Browsing Quantum Mechanics by Title
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ACConductivity Measure from Heat Production of Free Fermions in Disordered Media
(20151231)We extend (Bru et al. in J Math Phys 56:051901151, 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 ... 
Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media
(20190122)The growing need for smaller electronic components has recently sparked the interest in the breakdown of the classical conductivity theory near the atomic scale, at which quantum effects should dominate. In 2012, experimental ... 
Characterization of the QuasiStationary State of an Impurity Driven by Monochromatic Light II: Microscopic Foundations
(20151231)From quantum mechanical first principles only, we rigorously study the timeevolution of a Nlevel atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at ... 
Classical dynamics generated by longrange interactions for lattice fermions and quantum spins
(2021)We study the macroscopic dynamical properties of fermion and quantumspin systems with longrange, or meanfield, interactions. The results obtained are far beyond previous ones and require the development of a mathematical ... 
DWave pairing driven by bipolaric modes related to giant electronphonon anomalies in highTc superconductors
(20151231)Taking into account microscopic properties of most usual highTc superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the ... 
Decay of Complextime Determinantal and Pfaffian\ Correlation Functionals in Lattices
(20180124)We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903931, 2016) for manybody localization of quasifree fermions, by considering the high dimensional case and complextime ... 
Diagonalizing quadratic bosonic operators by nonautonomous flow equations volker bach
(20160101)We study a nonautonomous, nonlinear 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 ... 
The Discretenessdriven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, Ndependence, and the Role of Chaos
(20190110)We investigate the old problem of the fast relaxation of collisionless Nbody systems that are collapsing or perturbed, emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in ... 
Equilibrium and Transport Properties of Quantum ManyBody Systems
(20191030)This thesis is a study of equilibrium and dynamical properties of macroscopic quantum manybody problems. An important part of the manuscript concerns the study of heat and charge transport properties of fermions on the ... 
Existence of “$d$wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors
(20180321)Hightemperature superconductors have different properties than conventional superconductors, one of these important properties is nonisotropic symmetry of the order parameter. In this work we present a model that shows ... 
From the 2nd Law of Thermodynamics to AC–Conductivity Measures of Interacting Fermions in Disordered Media
(20150520)We study the dynamics of interacting lattice fermions with random hopping amplitudes and random static potentials, in presence of timedependent electromagnetic fields. The interparticle interaction is shortrange and ... 
Geometric inequalities from phase space translations
(20160722)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 ... 
Heat production of noninteracting fermions subjected to electric fields
(20140721)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 ... 
Isotropic BipolaronFermionExchange Theory and Unconventional Pairing in Cuprate Superconductors
(20170503)The discovery of hightemperature 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 ... 
Isotropic BipolaronFermionExchange Theory and Unconventional Pairing in Cuprate Superconductors
(20181210)The discovery of hightemperature 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 ... 
Kinetic energy estimates for the accuracy of the timedependent HartreeFock approximation with Coulomb interaction
(20160101)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 ... 
Large Deviations in Weakly Interacting Fermions  Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians
(2021)We prove that the G\"{a}rtnerEllis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin ... 
Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory
(20160101)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) ... 
Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory
(2017)We generalize to multicommutators 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 ... 
Macroscopic conductivity of free fermions in disordered media
(20141231)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 ...