Multitime Landau–Zener model: classification of solvable Hamiltonians

Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen

doi:10.1088/1751-8121/ab7fdd

Title: 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:

Chernyak, Vladimir Y. ^[1];

^[2];

^[3]

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:: 2020-04-16

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.

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                    Chernyak, Vladimir Y., Sinitsyn, Nikolai A., & Sun, Chen. Multitime Landau–Zener model: classification of solvable Hamiltonians.  United States.  https://doi.org/10.1088/1751-8121/ab7fdd

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                    Chernyak, Vladimir Y., Sinitsyn, Nikolai A., and Sun, Chen. Thu .  
"Multitime Landau–Zener model: classification of solvable Hamiltonians".  United States.  https://doi.org/10.1088/1751-8121/ab7fdd.  https://www.osti.gov/servlets/purl/1726183.

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@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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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
DOI: 10.1088/1751-8121/aac3b2

Multiparticle Landau-Zener problem: Application to quantum dots
journal, November 2002

Sinitsyn, N. A.
Physical Review B, Vol. 66, Issue 20
DOI: 10.1103/physrevb.66.205303

Integrable Time-Dependent Quantum Hamiltonians
journal, May 2018

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.
Physical Review Letters, Vol. 120, Issue 19
DOI: 10.1103/physrevlett.120.190402

Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets
journal, May 2018

Yuzbashyan, Emil A.
Annals of Physics, Vol. 392
DOI: 10.1016/j.aop.2018.01.017

Dynamic spin localization and $γ$ -magnets
journal, December 2019

Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen
Physical Review B, Vol. 100, Issue 22
DOI: 10.1103/physrevb.100.224304

Multistate Landau-Zener 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
DOI: 10.1103/physreva.96.022107

Atomi orientati in campo magnetico variabile
journal, February 1932

Majorana, Ettore
Il Nuovo Cimento, Vol. 9, Issue 2
DOI: 10.1007/bf02960953

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
DOI: 10.1103/physrevlett.95.245701

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Similar Records

Title: Multitime Landau–Zener model: classification of solvable Hamiltonians

Abstract

Citation Formats

A large class of solvable multistate Landau–Zener models and quantum integrability journal, May 2018

Multiparticle Landau-Zener problem: Application to quantum dots journal, November 2002

Integrable Time-Dependent Quantum Hamiltonians journal, May 2018

Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets journal, May 2018

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Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model journal, December 2005

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journal, May 2018

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journal, November 2002

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journal, May 2018

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journal, May 2018

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journal, December 2019

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journal, August 2017

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journal, February 1932

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journal, December 2005