Titlebook: Macroscopic Limits of Quantum Systems; Munich, Germany, Mar Daniela Cadamuro,Maximilian Duell,Sergio Simonella Conference proceedings 2018

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Etymology

Effective Dynamics of Two Tracer Particles Coupled to a Fermi Gas in the High-Density Limit,ed to a dense and homogeneous ideal Fermi gas in two spatial dimensions. In that paper, closeness of the time evolution to an effective . dynamics for . of the gas was proven. The main point of interest of this result was to consider coupling constants that do not scale with the density of the gas.

繁殖

Mean-Field Evolution of Fermions with Singular Interaction, solution of the many-body Schrödinger equation to a solution of the time-dependent Hartree–Fock equation in the sense of reduced density matrices, for a specific class of initial data, namely translation-invariant states. We stress the dependence on the singularity of the potential in the regularit

GULLY

Recent Advances in the Theory of Bogoliubov Hamiltonians, natural way as an approximation to the full many-body problem. In this note, we would like to give an overview of recent advances in the study of bosonic quadratic Hamiltonians. In particular, we relate the reported results to what can be called the time-dependent diagonalization problem.

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Peculate

Blow-Up Profile of Rotating 2D Focusing Bose Gases,hich rotates at a fixed speed of rotation .. First, we study the behavior of the ground state when the coupling constant approaches ., the critical strength of the cubic nonlinearity for the focusing nonlinear Schrödinger equation. We prove that blow-up always happens at the center of the trap, with

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,Gross–Pitaevskii Evolution for Bose–Einstein Condensates,r the time evolution of initially trapped Bose–Einstein condensates, in a scaling limit where the interaction has a small scattering length. We show that the condensation is preserved by the many-body dynamics and that the evolution of the condensate wave function is governed by the nonlinear Gross–

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