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Title: Wave-packet evolution in non-Hermitian quantum systems

Abstract

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit ({h_bar}/2{pi}){yields}0 this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase-space metric - a phenomenon having no analog in Hermitian theories.

Authors:
 [1];  [2]
  1. Department of Mathematics, Imperial College London, London, SW7 2AZ (United Kingdom)
  2. Department of Mathematics, University of Bristol, Bristol, BS8 1TW (United Kingdom)
Publication Date:
OSTI Identifier:
21550009
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 83; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.83.060101; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS OF MOTION; HAMILTONIANS; METRICS; PHASE SPACE; QUANTUM MECHANICS; SEMICLASSICAL APPROXIMATION; WAVE PACKETS; WIGNER THEORY; APPROXIMATIONS; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS; SPACE

Citation Formats

Graefe, Eva-Maria, and Schubert, Roman. Wave-packet evolution in non-Hermitian quantum systems. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.060101.
Graefe, Eva-Maria, & Schubert, Roman. Wave-packet evolution in non-Hermitian quantum systems. United States. https://doi.org/10.1103/PHYSREVA.83.060101
Graefe, Eva-Maria, and Schubert, Roman. 2011. "Wave-packet evolution in non-Hermitian quantum systems". United States. https://doi.org/10.1103/PHYSREVA.83.060101.
@article{osti_21550009,
title = {Wave-packet evolution in non-Hermitian quantum systems},
author = {Graefe, Eva-Maria and Schubert, Roman},
abstractNote = {The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit ({h_bar}/2{pi}){yields}0 this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase-space metric - a phenomenon having no analog in Hermitian theories.},
doi = {10.1103/PHYSREVA.83.060101},
url = {https://www.osti.gov/biblio/21550009}, journal = {Physical Review. A},
issn = {1050-2947},
number = 6,
volume = 83,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2011},
month = {Wed Jun 15 00:00:00 EDT 2011}
}