Quantum Integrability in Generic Time Dependent Hamiltonians

ORAL

Abstract

We formulate a set of conditions under which the scattering problem for a time-dependent quantum Hamiltonian is integrable. The main requirement is the existence of a nonabelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method produces a strategy to incorporate time-dependence into various models that are convensionally known as integrable, so that the resulting non-stationary Schrodinger equation is explicitly solvable. We also validate some prior conjectures, including the solution of the driven Tavis-Cummings model.

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Presenters

  • Aniket Patra

    Rutgers University, Department of Physics and Astronomy, Rutgers University

Authors

  • Nikolai Sinitsyn

    Theoretical Division, Los Alamos National Laborary, Los Alamos National Laboratory, Theoretical Division, Los Alamos National Laboratory, Theoretical Division, Los Alamos National Lab

  • Emil Yuzbashyan

    Rutgers University, Department of Physics and Astronomy, Rutgers University

  • Vladimir Chernyak

    Wayne State University, Department of Chemistry and Department of Mathematics, Wayne State University

  • Aniket Patra

    Rutgers University, Department of Physics and Astronomy, Rutgers University

  • Chen Sun

    Physics and Astronomy, Texas A&M University, Texas A&M University, Department of Physics, Texas A&M University, Texas A&M Univ, Physics, Texas A&M Univ