Phase transitions in the Interacting Boson Fermion Model: the gamma-unstable case

The phase transition around the critical point in the evolution from spherical to deformed gamma-unstable shapes is investigated in odd nuclei within the Interacting Boson Fermion Model. We consider the particular case of an odd j=3/2 particle coupled to an even-even boson core that undergoes a transition from spherical U(5) to gamma-unstable O(6) situation. The particular choice of the j=3/2 orbital preserves in the odd case the condition of gamma-instability of the system. As a consequence, energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviours qualitatively similar to those of the even core. The results are also in qualitative agreement with the recently proposed E(5/4) model, although few differences are present, due to the different nature of the two schemes.Comment: In press in PRC as rapid communication. 7 pages, 4 figure

Cross-Dimensional relaxation in Bose-Fermi mixtures

We consider the equilibration rate for fermions in Bose-Fermi mixtures undergoing cross-dimensional rethermalization. Classical Monte Carlo simulations of the relaxation process are performed over a wide range of parameters, focusing on the effects of the mass difference between species and the degree of initial departure from equilibrium. A simple analysis based on Enskog's equation is developed and shown to be accurate over a variety of different parameter regimes. This allows predictions for mixtures of commonly used alkali atoms.Comment: 7 pages, 4 figures, uses Revtex 4. This is a companion paper to [PRA 70, 021601(R) (2004)] (cond-mat/0405419

Interacting Particles and Strings in Path and Surface Representations

Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a Kalb-Ramond field in four dimensions, the topological interaction of two particles due to a BF term in 2+1 dimensions, and the string-particle interaction mediated by a BF term in 3+1 dimensions. In the first case one finds that a consistent "surface-representation" can be built provided that the coupling constant is quantized. The geometrical setting that arises corresponds to a generalized version of the Faraday's lines picture: quantum states are labeled by the shape of the string, from which emanate "Faraday`s surfaces". In the other models, the topological interaction can also be described by geometrical means. It is shown that the open-path (or open-surface) dependence carried by the wave functional in these models can be eliminated through an unitary transformation, except by a remaining dependence on the boundary of the path (or surface). These feature is closely related to the presence of anomalous statistics in the 2+1 model, and to a generalized "anyonic behavior" of the string in the other case.Comment: RevTeX 4, 28 page

Proximal methods for stationary mean field games with local couplings

© 2018 Society for Industrial and Applied Mathematics. We address the numerical approximation of mean field games with local couplings. For power-like Hamiltonians, we consider a stationary system and also a system involving density constraints modeling hard congestion effects. For finite difference discretization of the mean field game system developed in [Y. Achdou and I. Capuzzo-Dolcetta, SIAM J. Numer. Anal., 48 (2010), pp. 1136-1162], we follow a variational approach. We prove that the aforementioned schemes can be obtained as the optimality system of suitably defined optimization problems. In order to prove the existence of solutions of the scheme with a variational argument, monotonicity assumptions on the coupling term are not needed, which allows us to recover general existence results proved by Achdou and Capuzzo-Dolcetta. Next, assuming that the coupling term is nondecreasing, the variational problem is cast as a convex optimization problem, for which we study and compare several proximal-type methods. These algorithms have several interesting features, such as global convergence and stability with respect to the viscosity parameter, which can eventually be zero. We assess the performance of the methods via numerical experiments