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. ...
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 ...
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...
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: 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: 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...
We consider lattice approximations of the Allen-Cahn equation on the torus perturbed by small space-time white noise and discuss metastable transition times between the two stable phases....
We consider an arbitrary family of stochastically ordered distribution functions dependent on parameters from an interval in the real line. We compare distribution functions and moments of random vari...
After the brilliant result of Papanicolau and Varadhan (1979) in the case of bounded stationary and ergodic environments, there has been a recent upsurge in the research of quenched homogenization in ...
Group testing has its origins in the identication of syphilis in the US army during World War II. It is a useful method that has broad applications in medicine, engineering, and even in airport securi...
We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations principle for the (k-layer, enhanced) empirical measure of we...
