Now showing items 8-27 of 42

• 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 ...
• 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 ...
• 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 ...
• The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos ﻿

(2019-01-10)
We investigate the old problem of the fast relaxation of collisionless N-body systems that are collapsing or perturbed, emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in ...
• Entanglement of classical and quantum short-range dynamics in mean-field systems ﻿

(2021-11-01)
The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity ...
• Equilibrium and Transport Properties of Quantum Many-Body Systems ﻿

(2019-10-30)
This thesis is a study of equilibrium and dynamical properties of macroscopic quantum many-body 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 ﻿

(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 ...
• Extended State Space for Describing Renormalized Fock Spaces in QFT ﻿

(2022-06-04)
In quantum field theory (QFT) models, it often seems natural to use, instead of wave functions from Fock space, wave functions that are not square-integrable and have prefactors involving divergent integrals (known as ...
• 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 ...
• 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 ...
• 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 ...
• High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph ﻿

(2021-08-01)
The Kubo-Martin-Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and ...
• Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition ﻿

(2022-04-28)
We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on ...
• Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors ﻿

(2018-12-10)
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 ...
• 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 ...
• 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 ...
• Large Deviations in Weakly Interacting Fermions - Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians ﻿

(2021)
We prove that the G\"{a}rtner--Ellis 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 ﻿

(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 ...
• 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) ...
• 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 ...