Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 51: Statistical physics (general) I
DY 51.2: Talk
Friday, March 28, 2003, 10:30–10:45, G\"OR/229
Quantum Heat Conductance and the Emergence of Fourier’s Law — •Michael Hartmann1,2, Günter Mahler2, and Ortwin Hess1 — 1Theoretical Quantum Electronics, Institut für Technische Physik, DLR-Stuttgart, Pfaffenwaldring 38-40, D-70569 Stuttgart — 2Institut für Theoretische Physik 1, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart
The derivation of Fourier’s law of heat conductance from the quantum theory of the underlying microscopic dynamics still remains unclear. In particular, it is not well understood how and when a finite temperature gradient forms within the conductor. Here we consider a chain of interacting quantum systems with next neighbor coupling that connects two baths held at different temperatures. We find that a finite temperature gradient in the chain builds up whenever the dynamics becomes purely stochastic and coherent features are negligible. A necessary condition for this to happen is that the Hilbert space dimension, n, of each of the subspaces that are connected by the next neighbor couplings is large enough. For the case of weakly coupled effective 2-level sytems, we derive a set of coupled rate equations for the subsystems using Hilbert space averages to approximate the relevant quantities and solve it to obtain Fourier’s law. This behavior can be contrasted with the No-dqnon-classicalNo-dq limit (ballistic regime) with completely different temperature profiles.