Integrable Time-Dependent Quantum Hamiltonians

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

doi:10.1103/PhysRevLett.120.190402

Title: Integrable Time-Dependent Quantum Hamiltonians

Journal Article · Fri May 11 00:00:00 EDT 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.120.190402· OSTI ID:1482922

Sinitsyn, Nikolai A. ^[1]; Yuzbashyan, Emil A. ^[2]; Chernyak, Vladimir Y. ^[3]; Patra, Aniket ^[4]; Sun, Chen ^[5]

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

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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Rutgers Univ., Piscataway, NJ (United States); Wayne State Univ., Detroit, MI (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); LANL Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)

Grant/Contract Number:: AC52-06NA25396; DMR-1609829; CHE-1111350

OSTI ID:: 1482922

Alternate ID(s):: OSTI ID: 1436899

Report Number(s):: LA-UR-17-28411

Journal Information:: Physical Review Letters, Vol. 120, Issue 19; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 37 works

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