Time dynamics of Bethe ansatz solvable models

Abstract

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.

arXiv comment9 pages, 1 figure

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Cited by in corpus (2)

• Stochastic growth in time dependent environments
• A map between time-dependent and time-independent quantum many-body Hamiltonians