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From the second law of thermodynamics to AC-conductivity measures of interacting fermions in disordered media

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We study the dynamics of interacting lattice fermions with random hopping amplitudes
and random static potentials, in presence of time-dependent electromagnetic fields. The
interparticle interaction is short-range and translation invariant. Electromagnetic fields
are compactly supported in time and space. In the limit of infinite space supports (macroscopic
limit) of electromagnetic fields, we derive Ohm and Joule’s laws in the AC-regime.
An important outcome is the extension to interacting fermions of the notion of macroscopic
AC-conductivity measures, known so far only for free fermions with disorder.
Such excitation measures result from the second law of thermodynamics and turn out
to be L´evy measures. As compared to the Drude (Lorentz–Sommerfeld) model, widely
used in Physics, the quantum many-body problem studied here predicts a much smaller
AC-conductivity at large frequencies. This indicates (in accordance with experimental
results) that the relaxation time of the Drude model, seen as an effective parameter
for the conductivity, should be highly frequency-dependent. We conclude by proposing
an alternative effective description — using L´evy processes in Fourier space — of the
phenomenon of electrical conductivity.

Keywords: Disordered systems; transport processes; conductivity measure.

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Informasi Detail

Judul Seri

Mathematical Models and Methods in Applied Sciences

No. Panggil

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Penerbit

: World Scientific., 2015

Deskripsi Fisik

Mathematical Models and Methods in Applied Sciences (2015)

Bahasa

English

ISBN/ISSN

DOI: 10.1142/S021820

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

(2015)

Subjek

KESEHATAN

Info Detail Spesifik

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Pernyataan Tanggungjawab

Wati/Agus

Versi lain/terkait

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