相关论文: Mean field theory and coherent structures for vort…
We derive an equilibrium statistical theory for the macroscopic description of a ferromagnetic material at positive finite temperatures. Our formulation describes the most-probable equilibrium macrostates that yield a coherent deterministic…
We prove some improved estimates for the Ginzburg-Landau energy (with or without magnetic field) in two dimensions, relating the asymptotic energy of an arbitrary configuration to its vortices and their degrees, with possibly unbounded…
This course explains how the usual mean field evolution partial differential equations (PDEs) in Statistical Physics - such as the Vlasov-Poisson system, the vorticity formulation of the two-dimensional Euler equation for incompressible…
The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous…
This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is…
Rigorous bounds on the rate of energy exchanges between vibrational and translational degrees of freedom are established in simple classical models of diatomic molecules. The results are in agreement with an elementary approximation…
Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
We propose a mean field (MF) theory for a homogeneously driven granular gas of inelastic particles with Coulomb friction. The model contains three parameters, a normal restitution coefficient $r_n$, a maximum tangential restitution…
A stochastic theory is presented for a quantum vortex that is expected to occur in superfluids coated on two dimensional sphere $ {\rm S}^2 $. The starting point is the canonical equation of motion (the Kirchhoff equation) for a point…
Starting from the Liouville equation, we derive the exact hierarchy of equations satisfied by the reduced distribution functions of the single species point vortex gas in two dimensions. Considering an expansion of the solution in powers of…
We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…
The quantum theory of near horizon regions of spacetimes with classical spatially flat, homogeneous and isotropic Friedman-Robertson-Walker geometry can be approximately described by a two dimensional conformal field theory. The central…
The Onsager rule determines the frequencies of quantum oscillations in magnetic fields. We show that this rule remains intact to an excellent approximation in the mixed-vortex state of the underdoped cuprates even though the Landau level…
This work extends the theory presented in Mean Field Games with a Dominating Player by Bensoussan, Chau and Yam on mean field games with a dominating player, to the case in which the utility and cost functions depend not only on the law of…
We consider the error arising from the approximation of an N-particle dynamics with its description in terms of a one-particle kinetic equation. We estimate the distance between the j-marginal of the system and the factorized state,…
An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of…
The paper shows that inhomogeneity of translation properties of condensate leads to the interaction of local order parameter (OP) and its compensating field which is similar to gauge fields in the field theory. Dynamic models were…
Starting from the Liouville equation, and using a BBGKY-like hierarchy, we derive a kinetic equation for the point vortex gas in two-dimensional (2D) hydrodynamics, taking two-body correlations and collective effects into account. This…
We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy between the joint law of the particle system and the…