Browsing by Author "Mitrouskas, D"

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Open Access
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 field Hartree state, we introduce an auxiliary Hamiltonian on the N-particle space that is very similar to the one obtained from Bogoliubov theory. We show convergence of the auxiliary time evolution to the fully interacting dynamics in the norm of the N-particle space. This result allows us to prove several other results: convergence of reduced density matrices in trace norm with optimal rate, convergence in energy trace norm, and convergence to a time evolution obtained from the Bogoliubov Hamiltonian on Fock space with expected optimal rate. We thus extend and quantify several previous results, e.g., by providing the physically important convergence rates, including time-dependent external fields and singular interactions, and allowing for general initial states, e.g., those that are expected to be ground states of interacting systems.
Open Access
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 scaling of the interaction. For fermions, however, we find an important qualitative difference. Not only are fermions much more homogeneously distributed than bosons but also deviations from the mean are due only to fast degrees of freedom in the gas. This observation leads to an explanation of why a tracer particle behaves freely in the dense homogeneous fermion gas despite of a non-scaled interaction, i.e., despite of non-vanishing statistical fluctuations. Finally, we indicate how the gained insight can be rigorously justified.
Open Access
Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit
(Communications in Mathematical Physics, 2017-11) Jeblick, M; Mitrouskas, D; Petrat, S; Pickl, P
© 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 weak coupling regime), and prove closeness of the time evolution to an effective dynamics for large densities of the gas and for long time scales of the order of some power of the density. The effective dynamics is generated by the free Hamiltonian with a large but constant energy shift which is given at leading order by the spatially homogeneous mean field potential of the gas particles. Here, the mean field approximation turns out to be accurate although the fluctuations of the potential around its mean value can be arbitrarily large. Our result is in contrast to a dense bosonic gas in which the free motion of a tracer particle would be disturbed already on a very short time scale. The proof is based on the use of strong phase cancellations in the deviations of the microscopic dynamics from the mean field time evolution.