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

Abstract

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.

Authors:
 [1];  [2]; ORCiD logo [3]
  1. Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry, and Dept. of Mathematics
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Texas A & M Univ., College Station, TX (United States). Dept. of Physics
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1471351
Report Number(s):
LA-UR-17-26367
Journal ID: ISSN 1751-8113
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Physics. A, Mathematical and Theoretical
Additional Journal Information:
Journal Volume: 51; Journal Issue: 24; Journal ID: ISSN 1751-8113
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum annealing; landau-zener; quantum integrability

Citation Formats

Chernyak, Vladimir Y., Sinitsyn, Nikolai A., and Sun, Chen. A large class of solvable multistate Landau–Zener models and quantum integrability. United States: N. p., 2018. Web. doi:10.1088/1751-8121/aac3b2.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., & Sun, Chen. A large class of solvable multistate Landau–Zener models and quantum integrability. United States. doi:10.1088/1751-8121/aac3b2.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., and Sun, Chen. Thu . "A large class of solvable multistate Landau–Zener models and quantum integrability". United States. doi:10.1088/1751-8121/aac3b2. https://www.osti.gov/servlets/purl/1471351.
@article{osti_1471351,
title = {A large class of solvable multistate Landau–Zener models and quantum integrability},
author = {Chernyak, Vladimir Y. and Sinitsyn, Nikolai A. and Sun, Chen},
abstractNote = {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.},
doi = {10.1088/1751-8121/aac3b2},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 24,
volume = 51,
place = {United States},
year = {2018},
month = {5}
}

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