Nonequilibrium and Time-Dependent Interactions

J. Nicolas

I. V. Tokatly

Using the functional integral formulation of nonequilibrium quantum many-body theory we develop a regular description of a Fermi system with a strong attractive interaction in the presence of an external time-dependent potential. In the strong coupling limit this fermionic system is equivalent to a nonequilibrium dilute Bose gas of diatomic molecules. We also consider nonequilibrium strongly coupled Bardeen-Cooper-Schrieffer theory and show that it reduces to the full nonlinear time-dependent Gross-Pitaevski equation, which determines the evolution of the condensate wave function.

Eric Dohner, Hanna Terletska, Ka-Ming Tam +2 more

We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. The real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.

Kaspar Sakmann, Alexej I. Streltsov, Ofir E. Alon +1 more

Lattice models are central to the physics of ultracold atoms and condensed matter. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on time-dependent Wannier functions and the variational principle that leads to optimal time-dependent lattice models. As an application, we use the Bose–Hubbard model with time-dependent Wannier functions to study an interaction quench scenario involving higher bands. We find a separation of time-scales in the dynamics. The results are compared with numerically exact results of the time-dependent many-body Schrödinger equation. We thereby show that—under some circumstances—the multi-band nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a single-band model.