124 research outputs found
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
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