| Grant number: | 13/13215-5 |
| Support Opportunities: | Regular Research Grants |
| Start date: | October 01, 2013 |
| End date: | September 30, 2015 |
| Field of knowledge: | Physical Sciences and Mathematics - Physics |
| Principal Investigator: | Walter Alberto de Siqueira Pedra |
| Grantee: | Walter Alberto de Siqueira Pedra |
| Host Institution: | Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| City of the host institution: | São Paulo |
| Associated researchers: | Jean Bernard Bru |
Abstract
Electrical resistance in conducting media is related to heat (or, equivalently, entropy) production in presence of electric fields. From a microscopic point of view, such a resistance is due to the presence of disorder or interaction between charge carriers. Our aim is to use a notion of relative entropy for the states of infinite quantum systems in order to mathematically define and analyze the entropy production for fermions in infinitely extended crystals subjected to an electric field. More precisely, we will consider the entropy production for the non-autonomous C* dynamical system obtained from the CAR (which implements the Pauli exclusion principle of fermions) of the three-dimensional cubic lattice (representing the crystal) equipped with a dynamics encoding in a convenient way the presence of disorder, the interparticle interaction and the presence of a time-dependent electric field. The challenge of the present project is to provide mathematical proofs starting from purely quantum models that the laws of Ohm and Joule correctly describe the heat production in conducting media as a function of the applied electric field and that this production is due to the presence of disorder or to the interaction between charge carriers. (AU)
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