Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 9: Dynamics in many-body systems: Equilibration and localization II (joint session DY/TT)

DY 9.3: Talk

Monday, April 1, 2019, 16:00–16:15, H19

How to teach equilibration to the Boltzmann equation: a noisy relaxation time approximation — •Philipp Weiß and Achim Rosch — Institute for Theoretical Physics, University of Cologne, Germany

Equilibration of closed systems is controlled by diffusive transport of conserved quantities. After a quench these systems approach thermal equilibrium only slowly, hydrodynamic long-time tails emerge. As an analog in space one expects long-distance tails to appear when the system is perturbed only locally. A natural example for this situation is a current-carrying wire coupled to leads. We expect the connections to induce long-distance tails which show up as correction in the voltage drop.

The Boltzmann equation is widely used for tackling transport problems. However, it predicts exponential relaxation as it does not capture fluctuations of the hydrodynamic modes. Close to equilibrium a fluctuation-dissipation relation restores the missing piece of information, giving rise to a stochastic Boltzmann-Langevin equation.

Here, we present a simplified version, a “noisy relaxation time approximation”, which we derive from a conserving relaxation time approximation supplemented with a suitably correlated noise term. We use our new tool to track the equilibration of a one-dimensional wire after a quench. Our prime goal is to detect long-time tails and long-distance tails indicating the diffusive built-up of the equilibrium correlations.