In the mean field approximation, we evaluate the temperature dependence of the anchoring energy strength of a nematic liquid crystal in contact with a solid substrate due to thermal fluctuations. Our study is limited to the weak anchoring case, where the microscopic surface energy is small with respect to the mean field energy due to the nematic phase. We assume furthermore that the physical pr...

In this paper, we study the low temperature limit of the spherical Crisanti-Sommers variational problem. We identify the Γ-limit of the Crisanti-Sommers functionals, thereby establishing a rigorous variational problem for the ground state energy of spherical mixed p-spin glasses. As an application, we compute moderate deviations of the corresponding minimizers in the low temperature limit. In p...

We review the application of zero-temperature, mean-field theory to current experimental atomic Bose-Einstein condensates. We assess the validity of the approximations made by comparing the mean-field results with a variety of experimental data.

We calculate the nonequilibrium mean-field "temperature" of a brownian system in contact with a heat bath. We consider two different cases: an equilibrium bath in the presence of strong external forces, and a nonequilibrium bath. By proving the existence of a generalized fluctuation-dissipation relation, this mean-field "temperature" can be used to describe a nonequilibrium system as is if it w...