Multitime Landau–Zener model: classification of solvable Hamiltonians

Journal Article · 16 April 2020 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/ab7fdd · OSTI ID:1726183

Chernyak, Vladimir Y. ^[1]; Sinitsyn, Nikolai A.  ^[2]; Sun, Chen  ^[3]

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1. Wayne State Univ., Detroit, MI (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
3. Brown Univ., Providence, RI (United States)

We discuss a class of models that generalize the two-state Landau–Zener Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number N of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system's dynamics. Furthermore, due to the possibility of such a detailed classification, the multitime Landau–Zener model defines a useful special function of theoretical physics.

• 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
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1726183
• Report Number(s): LA-UR--19-31939
• Journal Information: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 18 Vol. 53; ISSN 1751-8113
• Publisher: IOP PublishingCopyright Statement
• Country of Publication: United States
• Language: English