This paper reviews recent experimental and theoretical progress concerning many-body
phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling …

From a theoretical point of view, we discuss a variety of phenomena linked to the spin and
polarization degree of freedom of exciton-polaritons in semiconductor microcavities. We start …

We calculate the energy of one-and two-dimensional weakly interacting Bose-Bose mixtures
analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo …

The mathematical study of the Bose gas goes back to the? rst quarter of the twentieth
century, with the invention of quantum mechanics. The name refers to the Indian physicist …

On June 19th 1999, the European Ministers of Education signed the Bologna Declaration,
with which they agreed that the European university education should be uniformized …

This paper summarizes the experimental frontier of ultracold fermionic gases. It is based on
three lectures which one of the authors gave at the Varenna Summer School describing the …

We present an extension of the well-known Bogoliubov theory to treat low-dimensional
degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use …

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-
Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body …

The weakly interacting Bose gas in two dimensions is considered in the dilute limit n 1/2 a≪
1, where n is the particle density and a is the range of the potential. The standard many-body …

We derive exact general relations between various observables for N spin-1/2 fermions with
zero-range or short-range interactions, in continuous space or on a lattice, in two or three …