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

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 macrosc...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2016-05, Vol.220 (2), p.445-504
Main Authors: Bru, J.-B., de Siqueira Pedra, W., Hertling, C.
Format: Article
Language:English
Subjects:
Alternating current
Boson fields
Classical Mechanics
Complex Systems
Continuity (mathematics)
Electric potential
Fermions
Fluctuation
Fluid- and Aerodynamics
Fourier transforms
Lattices
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Thermal cycling
Time correlation functions
Time dependence
Variations
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-015-0935-1