Dynamic symmetries and quantum nonadiabatic transitions
Abstract
Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the timereversal symmetry makes each energy level of a halfinteger 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 timedependent 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:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies, Theoretical Division
 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):
 LAUR1622273
Journal ID: ISSN 03010104
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Chemical Physics
 Additional Journal Information:
 Journal Name: Chemical Physics; Journal ID: ISSN 03010104
 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. doi:10.1016/j.chemphys.2016.05.029.
Li, Fuxiang, & Sinitsyn, Nikolai A. Dynamic symmetries and quantum nonadiabatic transitions. United States. doi:10.1016/j.chemphys.2016.05.029.
Li, Fuxiang, and Sinitsyn, Nikolai A. Mon .
"Dynamic symmetries and quantum nonadiabatic transitions". United States. doi: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 timereversal symmetry makes each energy level of a halfinteger 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 timedependent 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}
}
Web of Science