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Multitime Landau–Zener model: classification of solvable Hamiltonians
Abstract
We discuss a class of models that generalize the twostate 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):
 LAUR1931939
Journal ID: ISSN 17518113
 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 17518113
 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:10.1088/17518121/ab7fdd.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., & Sun, Chen. Multitime Landau–Zener model: classification of solvable Hamiltonians. United States. doi:10.1088/17518121/ab7fdd.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., and Sun, Chen. Thu .
"Multitime Landau–Zener model: classification of solvable Hamiltonians". United States. doi:10.1088/17518121/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 twostate 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 = {10.1088/17518121/ab7fdd},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 18,
volume = 53,
place = {United States},
year = {2020},
month = {4}
}
Works referenced in this record:
A large class of solvable multistate Landau–Zener models and quantum integrability
journal, May 2018
 Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen
 Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 24
Multiparticle LandauZener problem: Application to quantum dots
journal, November 2002
 Sinitsyn, N. A.
 Physical Review B, Vol. 66, Issue 20
Integrable TimeDependent Quantum Hamiltonians
journal, May 2018
 Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.
 Physical Review Letters, Vol. 120, Issue 19
Integrable timedependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets
journal, May 2018
 Yuzbashyan, Emil A.
 Annals of Physics, Vol. 392
Dynamic spin localization and $\gamma $ magnets
journal, December 2019
 Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen
 Physical Review B, Vol. 100, Issue 22
Multistate LandauZener models with all levels crossing at one point
journal, August 2017
 Li, Fuxiang; Sun, Chen; Chernyak, Vladimir Y.
 Physical Review A, Vol. 96, Issue 2
Atomi orientati in campo magnetico variabile
journal, February 1932
 Majorana, Ettore
 Il Nuovo Cimento, Vol. 9, Issue 2
Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model
journal, December 2005
 Dziarmaga, Jacek
 Physical Review Letters, Vol. 95, Issue 24