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:
-
- 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 Laboratory (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. doi: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 = {Mon May 30 00:00:00 EDT 2016},
month = {Mon May 30 00:00:00 EDT 2016}
}
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Dynamic spin localization and -magnets
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