Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles

Autor(es)

Bru, Jean-Bernard ^{[1, 2, 3]} ; Pedra, Walter de Siqueira ^[4]

Afiliação do(s) autor(es)

^[1] BCAM, Bilbao 48009 - Spain

^[2] Ikerbasque, Basque Fdn Sci, Bilbao 48013 - Spain

^[3] Univ Basque Country, Fac Ciencias & Tecnol, Dept Matemat, Bilbao 48080 - Spain

^[4] Univ Sao Paulo, Inst Phys, Dept Math Phys, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: LETTERS IN MATHEMATICAL PHYSICS; v. 106, n. 1, p. 81-107, JAN 2016.
• Citações Web of Science: 2

Resumo

We apply Lieb-Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb-Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) response of interacting fermions at thermal equilibrium to perturbations of the external electromagnetic field. This analysis leads to an extension of the results for quasi-free fermions of (Bru et al. Commun Pure Appl Math 68(6): 964-1013, 2015; Bru et al. J Math Phys 56: 051901-1-051901-51, 2015) to fermion systems on the lattice with short-range interactions. More precisely, we investigate entropy production and charge transport properties of non-autonomous C{*}-dynamical systems associated with interacting lattice fermions within bounded static potentials and in presence of an electric field that is time and space dependent. We verify the 1st law of thermodynamics for the heat production of the system under consideration. In linear response theory, the latter is related with Ohm and Joule's laws. These laws are proven here to hold at the microscopic scale, uniformly with respect to the size of the (microscopic) region where the electric field is applied. An important outcome is the extension of the notion of conductivity measures to interacting fermions. (AU)

• Processo FAPESP: 13/13215-5 - Produção de calor em sistemas fermiônicos infinitos sujeitos a campos elétricos
• Beneficiário: Walter Alberto de Siqueira Pedra
• Linha de fomento: Auxílio à Pesquisa - Regular