skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on April 16, 2021

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:
 [1]; ORCiD logo [2]; ORCiD logo [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)
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):
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.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., & Sun, Chen. Multitime Landau–Zener model: classification of solvable Hamiltonians. United States. doi:10.1088/1751-8121/ab7fdd.
Chernyak, Vladimir Y., Sinitsyn, Nikolai A., and Sun, Chen. Thu . "Multitime Landau–Zener model: classification of solvable Hamiltonians". United States. doi:10.1088/1751-8121/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 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}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on April 16, 2021
Publisher's Version of Record

Save / Share:

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


Integrable Time-Dependent Quantum Hamiltonians
journal, May 2018


Dynamic spin localization and γ -magnets
journal, December 2019


Multistate Landau-Zener models with all levels crossing at one point
journal, August 2017


Atomi orientati in campo magnetico variabile
journal, February 1932


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