AG Mathematische Physik, Anne van Grinsven (LMU): Mean-Field Approximation of the Ground State Energy of a Quasi-2D Bose Gas

Anne van Grinsven (LMU)

Mean-Field Approximation of the Ground State Energy of a Quasi-2D
Bose Gas

Abstract: We discuss a rigorous derivation of the mean-field
approximation for the ground state energy of a quasi-two-dimensional
Bose gas. This system consists of a trapped Bose gas with a potential
that is highly confining in one direction, leading to effective
two-dimensional behavior. Working in the mean-field regime, we consider
systems where particles interact weakly but frequently. The argument
builds on the method developed by Lewin, Nam and Rougerie for
three-dimensional trapped systems. The main focus is the adaptation of
this approach to account for the strong confinement and the associated
dimensional reduction. We conclude by commenting on possible extensions,
including the convergence of reduced density matrices and the
incorporation of dipole-dipole interactions.