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Title: Dynamic symmetries and quantum nonadiabatic transitions

Abstract

Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.

Authors:
 [1];  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies, Theoretical Division
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1304722
Alternate Identifier(s):
OSTI ID: 1556149
Report Number(s):
LA-UR-16-22273
Journal ID: ISSN 0301-0104
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Chemical Physics
Additional Journal Information:
Journal Name: Chemical Physics; Journal ID: ISSN 0301-0104
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Material Science

Citation Formats

Li, Fuxiang, and Sinitsyn, Nikolai A. Dynamic symmetries and quantum nonadiabatic transitions. United States: N. p., 2016. Web. https://doi.org/10.1016/j.chemphys.2016.05.029.
Li, Fuxiang, & Sinitsyn, Nikolai A. Dynamic symmetries and quantum nonadiabatic transitions. United States. https://doi.org/10.1016/j.chemphys.2016.05.029
Li, Fuxiang, and Sinitsyn, Nikolai A. Mon . "Dynamic symmetries and quantum nonadiabatic transitions". United States. https://doi.org/10.1016/j.chemphys.2016.05.029. https://www.osti.gov/servlets/purl/1304722.
@article{osti_1304722,
title = {Dynamic symmetries and quantum nonadiabatic transitions},
author = {Li, Fuxiang and Sinitsyn, Nikolai A.},
abstractNote = {Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.},
doi = {10.1016/j.chemphys.2016.05.029},
journal = {Chemical Physics},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {5}
}

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