Heat production in Infinitely extended fermion systems subjected to electric fields

• 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
• 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)

Scientific publications

(9)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BRU, JEAN-BERNARD; DE PASQUALE, ANTONIO DELGADO; PEDRA, WALTER DE SIQUEIRA. d-Wave pairing driven by bipolaric modes related to giant electron-phonon anomalies in high-T-c superconductors. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, MAR 2015. (13/13215-5)

BRU, J. -B.; DE SIQUEIRA PEDRA, W.; HERTLING, C.. Macroscopic conductivity of free fermions in disordered media. REVIEWS IN MATHEMATICAL PHYSICS, v. 26, n. 5, JUN 2014. (13/13215-5)

BRU, J. -B.; DE SIQUEIRA PEDRA, W.; HERTLING, C.. AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media. Archive for Rational Mechanics and Analysis, v. 220, n. 2, p. 445-504, MAY 2016. (13/13215-5)

BRU, JEAN-BERNARD; PEDRA, WALTER DE SIQUEIRA. Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light II: Microscopic Foundations. ANNALES HENRI POINCARE, v. 16, n. 6, p. 1429-1477, JUN 2015. (13/13215-5)

BRU, JEAN-BERNARD; PEDRA, WALTER DE SIQUEIRA; HERTLING, CAROLIN. Heat Production of Noninteracting Fermions Subjected to Electric Fields. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, v. 68, n. 6, p. 964-1013, JUN 2015. (13/13215-5)

BRU, JEAN-BERNARD; PEDRA, WALTER DE SIQUEIRA. Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles. LETTERS IN MATHEMATICAL PHYSICS, v. 106, n. 1, p. 81-107, JAN 2016. (13/13215-5)

BRU, JEAN-BERNARD; DE PASQUALE, ANTONIO DELGADO; PEDRA, WALTER DE SIQUEIRA. d-Wave pairing driven by bipolaric modes related to giant electron-phonon anomalies in high-T-c superconductors. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, v. N/A, p. 36-pg., 2015-03-01. (13/13215-5)

BRU, J. -B.; DE SIQUEIRA PEDRA, W.. From the second law of thermodynamics to AC-conductivity measures of interacting fermions in disordered media. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, v. 25, n. 14, p. 2587-2632, DEC 30 2015. (13/13215-5)

BRU, J. -B.; DE SIQUEIRA PEDRA, W.; HERTLING, C.. Microscopic conductivity of lattice fermions at equilibrium. I. Non-interacting particles. Journal of Mathematical Physics, v. 56, n. 5, MAY 2015. (13/13215-5)