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:
-
[3]
- Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry, and Dept. of Mathematics
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- 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:
- Journal Article: 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. https://doi.org/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. https://doi.org/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},
url = {https://www.osti.gov/biblio/1471351},
journal = {Journal of Physics. A, Mathematical and Theoretical},
issn = {1751-8113},
number = 24,
volume = 51,
place = {United States},
year = {2018},
month = {5}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 2 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
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
Solvable multistate model of Landau-Zener transitions in cavity QED
journal, June 2016
- Sinitsyn, Nikolai A.; Li, Fuxiang
- Physical Review A, Vol. 93, Issue 6
Algebraic bethe anzatz and the tavis-cummings model
journal, June 2000
- Bogolyubov, N. M.
- Journal of Mathematical Sciences, Vol. 100, Issue 2
Exact out-of-equilibrium central spin dynamics from integrability
journal, April 2014
- Fioretto, Davide; Caux, Jean-Sébastien; Gritsev, Vladimir
- New Journal of Physics, Vol. 16, Issue 4
Solvable four-state Landau-Zener model of two interacting qubits with path interference
journal, November 2015
- Sinitsyn, N. A.
- Physical Review B, Vol. 92, Issue 20
Non-equilibrium dynamics of Gaudin models
journal, October 2013
- Barmettler, Peter; Fioretto, Davide; Gritsev, Vladimir
- EPL (Europhysics Letters), Vol. 104, Issue 1
Exact solution for the inhomogeneous Dicke model in the canonical ensemble: Thermodynamical limit and finite-size corrections
journal, June 2017
- Pogosov, W. V.; Shapiro, D. S.; Bork, L. V.
- Nuclear Physics B, Vol. 919
Landau–Zener–Stueckelberg interferometry with driving fields in the quantum regime
journal, March 2017
- Ashhab, S.
- Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 13
Constraints on scattering amplitudes in multistate Landau-Zener theory
journal, January 2017
- Sinitsyn, Nikolai A.; Lin, Jeffmin; Chernyak, Vladimir Y.
- Physical Review A, Vol. 95, Issue 1
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
Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models
journal, September 2017
- Malla, Rajesh K.; Raikh, M. E.
- Physical Review B, Vol. 96, Issue 11
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
Exact transition probabilities in a 6-state Landau–Zener system with path interference
journal, April 2015
- Sinitsyn, N. A.
- Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 19
Multistate Landau-Zener models with all levels crossing at one point
journal, August 2017
- Li, Fuxiang; Sun, Chen; Chernyak, Vladimir Y.
- Physical Review A, Vol. 96, Issue 2
Integrability and level crossing manifolds in a quantum Hamiltonian system
journal, November 1998
- Stepanov, Vyacheslav V.; Müller, Gerhard
- Physical Review E, Vol. 58, Issue 5
Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor
journal, June 2017
- Troiani, F.; Godfrin, C.; Thiele, S.
- Physical Review Letters, Vol. 118, Issue 25
Atomi orientati in campo magnetico variabile
journal, February 1932
- Majorana, Ettore
- Il Nuovo Cimento, Vol. 9, Issue 2
Nonadiabatic bulk-surface oscillations in driven topological insulators
journal, November 2016
- Kolodrubetz, Michael; Fregoso, Benjamin M.; Moore, Joel E.
- Physical Review B, Vol. 94, Issue 19
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
Landau-Zener extension of the Tavis-Cummings model: Structure of the solution
journal, September 2016
- Sun, Chen; Sinitsyn, Nikolai A.
- Physical Review A, Vol. 94, Issue 3
Multiparticle Landau-Zener problem: Application to quantum dots
journal, November 2002
- Sinitsyn, N. A.
- Physical Review B, Vol. 66, Issue 20
Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems
journal, June 2016
- Mandarino, Antonio; Bina, Matteo; Porto, Carmen
- Physical Review A, Vol. 93, Issue 6
Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets
journal, May 2018
- Yuzbashyan, Emil A.
- Annals of Physics, Vol. 392
Quantum integrability in the multistate Landau–Zener problem
journal, May 2015
- Patra, A.; Yuzbashyan, E. A.
- Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 24
Separation of variables for integrable spin–boson models
journal, November 2010
- Amico, Luigi; Frahm, Holger; Osterloh, Andreas
- Nuclear Physics B, Vol. 839, Issue 3
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
Periodically driven three-level systems
journal, September 2016
- Kenmoe, M. B.; Fai, L. C.
- Physical Review B, Vol. 94, Issue 12
Quantum Integrability in Systems with Finite Number of Levels
journal, January 2013
- Yuzbashyan, Emil A.; Shastry, B. Sriram
- Journal of Statistical Physics, Vol. 150, Issue 4
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
Integrable Time-Dependent Quantum Hamiltonians
journal, May 2018
- Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.
- Physical Review Letters, Vol. 120, Issue 19
Role of multilevel Landau-Zener interference in extreme harmonic generation
journal, August 2016
- Stehlik, J.; Maialle, M. Z.; Degani, M. H.
- Physical Review B, Vol. 94, Issue 7
S-matrix for generalized Landau-Zener problem
journal, March 1993
- Brundobler, S.; Elser, Veit
- Journal of Physics A: Mathematical and General, Vol. 26, Issue 5
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
The Surveyor's Area Formula
journal, September 1986
- Braden, Bart
- The College Mathematics Journal, Vol. 17, Issue 4
Integrable Time-Dependent Quantum Hamiltonians
journal, May 2018
- Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.
- Physical Review Letters, Vol. 120, Issue 19
Integrability and level crossing manifolds in a quantum Hamiltonian system
journal, November 1998
- Stepanov, Vyacheslav V.; Müller, Gerhard
- Physical Review E, Vol. 58, Issue 5
Atomi orientati in campo magnetico variabile
journal, February 1932
- Majorana, Ettore
- Il Nuovo Cimento, Vol. 9, Issue 2
Solvable four-state Landau-Zener model of two interacting qubits with path interference
journal, November 2015
- Sinitsyn, N. A.
- Physical Review B, Vol. 92, Issue 20
Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models
journal, September 2017
- Malla, Rajesh K.; Raikh, M. E.
- Physical Review B, Vol. 96, Issue 11
Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor
journal, June 2017
- Troiani, F.; Godfrin, C.; Thiele, S.
- Physical Review Letters, Vol. 118, Issue 25
Role of multilevel Landau-Zener interference in extreme harmonic generation
journal, August 2016
- Stehlik, J.; Maialle, M. Z.; Degani, M. H.
- Physical Review B, Vol. 94, Issue 7
Periodically driven three-level systems
journal, September 2016
- Kenmoe, M. B.; Fai, L. C.
- Physical Review B, Vol. 94, Issue 12
Nonadiabatic bulk-surface oscillations in driven topological insulators
journal, November 2016
- Kolodrubetz, Michael; Fregoso, Benjamin M.; Moore, Joel E.
- Physical Review B, Vol. 94, Issue 19
Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems
journal, June 2016
- Mandarino, Antonio; Bina, Matteo; Porto, Carmen
- Physical Review A, Vol. 93, Issue 6
Solvable multistate model of Landau-Zener transitions in cavity QED
journal, June 2016
- Sinitsyn, Nikolai A.; Li, Fuxiang
- Physical Review A, Vol. 93, Issue 6
Landau-Zener extension of the Tavis-Cummings model: Structure of the solution
journal, September 2016
- Sun, Chen; Sinitsyn, Nikolai A.
- Physical Review A, Vol. 94, Issue 3
Multiparticle Landau-Zener problem: Application to quantum dots
journal, November 2002
- Sinitsyn, N. A.
- Physical Review B, Vol. 66, Issue 20
Multistate Landau-Zener models with all levels crossing at one point
journal, August 2017
- Li, Fuxiang; Sun, Chen; Chernyak, Vladimir Y.
- Physical Review A, Vol. 96, Issue 2
Algebraic bethe anzatz and the tavis-cummings model
journal, June 2000
- Bogolyubov, N. M.
- Journal of Mathematical Sciences, Vol. 100, Issue 2
Constraints on scattering amplitudes in multistate Landau-Zener theory
journal, January 2017
- Sinitsyn, Nikolai A.; Lin, Jeffmin; Chernyak, Vladimir Y.
- Physical Review A, Vol. 95, Issue 1
Works referencing / citing this record:
Dynamic spin localization and -magnets
journal, December 2019
- Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen
- Physical Review B, Vol. 100, Issue 22