Integrable time-dependent quantum Hamiltonians

TL;DR

This paper establishes conditions for the integrability of time-dependent quantum Hamiltonians, enabling exact solutions for non-stationary Schrödinger equations and validating prior models like the driven Tavis-Cummings model.

Contribution

It introduces a gauge field-based framework to identify integrable time-dependent quantum systems, expanding the class of exactly solvable models.

Findings

Known Landau-Zener models satisfy the integrability conditions.

Provides a method to incorporate time dependence into quantum integrable models.

Validates the solution of the driven generalized Tavis-Cummings model.

Abstract

We formulate a set of conditions under which dynamics of a time-dependent quantum Hamiltonian are integrable. The main requirement is the existence of a nonabelian 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, so that the resulting non-stationary Schrodinger equation is exactly solvable. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.