AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media
arXiv:1611.07740 · doi:10.1007/s00205-015-0935-1
Abstract
We extend [Bru-de Siqueira Pedra-Hertling, J. Math. Phys. 56 (2015) 051901] in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric field that is time- and space-dependent. We obtain the notion of a macroscopic AC-conductivity measure which only results from the second principle of thermodynamics. The latter corresponds here to the positivity of the heat production for cyclic processes on equilibrium states. Its Fourier transform is a continuous bounded function which is naturally called (macroscopic) conductivity. We additionally derive Green-Kubo relations involving time-correlations of bosonic fields coming from current fluctuations in the system. This is reminiscent of non-commutative central limit theorems.
References in corpus (4)
- Linear response theory for magnetic Schroedinger operators in disordered media
- On Mott's formula for the ac-conductivity in the Anderson model
- Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles
- Heat Production of Non-Interacting Fermions Subjected to Electric Fields
Cited by in corpus (4)
- Adiabatic Theorem for Quantum Spin Systems
- Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles
- Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media
- Microscopic Conductivity of Lattice Fermions at Equilibrium - Part II: Interacting Particles