A large class of solvable multistate Landau–Zener models and quantum integrability

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

doi:10.1088/1751-8121/aac3b2

A large class of solvable multistate Landau–Zener models and quantum integrability

Journal Article · Thu May 10 00:00:00 EDT 2018 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/aac3b2· OSTI ID:1471351

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

Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry, and Dept. of Mathematics
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Texas A & M Univ., College Station, TX (United States). Dept. of Physics

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor. 50 255203). Here in this paper we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number N$$\geqslant$$4 of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1471351

Alternate ID(s):: OSTI ID: 22982710

Report Number(s):: LA-UR--17-26367

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 24 Vol. 51; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Multistate Landau-Zener models with all levels crossing at one point Li, Fuxiang; Sun, Chen; Chernyak, Vladimir Y. Physical Review A, Vol. 96, Issue 2 https://doi.org/10.1103/physreva.96.022107	journal	August 2017
Multiparticle Landau-Zener problem: Application to quantum dots Sinitsyn, N. A. Physical Review B, Vol. 66, Issue 20 https://doi.org/10.1103/physrevb.66.205303	journal	November 2002
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Role of multilevel Landau-Zener interference in extreme harmonic generation Stehlik, J.; Maialle, M. Z.; Degani, M. H. Physical Review B, Vol. 94, Issue 7 https://doi.org/10.1103/physrevb.94.075307	journal	August 2016
Periodically driven three-level systems Kenmoe, M. B.; Fai, L. C. Physical Review B, Vol. 94, Issue 12 https://doi.org/10.1103/physrevb.94.125101	journal	September 2016
Nonadiabatic bulk-surface oscillations in driven topological insulators Kolodrubetz, Michael; Fregoso, Benjamin M.; Moore, Joel E. Physical Review B, Vol. 94, Issue 19 https://doi.org/10.1103/physrevb.94.195124	journal	November 2016
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Cited By (2)

Integrable time-dependent quantum Hamiltonians Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y. arXiv https://doi.org/10.48550/arxiv.1711.09945	text	January 2017
Dynamic spin localization and γ -magnets Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen Physical Review B, Vol. 100, Issue 22 https://doi.org/10.1103/physrevb.100.224304	journal	December 2019

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
landau-zener
quantum annealing
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A large class of solvable multistate Landau–Zener models and quantum integrability

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