AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media

Author(s)

Bru, J. -B. ^[1] ; de Siqueira Pedra, W. ; Hertling, C.

Affiliation

^[1] Basque Fdn Sci, Ikerbasque, Maria Diaz de Haro 3, Bilbao 48013 - Spain

• Document type: Journal article
• Source: Archive for Rational Mechanics and Analysis; v. 220, n. 2, p. 445-504, MAY 2016.
• Web of Science Citations: 3

Abstract

We extend (Bru et al. in J Math Phys 56: 051901-1-51, 2015) 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. (AU)

• FAPESP's process: 13/13215-5 - Heat production in Infinitely extended fermion systems subjected to electric fields
• Grantee: Walter Alberto de Siqueira Pedra
• Support Opportunities: Regular Research Grants