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Multitime Landau–Zener model: classification of solvable Hamiltonians
Abstract
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.
- Authors:
-
- Wayne State Univ., Detroit, MI (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Brown Univ., Providence, RI (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1726183
- Report Number(s):
- LA-UR-19-31939
Journal ID: ISSN 1751-8113
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics. A, Mathematical and Theoretical
- Additional Journal Information:
- Journal Volume: 53; Journal Issue: 18; Journal ID: ISSN 1751-8113
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., and Sun, Chen. Multitime Landau–Zener model: classification of solvable Hamiltonians. United States: N. p., 2020.
Web. doi:10.1088/1751-8121/ab7fdd.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., & Sun, Chen. Multitime Landau–Zener model: classification of solvable Hamiltonians. United States. doi:10.1088/1751-8121/ab7fdd.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., and Sun, Chen. Thu .
"Multitime Landau–Zener model: classification of solvable Hamiltonians". United States. doi:10.1088/1751-8121/ab7fdd.
@article{osti_1726183,
title = {Multitime Landau–Zener model: classification of solvable Hamiltonians},
author = {Chernyak, Vladimir Y. and Sinitsyn, Nikolai A. and Sun, Chen},
abstractNote = {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.},
doi = {10.1088/1751-8121/ab7fdd},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 18,
volume = 53,
place = {United States},
year = {2020},
month = {4}
}
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