Integrable Time-Dependent Quantum Hamiltonians
Abstract
Here we formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. Finally, we also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Rutgers Univ., Piscataway, NJ (United States). Center for Materials Theory. Dept. of Physics and Astronomy
- Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry. Dept. of Mathematics
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Rutgers Univ., Piscataway, NJ (United States). Center for Materials Theory. Dept. of Physics and Astronomy
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Texas A & M Univ., College Station, TX (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Rutgers Univ., Piscataway, NJ (United States); Wayne State Univ., Detroit, MI (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); LANL Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)
- OSTI Identifier:
- 1482922
- Alternate Identifier(s):
- OSTI ID: 1436899
- Report Number(s):
- LA-UR-17-28411
Journal ID: ISSN 0031-9007
- Grant/Contract Number:
- AC52-06NA25396; DMR-1609829; CHE-1111350
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 120; Journal Issue: 19; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; coherent control; mathematical physics; quantum theory; scattering theory
Citation Formats
Sinitsyn, Nikolai A., Yuzbashyan, Emil A., Chernyak, Vladimir Y., Patra, Aniket, and Sun, Chen. Integrable Time-Dependent Quantum Hamiltonians. United States: N. p., 2018.
Web. doi:10.1103/PhysRevLett.120.190402.
Sinitsyn, Nikolai A., Yuzbashyan, Emil A., Chernyak, Vladimir Y., Patra, Aniket, & Sun, Chen. Integrable Time-Dependent Quantum Hamiltonians. United States. https://doi.org/10.1103/PhysRevLett.120.190402
Sinitsyn, Nikolai A., Yuzbashyan, Emil A., Chernyak, Vladimir Y., Patra, Aniket, and Sun, Chen. Fri .
"Integrable Time-Dependent Quantum Hamiltonians". United States. https://doi.org/10.1103/PhysRevLett.120.190402. https://www.osti.gov/servlets/purl/1482922.
@article{osti_1482922,
title = {Integrable Time-Dependent Quantum Hamiltonians},
author = {Sinitsyn, Nikolai A. and Yuzbashyan, Emil A. and Chernyak, Vladimir Y. and Patra, Aniket and Sun, Chen},
abstractNote = {Here we formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. Finally, we also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.},
doi = {10.1103/PhysRevLett.120.190402},
journal = {Physical Review Letters},
number = 19,
volume = 120,
place = {United States},
year = {Fri May 11 00:00:00 EDT 2018},
month = {Fri May 11 00:00:00 EDT 2018}
}
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Figures / Tables:
FIG. 1: (color online) Paths in the space of parameters ϵj and time used to evaluate transition probabilities for the driven generalized Tavis-Cummings model (9), ω = t. On Pω, ω changes from –R to +R, all ϵj are fixed. Since this model is a part of a commuting familymore »
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