Limited validity of the Kubo formula for thermal conduction in modular quantum systems
arXiv:cond-mat/0602042 · doi:10.1103/PhysRevB.73.104302
Abstract
The Kubo formula describes a current as a response to an external field. In the case of heat conduction there is no such external field. We analyze why and to what extend it is nevertheless justified to describe heat conduction in modular quantum systems by the Kubo formula. Modular we call systems that may be described as consisting of weakly coupled identical subsystems. We explain in what sense this description applies to a large class of systems. Furthermore, we numerically evaluate the Kubo formula for some finite modular systems. We compare the results with data obtained from the direct numerical solution of the corresponding time-dependent Schroedinger equation.
11 pages, 10 figures
References in corpus (6)
- Fourier's Law confirmed for a class of small quantum systems
- Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
- Heat conductivity in small quantum systems: Kubo formula in Liouville space
- From Pure Schroedingerian to Statistical Dynamics
- Thermal conductivity of one-dimensional spin-1/2 systems
- Quantum Heat Transport: Perturbation Theory in Liouville Space
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