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Multitime Landau–Zener model: classification of solvable Hamiltonians

Journal Article · · Journal of Physics. A, Mathematical and Theoretical
 [1];  [2];  [3]
  1. Wayne State Univ., Detroit, MI (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Brown Univ., Providence, RI (United States)
+ Show Author Affiliations
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.
Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1726183
Alternate ID(s):
OSTI ID: 23025342
Report Number(s):
LA-UR--19-31939
Journal Information:
Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 18 Vol. 53; ISSN 1751-8113
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English

References (9)

Atomi orientati in campo magnetico variabile journal February 1932
Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets journal May 2018
A large class of solvable multistate Landau–Zener models and quantum integrability journal May 2018
Multistate Landau-Zener models with all levels crossing at one point journal August 2017
Dynamic spin localization and γ -magnets journal December 2019
Multiparticle Landau-Zener problem: Application to quantum dots journal November 2002
Integrable Time-Dependent Quantum Hamiltonians journal May 2018
Universal Statistics of Topological Defects Formed in a Quantum Phase Transition journal November 2018
Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model journal December 2005

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS