DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Integrable Time-Dependent Quantum Hamiltonians

Abstract

Here we formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. Finally, we also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Authors:
 [1];  [2];  [3];  [4];  [5]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Rutgers Univ., Piscataway, NJ (United States). Center for Materials Theory. Dept. of Physics and Astronomy
  3. Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry. Dept. of Mathematics
  4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Rutgers Univ., Piscataway, NJ (United States). Center for Materials Theory. Dept. of Physics and Astronomy
  5. 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 Laboratory (LANL), Los Alamos, NM (United States); Rutgers Univ., Piscataway, NJ (United States); Wayne State Univ., Detroit, MI (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); LANL Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)
OSTI Identifier:
1482922
Alternate Identifier(s):
OSTI ID: 1436899
Report Number(s):
LA-UR-17-28411
Journal ID: ISSN 0031-9007
Grant/Contract Number:  
AC52-06NA25396; DMR-1609829; CHE-1111350
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 120; Journal Issue: 19; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; coherent control; mathematical physics; quantum theory; scattering theory

Citation Formats

Sinitsyn, Nikolai A., Yuzbashyan, Emil A., Chernyak, Vladimir Y., Patra, Aniket, and Sun, Chen. Integrable Time-Dependent Quantum Hamiltonians. United States: N. p., 2018. Web. doi:10.1103/PhysRevLett.120.190402.
Sinitsyn, Nikolai A., Yuzbashyan, Emil A., Chernyak, Vladimir Y., Patra, Aniket, & Sun, Chen. Integrable Time-Dependent Quantum Hamiltonians. United States. https://doi.org/10.1103/PhysRevLett.120.190402
Sinitsyn, Nikolai A., Yuzbashyan, Emil A., Chernyak, Vladimir Y., Patra, Aniket, and Sun, Chen. Fri . "Integrable Time-Dependent Quantum Hamiltonians". United States. https://doi.org/10.1103/PhysRevLett.120.190402. https://www.osti.gov/servlets/purl/1482922.
@article{osti_1482922,
title = {Integrable Time-Dependent Quantum Hamiltonians},
author = {Sinitsyn, Nikolai A. and Yuzbashyan, Emil A. and Chernyak, Vladimir Y. and Patra, Aniket and Sun, Chen},
abstractNote = {Here we formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. Finally, we also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.},
doi = {10.1103/PhysRevLett.120.190402},
journal = {Physical Review Letters},
number = 19,
volume = 120,
place = {United States},
year = {Fri May 11 00:00:00 EDT 2018},
month = {Fri May 11 00:00:00 EDT 2018}
}

Journal Article:

Citation Metrics:
Cited by: 37 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: (color online) Paths in the space of parameters ϵj and time used to evaluate transition probabilities for the driven generalized Tavis-Cummings model (9), ω = t. On Pω, ω changes from –R to +R, all ϵj are fixed. Since this model is a part of a commuting familymore » of Hj that satisfies the zero curvature condition, we can deform Pω into a new path P without modifying the scattering matrix.« less

Save / Share:

Works referenced in this record:

Interplay of charge and spin coherence in Landau-Zener-Stückelberg-Majorana interferometry
journal, June 2013


Relaxation and Prethermalization in an Isolated Quantum System
journal, September 2012


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


Quantum simulation of the Kibble-Zurek mechanism using a semiconductor electron charge qubit
journal, February 2014


Quantum annealing with all-to-all connected nonlinear oscillators
journal, June 2017

  • Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L.
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms15785

Classification of parameter-dependent quantum integrable models, their parameterization, exact solution and other properties
journal, September 2011


Integrability of the pairing hamiltonian
journal, October 1997


Experiments on spontaneous vortex formation in Josephson tunnel junctions
journal, October 2006


Dynamical Control of Matter-Wave Tunneling in Periodic Potentials
journal, November 2007


Ultrahigh-Resolution NMR Spectroscopy
journal, May 2014

  • Foroozandeh, Mohammadali; Adams, Ralph W.; Meharry, Nicola J.
  • Angewandte Chemie International Edition, Vol. 53, Issue 27
  • DOI: 10.1002/anie.201404111

Coherent control of three-spin states in a triple quantum dot
journal, November 2011

  • Gaudreau, L.; Granger, G.; Kam, A.
  • Nature Physics, Vol. 8, Issue 1
  • DOI: 10.1038/nphys2149

Quantum Spin Dynamics of Mode-Squeezed Luttinger Liquids in Two-Component Atomic Gases
journal, April 2008


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

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


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


Spontaneous vortices in the formation of Bose–Einstein condensates
journal, October 2008

  • Weiler, Chad N.; Neely, Tyler W.; Scherer, David R.
  • Nature, Vol. 455, Issue 7215
  • DOI: 10.1038/nature07334

Current algebra and Wess-Zumino model in two dimensions
journal, December 1984


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


The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions
journal, April 2014


Non-Adiabatic Crossing of Energy Levels
journal, September 1932

  • Zener, C.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 137, Issue 833
  • DOI: 10.1098/rspa.1932.0165

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


Higgs Amplitude Mode in the BCS Superconductors Nb 1 x Ti x N Induced by Terahertz Pulse Excitation
journal, July 2013


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

  • Chen, Yu-Ao; Huber, Sebastian D.; Trotzky, Stefan
  • Nature Physics, Vol. 7, Issue 1
  • DOI: 10.1038/nphys1801

Characterization of Qubit Dephasing by Landau-Zener-Stückelberg-Majorana Interferometry
journal, March 2014


Adiabatic perturbation theory and geometry of periodically-driven systems
journal, May 2017


Integrable dynamics of coupled Fermi-Bose condensates
journal, October 2005

  • Yuzbashyan, Emil A.; Kuznetsov, Vadim B.; Altshuler, Boris L.
  • Physical Review B, Vol. 72, Issue 14
  • DOI: 10.1103/PhysRevB.72.144524

Ultrafast universal quantum control of a quantum-dot charge qubit using Landau–Zener–Stückelberg interference
journal, January 2013

  • Cao, Gang; Li, Hai-Ou; Tu, Tao
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms2412

Many Body Generalization of the Landau-Zener Problem
journal, February 2008


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

Condensation of Pairs of Fermionic Atoms near a Feshbach Resonance
journal, March 2004


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


Multi-time Schrödinger equations cannot contain interaction potentials
journal, March 2014

  • Petrat, Sören; Tumulka, Roderich
  • Journal of Mathematical Physics, Vol. 55, Issue 3
  • DOI: 10.1063/1.4867524

Quantum quench phase diagrams of an s -wave BCS-BEC condensate
journal, March 2015


Nonadiabaticity and large fluctuations in a many-particle Landau-Zener problem
journal, April 2009


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

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


Quenching of dynamic nuclear polarization by spin–orbit coupling in GaAs quantum dots
journal, July 2015

  • Nichol, John M.; Harvey, Shannon P.; Shulman, Michael D.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8682

Boundary Wess-Zumino-Novikov-Witten model from the pairing Hamiltonian
journal, December 2010


Conformal field theory and the exact solution of the BCS Hamiltonian
journal, April 2000


Observation of Resonance Condensation of Fermionic Atom Pairs
journal, January 2004


Complete Generalized Gibbs Ensembles in an Interacting Theory
journal, October 2015


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


Quantum Tunneling in Half-Integer Spin Systems
journal, September 2001

  • Miyashita, S.; Nagaosa, N.
  • Progress of Theoretical Physics, Vol. 106, Issue 3
  • DOI: 10.1143/PTP.106.533

Off-shell Bethe ansatz equations and N-point correlators in the SU(2) WZNW theory
journal, December 1993


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


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


Exact results for models of multichannel quantum nonadiabatic transitions
journal, December 2014


Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas
journal, February 2012

  • Trotzky, S.; Chen, Y-A.; Flesch, A.
  • Nature Physics, Vol. 8, Issue 4
  • DOI: 10.1038/nphys2232

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

  • Demkov, Yu N.; Ostrovsky, V. N.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 34, Issue 12
  • DOI: 10.1088/0953-4075/34/12/309

A quantum Newton's cradle
journal, April 2006

  • Kinoshita, Toshiya; Wenger, Trevor; Weiss, David S.
  • Nature, Vol. 440, Issue 7086
  • DOI: 10.1038/nature04693

Ultrahigh-Resolution NMR Spectroscopy
journal, May 2014

  • Foroozandeh, Mohammadali; Adams, Ralph W.; Meharry, Nicola J.
  • Angewandte Chemie, Vol. 126, Issue 27
  • DOI: 10.1002/ange.201404111

Beautiful models
journal, November 2006


Dynamical control of matter-wave tunneling in periodic potentials
text, January 2007


Quantum Spin Dynamics of Mode-Squeezed Luttinger Liquids in Two-Component Atomic Gases
text, January 2007


Non-adiabacity and large flucutations in a many particle Landau Zener problem
text, January 2008


Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian
text, January 2010


Coherent control of three-spin states in a triple quantum dot
text, January 2011


Quantum quench phase diagrams of an s-wave BCS-BEC condensate
text, January 2014


Complete Generalized Gibbs Ensemble in an interacting Theory
text, January 2015


Solvable multistate model of Landau-Zener transitions in cavity QED
text, January 2016


Nonadiabatic Landau Zener tunneling in Fe_8 molecular nanomagnets
text, January 2000


Quantum Tunneling in Half-Integer Spin Systems
text, January 2001


Landau-Zener transitions in a linear chain
text, January 2001


Observation of resonance condensation of fermionic atom pairs
text, January 2004


Gauging a quantum heat bath with dissipative Landau-Zener transitions
text, January 2006


Integrability of the pairing hamiltonian
text, January 1997


Works referencing / citing 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

Detuning-induced robustness of a three-state Landau-Zener model against dissipation
journal, June 2019


Dynamic spin localization and γ -magnets
journal, December 2019


Resonant Transitions Due to Changing Boundaries
journal, June 2019

  • Anzà, Fabio; Messina, Antonino; Militello, Benedetto
  • Open Systems & Information Dynamics, Vol. 26, Issue 02
  • DOI: 10.1142/s1230161219500069

Counterdiabatic Hamiltonians for multistate Landau-Zener problem
journal, January 2018


Resonant transitions due to changing boundaries
text, January 2015


Integrable Floquet Hamiltonian for a Periodically Tilted 1D Gas
text, January 2019


Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.