Now showing items 1-17 of 17

    • A Mean Field Limit for the Vlasov–Poisson System 

      Lazarovici, D; Pickl, P (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 New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics 

      Petrat, S; Pickl, P (Mathematical Physics, Analysis and Geometry, 2016-03)
      © 2016, The Author(s). We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle ...
    • A Simple Derivation of Mean Field Limits for Quantum Systems 

      Pickl, P (Letters in Mathematical Physics, 2011-08)
      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 mean-field description of a many ...
    • Bogoliubov corrections and trace norm convergence for the Hartree dynamics 

      Mitrouskas, D; Petrat, S; Pickl, P
      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 ...
    • Derivation of the Bogoliubov Time Evolution for Gases with Finite Speed of Sound 

      Petrat, S; Pickl, P; Soffer, A
      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 

      Leopold, N; Pickl, P
      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 Without Positivity Condition on the Interaction 

      Pickl, P (Journal of Statistical Physics, 2010-07)
      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, 2015-02)
      © 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, P
      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 ...
    • Dynamics of sound waves in an interacting Bose gas 

      Deckert, DA; Fröhlich, J; Pickl, P; Pizzo, A (Advances in Mathematics, 2016-04)
      © 2016 Elsevier Inc. We consider a non-relativistic 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, P
      We 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, 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 ...
    • Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit 

      Jeblick, M; Mitrouskas, D; Petrat, S; Pickl, P (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 ...
    • Kinetic energy estimates for the accuracy of the time-dependent Hartree–Fock approximation with Coulomb interaction 

      Bach, V; Breteaux, S; Petrat, S; Pickl, P; Tzaneteas, T (Journal de Mathématiques Pures et Appliquées, 2016-01)
      © 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, 2016-07)
      © 2015, Springer Science+Business Media New York. We present a purely probabilistic proof of propagation of molecular chaos for N-particle systems in dimension 3 with interaction forces scaling like 1 / | q| 3 λ - 1 with ...
    • On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system 

      Huang, H; Liu, JG; Pickl, P
      We devise and study a random particle blob method for approximating the Vlasov-Poisson-Fokkker-Planck (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, D
      Recently 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 ...