Variational Truncated Wigner Approximation

In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short time limit by minimizing the Hilbert-Schmidt distance between the semiclassical approximation and the real state of the system. The method is illustrated for the quartic oscillator

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation

Stationary ensemble approximations of dynamic quantum states: Optimizing the Generalized Gibbs Ensemble

We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to the time dependent density matrix. Our procedure allows for a systematic construction of the GGE by a constrained minimization of the distance between the latter and the true state. Moreover, we show that the entropy of the GGE is a direct measure for the quality of the approximation. We apply our method to a quenched hard core bose gas. In contrast to the standard GGE, our correlated GGE properly describes the higher order correlation functions

Chaos and thermalization in small quantum systems

Chaos and ergodicity are the cornerstones of statistical physics and thermodynamics. While classically even small systems like a particle in a two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a microcanonical ensemble, quantum systems formally can not. Recent theoretical breakthroughs and, in particular, the eigenstate thermalization hypothesis (ETH) however indicate that quantum systems can also thermalize. In fact ETH provided us with a framework connecting microscopic models and macroscopic phenomena, based on the notion of highly entangled quantum states. Such thermalization was beautifully demonstrated experimentally by A. Kaufman et. al. who studied relaxation dynamics of a small lattice system of interacting bosonic particles. By directly measuring the entanglement entropy of subsystems, as well as other observables, they showed that after the initial transient time the system locally relaxes to a thermal ensemble while globally maintaining a zero-entropy pure state.Comment: Perspectiv

Self-energy correction to dynamic polaron response

We present the first order self-energy correction to the linear response coefficients of polaronic systems within the truncated phase space approach developed by the present authors. Due to the system-bath coupling, the external pertubation induces a retarded internal field which dynamically screens the external force. Whereas the effect on the mobility is of second order, dynamical properties such as the effective mass and the optical absorption are modified in first order. The Fr\"ohlich polaron is used to illustrate the results