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

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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

No-go theorem for bands of potential curves in multistate Landau–Zener model
journal, March 2005

  • Volkov, M. V.; Ostrovsky, V. N.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 38, Issue 7
  • DOI: 10.1088/0953-4075/38/7/011

Solvable multistate model of Landau-Zener transitions in cavity QED
journal, June 2016


Algebraic bethe anzatz and the tavis-cummings model
journal, June 2000

  • Bogolyubov, N. M.
  • Journal of Mathematical Sciences, Vol. 100, Issue 2
  • DOI: 10.1007/bf02675727

Exact out-of-equilibrium central spin dynamics from integrability
journal, April 2014


Solvable four-state Landau-Zener model of two interacting qubits with path interference
journal, November 2015


Non-equilibrium dynamics of Gaudin models
journal, October 2013


Landau–Zener–Stueckelberg interferometry with driving fields in the quantum regime
journal, March 2017


Constraints on scattering amplitudes in multistate Landau-Zener theory
journal, January 2017


The quest for solvable multistate Landau-Zener models
journal, May 2017

  • Sinitsyn, Nikolai A.; Chernyak, Vladimir Y.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 25
  • DOI: 10.1088/1751-8121/aa6800

Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models
journal, September 2017


The su(1,1) Tavis-Cummings model
journal, May 1998

  • Rybin, Andrei; Kastelewicz, Georg; Timonen, Jussi
  • Journal of Physics A: Mathematical and General, Vol. 31, Issue 20
  • DOI: 10.1088/0305-4470/31/20/009

Exact transition probabilities in a 6-state Landau–Zener system with path interference
journal, April 2015


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


Integrability and level crossing manifolds in a quantum Hamiltonian system
journal, November 1998


Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor
journal, June 2017


Atomi orientati in campo magnetico variabile
journal, February 1932


Nonadiabatic bulk-surface oscillations in driven topological insulators
journal, November 2016


Exact analytical solution of the N -level Landau - Zener-type bow-tie model
journal, October 1997

  • Ostrovsky, Valentine N.; Nakamura, Hiroki
  • Journal of Physics A: Mathematical and General, Vol. 30, Issue 19
  • DOI: 10.1088/0305-4470/30/19/028

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution
journal, September 2016


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


Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems
journal, June 2016


Quantum integrability in the multistate Landau–Zener problem
journal, May 2015


Separation of variables for integrable spin–boson models
journal, November 2010


Exact results for survival probability in the multistate Landau–Zener model
journal, October 2004

  • Volkov, M. V.; Ostrovsky, V. N.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 37, Issue 20
  • DOI: 10.1088/0953-4075/37/20/003

Periodically driven three-level systems
journal, September 2016


Quantum Integrability in Systems with Finite Number of Levels
journal, January 2013


Exact solution of generalized Tavis - Cummings models in quantum optics
journal, October 1996

  • Bogoliubov, N. M.; Bullough, R. K.; Timonen, J.
  • Journal of Physics A: Mathematical and General, Vol. 29, Issue 19
  • DOI: 10.1088/0305-4470/29/19/015

Integrable Time-Dependent Quantum Hamiltonians
journal, May 2018


Role of multilevel Landau-Zener interference in extreme harmonic generation
journal, August 2016


S-matrix for generalized Landau-Zener problem
journal, March 1993


The link between integrability, level crossings and exact solution in quantum models
journal, December 2008

  • Owusu, H. K.; Wagh, K.; Yuzbashyan, E. A.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 3
  • DOI: 10.1088/1751-8113/42/3/035206

The Surveyor's Area Formula
journal, September 1986


Integrable Time-Dependent Quantum Hamiltonians
journal, May 2018


Integrability and level crossing manifolds in a quantum Hamiltonian system
journal, November 1998


Atomi orientati in campo magnetico variabile
journal, February 1932


Solvable four-state Landau-Zener model of two interacting qubits with path interference
journal, November 2015


Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models
journal, September 2017


Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor
journal, June 2017


Role of multilevel Landau-Zener interference in extreme harmonic generation
journal, August 2016


Periodically driven three-level systems
journal, September 2016


Nonadiabatic bulk-surface oscillations in driven topological insulators
journal, November 2016


Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems
journal, June 2016


Solvable multistate model of Landau-Zener transitions in cavity QED
journal, June 2016


Landau-Zener extension of the Tavis-Cummings model: Structure of the solution
journal, September 2016


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


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


Algebraic bethe anzatz and the tavis-cummings model
journal, June 2000

  • Bogolyubov, N. M.
  • Journal of Mathematical Sciences, Vol. 100, Issue 2
  • DOI: 10.1007/BF02675727

Constraints on scattering amplitudes in multistate Landau-Zener theory
journal, January 2017


    Works referencing / citing this record:

    Dynamic spin localization and γ -magnets
    journal, December 2019