相关论文: Mean field theory and coherent structures for vort…
We develop a field theory for a partially filled Landau level based on composite fermions with a finite vortex core, whose mean-field states are exactly those described by well-tested trial wave functions. Despite non-orthogonality of free…
Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the…
We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of the velocity fields generated by the remaining point vortices.…
Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we make a first step in the generalization of the mean field theory in [Caglioti, Lions, Marchioro, Pulvirenti; Comm. Math. Phys.…
In the mean-field regime, the evolution of a gas of $N$ interacting particles is governed in first approximation by a Vlasov type equation with a self-induced force field. This equation is conservative and describes return to equilibrium…
Kinetic equations are derived from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for point vortex systems in an infinite plane. As the level of approximation for the Landau equation, the collision term of the kinetic equation…
We complete the literature on the statistical mechanics of point vortices in two-dimensional hydrodynamics. Using a maximum entropy principle, we determine the multi-species Boltzmann-Poisson equation and establish a form of virial theorem.…
On the basis of the lattice Boltzmann method we have done a numerical experiment of a forced turbulence in real space and time. Our new findings are summarized into two points. First in the analysis of the mean-field behavior of the…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
A family of spin-lattice models are derived as convergent finite dimensional approximations to the rest frame kinetic energy of a barotropic fluid coupled to a massive rotating sphere. In not fixing the angular momentum of the fluid…
This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…
Photons mediate long-range optomechanical forces between atoms in high finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second order phase…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our…
We study a class of deterministic mean field games and related optimal control problems, with a finite time horizon and in which the state space is a network. An agent controls her velocity, and, when she occupies a vertex, she can either…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
We consider the Mean Field limit of Gibbsian ensembles of 2-dimensional point vortices on the torus. It is a classical result that in such limit correlations functions converge to 1, that is, point vortices decorrelate: we compute the rate…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
The Onsager linear relations between macroscopic flows and thermodynamics forces are derived from the point of view of large deviation theory. For a given set of macroscopic variables, we consider the short-time evolution of…