Integrable Time-Dependent Quantum Hamiltonians

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir; Patra, Aniket; Sun, Chen

doi:10.1103/physrevlett.120.190402

Cited by 62 publications

(121 citation statements)

References 71 publications

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“…It was also shown in Ref. 19 that among Hamiltonians satisfying these conditions are the multistate Landau-Zener model and the generalized Tavis-Cummings model. Earlier in Ref.…”

Section: Introductionmentioning

confidence: 90%

“…The dynamical Bethe equations are a set of first order coupled ordinary differential equations. As the initial condition for (19) we need to pick a set of parameters {λ(0)} = {λ 1 (0), ..., λ N (0)}, which parametrizes the initial state |Ψ N (0) . For example, if the initial state is an eigenstate, the set {λ(0)} should satisfy the static Bethe equations.…”

Section: Example: Bose-hubbard Dimermentioning

confidence: 99%

“…The set of differential dynamical Bethe equations (7) and (12) can be applied to any Bethe ansatz solvable (22) for the case of (a) driven detuning ∆(t) = ∆0 + cos(t 2 ) using (19); and (b) quenched detuning from ∆0 = 0.697 to ∆ = 1.697 using (23). Stroboscopic maps for the case of (c) driven detuning as in (a); (d) quench as in (b).…”

Section: Outlook and Conclusionmentioning

confidence: 99%

“…20 for the Tavis-Cummings model, where the set of dynamical Bethe equations for λ j (t) was found, and its connection of trajectories λ j (t) with classical motion in a potential was established. So far all the examples of the dynamically integrable models considered in [19][20][21] belong to the Gaudin class 26 of integrable models or models with a classical R-matrix. Here we show that (2) can be applied to a wider class of integrable models, which goes beyond Gaudin class.…”

Section: Introductionmentioning

confidence: 99%

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Time dynamics of Bethe ansatz solvable models

Ermakov

Byrnes

2020

Phys. Rev. B

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We develop a method for finding the time evolution of exactly solvable models by Bethe ansatz. The dynamical Bethe wavefunction takes the same form as the stationary Bethe wavefunction except for time varying Bethe parameters and a complex phase prefactor. From this, we derive a set of first order nonlinear coupled differential equations for the Bethe parameters, called the dynamical Bethe equations. We find that this gives the exact solution to particular types of exactly solvable models, including the Bose-Hubbard dimer and Tavis-Cummings model. These models go beyond the Gaudin class, and offers an interesting possibility for performing time evolution in exactly solvable models.

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“…It was also shown in Ref. 19 that among Hamiltonians satisfying these conditions are the multistate Landau-Zener model and the generalized Tavis-Cummings model. Earlier in Ref.…”

Section: Introductionmentioning

confidence: 90%

Section: Example: Bose-hubbard Dimermentioning

confidence: 99%

Section: Outlook and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Time dynamics of Bethe ansatz solvable models

Ermakov

Byrnes

2020

Phys. Rev. B

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“…Here however because of the momenta k j the spectrum has a continuous part, so the general validity of the approximation is unclear. We point out further references [10,50] on related questions.…”

Section: ) Time Inhomogeneous Evolutionmentioning

confidence: 99%

Stochastic growth in time-dependent environments

2020

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We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance c(t) depending on time. We find that for c(t) ∝ t −α there is a transition at α = 1/2. When α > 1/2, the solution saturates at large times towards a non-universal limiting distribution. When α < 1/2 the fluctuation field is governed by scaling exponents depending on α and the limiting statistics are similar to the case when c(t) is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the log-gamma polymer model (3) Numerical simulations.

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Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations

Sedrakyan

Babujian

2022

J. High Energ. Phys.

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We consider a set of non-stationary quantum models. We show that their dynamics can be studied using links to Knizhnik-Zamolodchikov (KZ) equations for correlation functions in conformal field theories. We specifically consider the boundary Wess-Zumino-Novikov-Witten model, where equations for correlators of primary fields are defined by an extension of KZ equations and explore the links to dynamical systems. As an example of the workability of the proposed method, we provide an exact solution to a dynamical system that is a specific multi-level generalization of the two-level Landau-Zenner system known in the literature as the Demkov-Osherov model. The method can be used to study the nonequilibrium dynamics in various multi-level systems from the solution of the corresponding KZ equations.

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Integrable Time-Dependent Quantum Hamiltonians

Cited by 62 publications

References 71 publications

Time dynamics of Bethe ansatz solvable models

Time dynamics of Bethe ansatz solvable models

Stochastic growth in time-dependent environments

Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations

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