Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

Malla, Rajesh Kumar; Chernyak, Vladimir Y.; Sinitsyn, Nikolai

doi:10.1103/physrevb.103.144301

Title: Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

Journal Article · Wed Apr 07 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.144301· OSTI ID:1825415

^[1]; Chernyak, Vladimir Y. ^[2];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Wayne State Univ., Detroit, MI (United States)

We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that provides analytical approximation for the transition probabilities in these models for all parameter values. Lastly, the results predict a dynamic phase transition, and show that similarly looking models belong to different topological classes.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1825415

Report Number(s):: LA-UR-21-20136; TRN: US2215798

Journal Information:: Physical Review. B, Vol. 103, Issue 14; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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