| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] BCAM Basque Ctr Appl Math Mazarredo, Bilbao 48009 - Spain
[2] Ikerbasque, Basque Fdn Sci, E-48011 Bilbao - Spain
[3] Univ Basque Country, Dept Matemat, Fac Ciencias & Tecnol, E-48080 Bilbao - Spain
[4] Univ Sao Paulo, Dept Fis Matemat, Inst Fis, BR-05314970 Sao Paulo, SP - Brazil
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES; v. 25, n. 14, p. 2587-2632, DEC 30 2015. |
| Web of Science Citations: | 3 |
| Abstract | |
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 Levy 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 Levy processes in Fourier space - of the phenomenon of electrical conductivity. (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 |