Integrability in multistate Landau-Zener and Landau-Zener-Coulomb problems

ORAL

Abstract

The multistate Landau-Zener (MLZ) problem is to find scattering amplitudes in models with linearly time-dependent evolution and Hamiltonians of the form H(t)=A+Bt, where A and B are arbitrary Hermitian matrices and t is time. This problem has long history. It originates from the work of Majorana in 1932 and finds numerous applications in modern atomic and mesocsopic physics. Recently, many new solvable MLZ classes have been found after the discovery of empirical integrability conditions. We use our theory of MLZ integrability in order to explain previous findings that so far have had the status of conjectures. We extend already known solutions to broader solvable classes, such as the Landau-Zener-Coulomb systems with H(t)=A+Bt+C/t, and show how to obtain solutions of highly nontrivial and physically interesting solvable many-body models, such as the BCS model with decaying as 1/t coupling.

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Presenters

  • Nikolai Sinitsyn

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

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