Heat Transport in Closed Quantum Systems

The relationship between microscopic and macroscopic levels of description has challenged physicists for centuries and in many branches of research. In the present article we demonstrate that a class of closed quantum systems gives rise to diffusive behavior (normal heat conduction) on a mesoscopic level while the microscopic dynamics is governed by the respective Schrödinger equation only. The key to understanding such qualitative differences is not just the mere system size but rather the complete or reduced description as dictated by observation. For example, quantum thermodynamics (see J. Gemmer et al., Quantum Thermodynamics, Springer (2004)) has been able to show that a partition of a closed quantum system into a small part of interest and a large environment will typically lead to thermal equilibrium properties with respect to the small part. In the same spirit, heat conduction and Fourier´s law emerge from closed system quantum dynamics under appropriate coarse-graining in real space! Such a behavior may show up already in suprisingly small composite quantum objects.