Berlin 2018 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 31: Dynamics in Many-Body Systems: Interference, Equilibration and Localization II (joint session DY/TT)

TT 31.2: Talk

Monday, March 12, 2018, 15:45–16:00, EB 107

Coupling of hydrodynamic fluctuations to diffusive modes in a one-dimensional current-carrying wire — •Philipp Weiß, Marcel Gievers, and Achim Rosch — Institute for Theoretical Physics, University of Cologne, Germany

Closed systems with conservation laws approach thermal equilibrium only algebraically slowly after a sudden perturbation. The reason is that the built-up of equilibrium fluctuations is tied to the diffusive transport of the conserved quantities which results in hydrodynamic long-time tails. A similar behavior is expected for a current-carrying wire, coupled to leads which serve as source and sink of electrons. Here, fluctuation corrections near the connections decay slowly in space along the wire. Though tailored to transport problems, the Boltzmann equation predicts exponentially fast relaxation indicating that the Boltzmann description omits crucial processes. This can be cured ad hoc by adding collision noise which gives rise to a stochastic Boltzmann-Langevin equation. However, the full equation is hard to solve and approximation schemes are needed when investigating a specific system.

We propose a “noisy relaxation time approximation” which satisfies the conservation laws and provides a properly correlated noise term. We examine this novel tool using the example of the one-dimensional current-carrying wire: Can we observe the expected long-distance tails? How does our approximation compare to the real dynamics? And to which extent can we control it?