Browsing by Subject "math-ph"
Now showing items 1-20 of 38
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A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)
(2017-04-23)Milestoning is a computational procedure that reduces the dynamics of complex systems to memoryless jumps between intermediates, or milestones, and only retains some information about the probability of these jumps and the ... -
A Mean Field Limit for the Vlasov–Poisson System
(Archive for Rational Mechanics and Analysis, 2017-09)© 2017, Springer-Verlag Berlin Heidelberg. We present a probabilistic proof of the mean field limit and propagation of chaos N-particle systems in three dimensions with positive (Coulomb) or negative (Newton) 1/r potentials ... -
A Quantum Kinetic Monte Carlo Method for Quantum Many-body Spin Dynamics
(2017-11-30)We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body ... -
A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue
(2017-04-23)The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain $\Omega$ by the largest mean first ... -
An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
(2017-04-23)We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the ... -
Bogoliubov corrections and trace norm convergence for the Hartree dynamics
We consider the dynamics of a large number N of nonrelativistic bosons in the mean field limit for a class of interaction potentials that includes Coulomb interaction. In order to describe the fluctuations around the mean ... -
Complex monopoles I: The Haydys monopole equation
We study complexified Bogomolny monopoles using the complex linear extension of the Hodge star operator, these monopoles can be interpreted as solutions to the Bogomolny equation with a complex gauge group. Alternatively, ... -
Defect resonances of truncated crystal structures
Defects in the atomic structure of crystalline materials may spawn electronic bound states, known as \emph{defect states}, which decay rapidly away from the defect. Simplified models of defect states typically assume the ... -
Derivation of the Bogoliubov Time Evolution for Gases with Finite Speed of Sound
The derivation of mean-field limits for quantum systems at zero temperature has attracted many researchers in the last decades. Recent developments are the consideration of pair correlations in the effective description, ... -
Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
We consider the spinless Pauli-Fierz Hamiltonian which describes a quantum system of non-relativistic identical particles coupled to the quantized electromagnetic field. We study the time evolution in a mean-field limit ... -
Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
We present a microscopic derivation of the time-dependent Gross-Pitaevskii equation starting from an interacting N-particle system of Bosons. We prove convergence of the reduced density matrix corresponding to the exact ... -
Derivation of the Time Dependent Gross-Pitaevskii Equation in Two Dimensions
We present a microscopic derivation of the defocusing two-dimensional cubic nonlinear Schr\"odinger equation as a mean field equation starting from an interacting $N$-particle system of Bosons. We consider the interactio... -
Derivation of the Time Dependent Two Dimensional Focusing NLS Equation
In this paper, we present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schr\"odinger equation starting from an interacting $N$-particle system of Bosons. The interaction potential we consider ... -
Detecting localized eigenstates of linear operators
(2017-11-30)We describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large. We define the family of functions $f_{\alpha}: \left\{1.2. ... -
Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas
(Communications in Mathematical Physics, 2014-06)We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the ... -
Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
(2017-11-30)We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure ... -
Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
Exponentially-localized Wannier functions (ELWFs) are a basis of the Fermi projection of a material consisting of functions which decay exponentially fast away from their maxima. When the material is insulating ... -
Existence of Spontaneous Pair Creation
A prove of the existence of spontaneous pair creation as an external field problem in second quantized Dirac theory. PHD Thesis -
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
(2017-04-23)We consider in this work stochastic differential equation (SDE) model for particles in contact with a heat bath when the memory effects are non-negligible. As a result of the fluctuation-dissipation theorem, the differential ... -
Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit
(Communications in Mathematical Physics, 2017-11)© 2017, Springer-Verlag GmbH Germany. The dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the model for coupling parameter g = 1 (i.e., not in the ...
