On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet...
On the dimer problem and the Ising problem in finite 3-dimensional lattices.
On the distribution of free path lengths for the periodic Lorentz gas II
On the distribution of free path lengths for the periodic Lorentz gas II
Consider the domain and let the free path length be defined as In the Boltzmann-Grad scaling corresponding to , it is shown that the limiting distribution of is bounded from below by an expression of the form C/t, for some C> 0. A numerical study seems to indicate that asymptotically for large t, . This is an extension of a previous work [J. Bourgain et al., Comm. Math. Phys.190 (1998) 491-508]. As a consequence, it is proved that the linear Boltzmann type transport equation is inappropriate...
On the distribution of the free path length of the linear flow in a honeycomb
Consider the region obtained by removing from the discs of radius , centered at the points of integer coordinates with . We are interested in the distribution of the free path length (exit time) of a point particle, moving from along a linear trajectory of direction , as . For every integer number , we prove the weak convergence of the probability measures associated with the random variables , explicitly computing the limiting distribution. For , respectively , this result leads...
On the distributional solution of the inverse problem induced by the heat kernel method.
On the domination of a random walk on a discrete cylinder by random interlacements.
On the double critical-state model for type-II superconductivity in 3D
In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...
On the doubly refined enumeration of alternating sign matrices and totally symmetric self-complementary plane partitions.
On the dynamics of Bose-Einstein condensation
On the equilibria of the extended nematic polymers under elongational flow.
On the exact solution of a generalized Pólya process.
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
On the free energy of a Gaussian disordered mean field model.
On the Gaussian random matrix ensembles with additional symmetry conditions.
On the geometry and dynamics of crystalline continua
On the Ginzburg-Landau and related equations
We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture of the vortex...
On the Ginzburg-Landau energy with weight
On the Ginzburg–Landau model of a superconducting ball in a uniform field