J.-B. Bru

Diagonalizing quadratic bosonic operators by non-autonomous flow equation

We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal infinity. We demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

Heat Production of Noninteracting Fermions Subjected to Electric Fields

Electric resistance in conducting media is related to heat (or entropy) production in presence of electric fields. In this paper, by using Arakis relative entropy for states, we mathematically define and analyze the heat production of free fermions within external potentials. More precisely, we investigate the heat production of the non-autonomous C*-dynamical system obtained from the fermionic second quantization of a discrete Schrodinger operator with bounded static potential in presence of an electric field that is time- and space-dependent. It is a first preliminary step towards a mathematical description of transport properties of fermions from thermal considerations. This program will be carried out in several papers. The regime of small and slowly varying in space electric fields is important in this context, and is studied the present paper. We use tree-decay bounds of the

Non–cooperative equilibria of Fermi systems with long range interactions

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Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory

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Microscopic foundations of Ohm and Joule's laws – The relevance of thermodynamics

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Macroscopic conductivity of free fermions in disordered media

, correlations of the many-fermion system to analyze this regime. We verify below the 1st law of thermodynamics for the system under consideration. The latter implies, for systems doing no work, that the heat produced by the electromagnetic field is exactly the increase of the internal energy resulting from the modification of the (infinite volume) state of the fermion system. The identification of heat production with an energy increment is, among other things, technically convenient. We initially focus our study on non-interacting (or free) fermions, but our approach will be later applied to weakly interacting fermions.

Inhomogeneous Fermi and quantum spin systems on lattices

Part 1. Main Results and Discussions: Fermi systems on lattices Fermi systems with long-range interactions Part 2. Complementary Results: Periodic boundary conditions and Gibbs equilibrium states The set

Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light I: The Effective Theory

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Universal Bounds for Large Determinants from Non-Commutative Hölder Inequalities in Fermionic Constructive Quantum Field Theory

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MICROSCOPIC FOUNDATIONS OF THE MEIßNER EFFECT: THERMODYNAMIC ASPECTS

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