Now showing items 1-20 of 30

(2013-07)
We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in ... • #### Heat production of noninteracting fermions subjected to electric fields ﻿ (2014-07-21) Electric resistance in conducting media is related to heat (or entropy) production in the presence of electric fields. In this paper, by using Araki's relative entropy for states, we mathematically define and analyze the ... • #### Macroscopic conductivity of free fermions in disordered media ﻿ (2014-12-31) We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic ... • #### From the 2nd Law of Thermodynamics to AC–Conductivity Measures of Interacting Fermions in Disordered Media ﻿ (2015-05-20) 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 ... • #### Microscopic conductivity of lattice fermions at equilibrium. I. Non-interacting particles ﻿ (2015-12-31) We consider free lattice fermions subjected to a static bounded potential and a timeand space-dependent electric field. For any bounded convex region R âŠ‚ â„ (d (d â‰¥ 1) of space, electric fields Îµ within R drive currents. ... • #### Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light II: Microscopic Foundations ﻿ (2015-12-31) From quantum mechanical first principles only, we rigorously study the time-evolution of a N-level atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at ... • #### D-Wave pairing driven by bipolaric modes related to giant electron-phonon anomalies in high-Tc superconductors ﻿ (2015-12-31) Taking into account microscopic properties of most usual high-Tc superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the ... • #### AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media ﻿ (2015-12-31) We extend (Bru et al. in J Math Phys 56:051901-1-51, 2015) in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric ... • #### Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles ﻿ (2015-12-31) 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) ... • #### Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction ﻿ (2016-01-01) We study the time evolution of a system of$N$spinless fermions in$\mathbb{R}^3$which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation ... • #### Diagonalizing quadratic bosonic operators by non-autonomous flow equations volker bach ﻿ (2016-01-01) 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 ... • #### Universal Bounds for Large Determinants from Non–Commutative Ho ̈lder Inequalities in Fermionic Constructive Quantum Field Theory ﻿ (2016-01-01) Efficiently bounding large determinants is an essential step in non–relati- vistic fermionic constructive quantum field theory, because, together with the summability of the interaction and the covariance, it implies the ... • #### Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory ﻿ (2016-01-01) We generalize to multi–commutators the usual Lieb–Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expan- sions) ... • #### Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles ﻿ (2016-01-01) We apply Liebâ€“Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Liebâ€“Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) ... • #### Geometric inequalities from phase space translations ﻿ (2016-07-22) We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results ... • #### Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory ﻿ (2017) We generalize to multi-commutators the usual Lieb–Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in ... • #### Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors ﻿ (2017-05-03) The discovery of high-temperature superconductors in 1986 represented a major experimental breakthrough (Nobel Prize 1987), but their theoretical explanation is still a subject of much debate. These materials have many ... • #### Universal bounds for large determinants from non-commutative Hölder inequalities in fermionic constructive quantum field theory ﻿ (2017-08-02) Efficiently bounding large determinants is an essential step in non-relativistic fermionic constructive quantum field theory to prove the absolute convergence of the perturbation expansion of correlation functions in terms ... • #### Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices ﻿ (2018-01-24) We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903--931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time ... • #### Existence of “$d\$-wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors ﻿

(2018-03-21)
High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows ...