Giuseppe Benfatto (Rome): One dimensional Fermi systems: rigorous results through renormalization group

After a short review on renormalization group analysis of many-body traslantion invariant states, I will discuss some rigorous results about the decay of correlations in weakly interacting one dimensional Fermi systems at small (up to zero) temperatures and their relation with the local gauge invariance of the interaction.

Pietro Caputo (Rome): On the energy gap above interface ground states of XXZ ferromagnets

We give estimates on the size of the energy gap above quantum interface ground states for spin-S anisotropic Heisenberg chains. The gap is shown to be of order S uniformly in the length of the chain. These results can be applied to diagonal interfaces in spin-S XXZ models. Here the low-lying excitations in a cylindrical region of linear size L are shown to be of order S/L². To prove our estimates we exploit a unitary map relating the quantum XXZ Hamiltonian to the Markov generator of an asymmetric exclusion process. In this way the original question is studied as a problem of relaxation to equilibrium for interacting particle systems and probabilistic reasoning naturally comes into play. This is joint work with Fabio Martinelli.

Pierluigi Contucci (Bologne): The ferromagnetic Heisenberg XXZ chain in a pinning field

The effect of a magnetic field supported at a single lattice site on the low-energy spectrum of the ferromagnetic Heisenberg XXZ chain is investigated for different boundary conditions, direction and strength of the magnetic field. This is joint work with B.Nachtergaele and W.Spitzer.

Tom Kennedy (Tucson & IHES): Quasi-particles and interfaces in quantum lattice systems

This talk will start with a review of results by several groups on quasi-particles and their spectrum in quantum lattice systems. Then the talk will focus on work by the speaker and N. Datta on the stability of the interface in anisotropic Heisenberg-like chains. The interface had been proven to be stable for the ferromagnetic anisotropic Heisenberg chain, and we show it is unstable for a wide class of highly anisotropic antiferromagnetic chains.

Jacques Magnen (Palaiseau): Interacting non-relativistic Fermions in three dimensions : a renormalization group approach

I will introduce a renormalization group approach to non-relativistic Fermions and explain its difficulties in three dimensions. I will explain how, at a given scale and weak coupling, one can resum all diagrams using a cluster expansion and the Hadamard inequality.

Bruno Nachtergaele (University of California at Davis): Interfaces and droplets in the XXZ Heisenberg model

In the first part of the talk I will review rigorous results on interface ground states and the low-lying excitations of the ferromagnetic XXZ Heisenberg model. In the second part I will discuss some recent results on the spectrum and dynamics of the XXZ chain perturbed by a localized external field.

Jakob Yngvason (Vienna): Superfluidity and Bose-Einstein condensation in dilute, trapped gases

The talk reviews recent work with E.H. Lieb and R. Seiringer on superfluidity and Bose-Einstein condensation in the ground state of a trapped Bose gase with a repulsive interaction in the Gross-Pitaevskii limit. This is the dilute limit where the particle number tends to infinity, while the ratio of the interaction energy per particle to the lowest excitation energy in the trap is kept constant.

Valentin A. Zagrebnov (Marseille): Conventional Bose-Einstein condensation in interacting continuous systems with a one-particle spectral gap

I shall discuss a proof of occurence of the conventional zero-mode Bose-Einstein Condensation (BEC) for a class of imperfect homogeneous boson systems with superstable interactions. This is an example of continuous Bose-system where the existence of the BEC in the presence of physically realistic particle interactions can be proved provided a gap in the one-particle excitations spectrum.