Browsing by Author "Pickl, P"
Now showing items 117 of 17

A Mean Field Limit for the Vlasov–Poisson System
Lazarovici, D; Pickl, P (Archive for Rational Mechanics and Analysis, 201709)© 2017, SpringerVerlag Berlin Heidelberg. We present a probabilistic proof of the mean field limit and propagation of chaos Nparticle systems in three dimensions with positive (Coulomb) or negative (Newton) 1/r potentials ... 
A New Method and a New Scaling for Deriving Fermionic MeanField Dynamics
Petrat, S; Pickl, P (Mathematical Physics, Analysis and Geometry, 201603)© 2016, The Author(s). We introduce a new method for deriving the timedependent Hartree or HartreeFock equations as an effective meanfield dynamics from the microscopic Schrödinger equation for fermionic manyparticle ... 
A Simple Derivation of Mean Field Limits for Quantum Systems
Pickl, P (Letters in Mathematical Physics, 201108)We shall present a new strategy for handling mean field limits of quantum mechanical systems. The new method is simple and effective. It is simple, because it translates the idea behind the meanfield description of a many ... 
Bogoliubov corrections and trace norm convergence for the Hartree dynamics
Mitrouskas, D; Petrat, S; Pickl, PWe 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 ... 
Derivation of the Bogoliubov Time Evolution for Gases with Finite Speed of Sound
Petrat, S; Pickl, P; Soffer, AThe derivation of meanfield 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 MaxwellSchrödinger Equations from the PauliFierz Hamiltonian
Leopold, N; Pickl, PWe consider the spinless PauliFierz Hamiltonian which describes a quantum system of nonrelativistic identical particles coupled to the quantized electromagnetic field. We study the time evolution in a meanfield limit ... 
Derivation of the Time Dependent GrossPitaevskii Equation Without Positivity Condition on the Interaction
Pickl, P (Journal of Statistical Physics, 201007)Using a new method (Pickl in A simple derivation of mean field limits for quantum systems, 2010) it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without ... 
Derivation of the time dependent Gross–Pitaevskii equation with external fields
Pickl, P (Reviews in Mathematical Physics, 201502)© 2015 World Scientific Publishing Company. Using a new method [19], it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without using BBGKY hierarchies. ... 
Derivation of the Time Dependent Two Dimensional Focusing NLS Equation
Jeblick, M; Pickl, PIn this paper, we present a microscopic derivation of the twodimensional focusing cubic nonlinear Schr\"odinger equation starting from an interacting $N$particle system of Bosons. The interaction potential we consider ... 
Dynamics of sound waves in an interacting Bose gas
Deckert, DA; Fröhlich, J; Pickl, P; Pizzo, A (Advances in Mathematics, 201604)© 2016 Elsevier Inc. We consider a nonrelativistic quantum gas of N bosonic atoms confined to a box of volume Λ in physical space. The atoms interact with each other through a pair potential whose strength is inversely ... 
Effective dynamics of a tracer particle in a dense homogeneous quantum gas
Jeblick, M; Mitrouskas, D; Petrat, S; Pickl, PWe investigate the mean field regime of the dynamics of a tracer particle in a homogenous quantum gas. For a bosonic gas, we show that this regime is constrained by the well known requirement of an appropriate mean field ... 
Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas
Deckert, DA; Fröhlich, J; Pickl, P; Pizzo, A (Communications in Mathematical Physics, 201406)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 ... 
Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the HighDensity Limit
Jeblick, M; Mitrouskas, D; Petrat, S; Pickl, P (Communications in Mathematical Physics, 201711)© 2017, SpringerVerlag 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 ... 
Kinetic energy estimates for the accuracy of the timedependent Hartree–Fock approximation with Coulomb interaction
Bach, V; Breteaux, S; Petrat, S; Pickl, P; Tzaneteas, T (Journal de Mathématiques Pures et Appliquées, 201601)© 2015 The Authors. We study the time evolution of a system of N spinless fermions in R3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's ... 
On Mean Field Limits for Dynamical Systems
Boers, N; Pickl, P (Journal of Statistical Physics, 201607)© 2015, Springer Science+Business Media New York. We present a purely probabilistic proof of propagation of molecular chaos for Nparticle systems in dimension 3 with interaction forces scaling like 1 /  q 3 λ  1 with ... 
On the meanfield limit for the VlasovPoissonFokkerPlanck system
Huang, H; Liu, JG; Pickl, PWe devise and study a random particle blob method for approximating the VlasovPoissonFokkkerPlanck (VPFP) equations by a $N$particle system subject to the Brownian motion in $\mathbb{R}^3$ space. More precisely, we show ... 
Spontaneous Pair Creation Revisited
Pickl, P; Duerr, DRecently the so called Spontaneous Pair Creation of electron positron pairs in a strong external field has been rigorously established. We give here the heuristic core of the proof, since the results differ from those given ...