Abstract: In this talk I will define and discuss some probability measures in infinite dimensions, which play an important role in (S)PDE, in Quantum Field Theory and for Bose-Einstein condensates. Th...
Abstract: A central topic in mathematical physics is the investigation of quantum systems subject to very short range potentials, virtually supported on a nite set of points. In this talk, after a pre...
Abstract: In 1978 Wannier discovered a Diophantine relation expressing the integrated density of states of a gapped group of bands of the Hofstadter Hamiltonian as a linear function of the magnetic fi...
Abstract: We consider a system of non-relativistic bosons interacting through a regular, positive potential vv with scattering length aa. We give a simple proof that the ground state energy density sa...
Abstract: We discuss the time-dependent Gross-Pitaevskii (GP) approximation for interacting bosons in the Thomas-Fermi (TF) regime, i.e., for a mean-field interaction potential with shrinking support ...
Abstract: I will present rigorous results on the effective properties of many-body systems consisting of multiple bosonic species. This will be based on joint works with A. Michelangeli and P.T. Nam. ...
In this course we will review recent work on the different upper bounds for the ground state energy of a gas of interacting bosons in the thermodynamic limit. We start by considering quasi-free states...
