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Title: 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:
 [1];  [2];  [3];  [4];  [5]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Rutgers Univ., Piscataway, NJ (United States). Center for Materials Theory. Dept. of Physics and Astronomy
  3. Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry. Dept. of Mathematics
  4. 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
  5. 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 Lab. (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. doi: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. doi: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 = {2018},
month = {5}
}

Journal Article:
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Cited by: 4 works
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Figures / Tables:

FIG. 1 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 » of Hj that satisfies the zero curvature condition, we can deform Pω into a new path P without modifying the scattering matrix.« less

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      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.