# Integrable Time-Dependent Quantum Hamiltonians.

@article{Sinitsyn2018IntegrableTQ, title={Integrable Time-Dependent Quantum Hamiltonians.}, author={Nikolai A Sinitsyn and Emil A. Yuzbashyan and Vladimir Y. Chernyak and Aniket Patra and Chen Sun}, journal={Physical review letters}, year={2018}, volume={120 19}, pages={ 190402 } }

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. We also… Expand

#### 25 Citations

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets.

- Physics, Mathematics
- 2018

We solve the non-stationary Schrodinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven… Expand

Multitime Landau–Zener model: classification of solvable Hamiltonians

- Physics, Mathematics
- 2019

We introduce a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum… Expand

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

- Physics, Mathematics
- 2017

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians. Within the multistate Landau-Zener (MLZ) theory, however, there has… Expand

Integrable Floquet Hamiltonian for a Periodically Tilted 1D Gas.

- Physics, Medicine
- Physical review letters
- 2019

It is shown that the Floquet Hamiltonian of theintegrable Lieb-Liniger model in the presence of a linear potential with a periodic time-dependent strength is instead integrable and its quasienergies can be determined using the Bethe ansatz approach. Expand

Time dynamics of Bethe ansatz solvable models

- Physics, Mathematics
- 2020

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… Expand

Counterdiabatic Hamiltonians for multistate Landau-Zener problem

- Physics
- 2018

We study the Landau-Zener transitions generalized to multistate systems. Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we introduce the auxiliary Hamiltonians that are… Expand

Dynamic spin localization and
γ
-magnets

- Physics, Mathematics
- 2019

We construct an explicitly solvable model of interacting quantum spins under the action of linearly time-dependent magnetic field. The Hamiltonian, which we call the gamma-magnet, does not conserve… Expand

Detuning-induced robustness of a three-state Landau-Zener model against dissipation

- Physics, Mathematics
- Physical Review A
- 2019

A three-state system subjected to a time-dependent Hamiltonian whose bare energies undergo one or more crossings, depending on the relevant parameters, is considered, also taking into account the… Expand

Quantum Annealing and Thermalization: Insights from Integrability.

- Physics, Medicine
- Physical review letters
- 2018

It is proved that quantum correlations can accelerate computations and, at the end of the annealing protocol, lead to the perfect Gibbs distribution of all microstates. Expand

Three-state Landau-Zener model in the presence of dissipation

- Physics
- Physical Review A
- 2019

A population transfer based on adiabatic evolutions in a three-state system undergoing an avoided crossing is considered. The efficiency of the process is analyzed in connection with the relevant… Expand

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