The quest for solvable multistate Landau-Zener models

doi:https://doi.org/10.1088/1751-8121/aa6800

Title: The quest for solvable multistate Landau-Zener models

Abstract

Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. Additionally, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.

Authors:

^[1]; Chernyak, Vladimir Y. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Wayne State Univ., Detroit, MI (United States)

Publication Date:: 2017-05-24

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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

OSTI Identifier:: 1375172

Report Number(s):: LA-UR-16-29453
Journal ID: ISSN 1751-8113

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Journal Article: Accepted Manuscript

Journal Name:: Journal of Physics. A, Mathematical and Theoretical

Additional Journal Information:: Journal Volume: 50; Journal Issue: 25; Journal ID: ISSN 1751-8113

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; mathematics; material science; driven matter; quantum control; integrability; Landau-Zener; quantum integrability; matrix product ansatz; nonadiabatic transitions

Citation Formats


                    Sinitsyn, Nikolai A., and Chernyak, Vladimir Y. The quest for solvable multistate Landau-Zener models.  United States: N. p., 2017. 
        Web.  doi:10.1088/1751-8121/aa6800.

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                    Sinitsyn, Nikolai A., & Chernyak, Vladimir Y. The quest for solvable multistate Landau-Zener models.  United States.  https://doi.org/10.1088/1751-8121/aa6800

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                    Sinitsyn, Nikolai A., and Chernyak, Vladimir Y. Wed .  
        "The quest for solvable multistate Landau-Zener models".  United States.  https://doi.org/10.1088/1751-8121/aa6800.  https://www.osti.gov/servlets/purl/1375172.

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@article{osti_1375172,

  title        = {The quest for solvable multistate Landau-Zener models},

  author       = {Sinitsyn, Nikolai A. and Chernyak, Vladimir Y.},

  abstractNote = {Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. Additionally, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.},

  doi          = {10.1088/1751-8121/aa6800},

  url          = {https://www.osti.gov/biblio/1375172},
  journal      = {Journal of Physics. A, Mathematical and Theoretical},

  issn         = {1751-8113},

  number       = 25,

  volume       = 50,

  place        = {United States},

  year         = {2017},

  month        = {5}

}

Copy to clipboard

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Works referencing / citing this record:

Dynamic spin localization and $γ$ -magnets
journal, December 2019

Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen
Physical Review B, Vol. 100, Issue 22
https://doi.org/10.1103/physrevb.100.224304

Suppression of Multiphoton Resonances in Driven Quantum Systems via Pulse Shape Optimization
journal, August 2017

Gagnon, Denis; Fillion-Gourdeau, François; Dumont, Joey
Physical Review Letters, Vol. 119, Issue 5
https://doi.org/10.1103/physrevlett.119.053203

Eigenmodes of a lamellar optical grating: Profile, propagation, reflection, transmission, and nonadiabatic mode coupling
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Kocharovsky, V. V.; Reynolds, C. B.; Kocharovsky, Vl. V.
Physical Review A, Vol. 100, Issue 5
https://doi.org/10.1103/physreva.100.053854

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
https://doi.org/10.1088/1751-8121/aac3b2

Integrable Time-Dependent Quantum Hamiltonians
journal, May 2018

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.
Physical Review Letters, Vol. 120, Issue 19
https://doi.org/10.1103/physrevlett.120.190402

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Similar Records

Title: The quest for solvable multistate Landau-Zener models

Abstract

Citation Formats

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

Atomi orientati in campo magnetico variabile journal, February 1932

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

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

Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory journal, February 2007

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

Quantum-to-classical correspondence and Hubbard-Stratonovich dynamical systems: A Lie-algebraic approach journal, July 2011

Local shortcut to adiabaticity for quantum many-body systems journal, June 2016

Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving journal, April 2014

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

Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids journal, October 2010

Critical dynamics of decoherence journal, June 2011

SU(3) Landau-Zener interferometry journal, December 2013

Gauging a Quantum Heat Bath with Dissipative Landau-Zener Transitions journal, November 2006

Nonadiabatic Landau-Zener tunneling in Fe 8 molecular nanomagnets journal, May 2000

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

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

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

Counterintuitive transitions between crossing energy levels journal, November 2005

Landau Zener scenario in a trapped atomic gas: multi-level multi-particle model journal, July 2015

Transition probabilities for the three-level Landau-Zener model journal, August 1986

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

The exact solution of the multistate Landau-Zener type model: the generalized bow-tie model journal, June 2001

Multipath interference in a multistate Landau-Zener-type model journal, February 2000

Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings journal, October 2004

Exponential Asymptotics in a Singular Limit for n-Level Scattering Systems journal, May 1997

Exact WKB analysis of non-adiabatic transition probabilities for three levels journal, March 2002

Coherent Particle Transfer in an On-Demand Single-Electron Source journal, November 2008

Dynamic spin localization and γ -magnets journal, December 2019

Suppression of Multiphoton Resonances in Driven Quantum Systems via Pulse Shape Optimization journal, August 2017

Eigenmodes of a lamellar optical grating: Profile, propagation, reflection, transmission, and nonadiabatic mode coupling journal, November 2019

A large class of solvable multistate Landau–Zener models and quantum integrability journal, May 2018

Integrable Time-Dependent Quantum Hamiltonians journal, May 2018

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

Atomi orientati in campo magnetico variabile
journal, February 1932

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

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

Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory
journal, February 2007

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

Quantum-to-classical correspondence and Hubbard-Stratonovich dynamical systems: A Lie-algebraic approach
journal, July 2011

Local shortcut to adiabaticity for quantum many-body systems
journal, June 2016

Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving
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S-matrix for generalized Landau-Zener problem
journal, March 1993

Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids
journal, October 2010

Critical dynamics of decoherence
journal, June 2011

SU(3) Landau-Zener interferometry
journal, December 2013

Gauging a Quantum Heat Bath with Dissipative Landau-Zener Transitions
journal, November 2006

Nonadiabatic Landau-Zener tunneling in Fe ₈ molecular nanomagnets
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Constraints on scattering amplitudes in multistate Landau-Zener theory
journal, January 2017

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

Solvable multistate model of Landau-Zener transitions in cavity QED
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Counterintuitive transitions between crossing energy levels
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Landau Zener scenario in a trapped atomic gas: multi-level multi-particle model
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Transition probabilities for the three-level Landau-Zener model
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Exact analytical solution of the N -level Landau - Zener-type bow-tie model
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The exact solution of the multistate Landau-Zener type model: the generalized bow-tie model
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Multipath interference in a multistate Landau-Zener-type model
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Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings
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Exponential Asymptotics in a Singular Limit for n-Level Scattering Systems
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Exact WKB analysis of non-adiabatic transition probabilities for three levels
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Coherent Particle Transfer in an On-Demand Single-Electron Source
journal, November 2008

Dynamic spin localization and $γ$ -magnets
journal, December 2019

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