigogine, I. (2007) The Liouville Space Extension of Quantum Mechanics, in Advances in Chemical Physics: Resonances, Instability, and Irreversibility, Volume 99 (eds I. Prigogine and S. A. Rice), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470141588.ch1

Editor Information

  1. 3

    Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas, Austin, Texas

  2. 4

    International Solvay Institutes, Université Librey de Bruxells, Brussels, Belgium

  3. 5

    Department of Chemistry and The James Franck Institues, The University of Chicago, Chacago, Illionios

Author Information

  1. 1

    Center for Studies in Statistical Mechanics and Complex Systems, University of Texas, Austin, Texas

  2. 2

    International Solvay Institutes, Université Libre de Bruxelles, Brussels, Belgium

Publication History

  1. Published Online: 14 MAR 2007
  2. Published Print: 1 JAN 1996

ISBN Information

Print ISBN: 9780471165262

Online ISBN: 9780470141588

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Keywords:

  • liouvillian formalism;
  • singular fourier expansions;
  • Lyapounov functions;
  • persistent potential scattering;
  • correlation flows

Summary

This chapter contains sections titled:

  • Introduction

  • Overview

  • The Liouvillian Formalism

  • Singular Fourier Expansions and Projection Operators

  • Complex Spectral Representations

  • Nonunitary Transformations and Subdynamics

  • Lyapounov Functions-�� Theorems

  • Linear and Nonlinear Lippmann-Schwinger Equations

  • Persistent Potential Scattering

  • Nonequilibrium Statistical Mechanics and Flow of Correlations

  • The Thermodynamic Limit

  • Illustrations

  • Concluding Remarks