相关论文: Lekner summations and Ewald summations for quasi-t…

We study spin diffusion and spin waves in paramagnetic quantum crystals (solid He-3, for example) by direct simulation of a square lattice of atoms interacting via a nearest-neighbor Heisenberg exchange Hamiltonian. Recently, Cowan and…

In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 71-76], fast deterministic algorithms based on…

We study the unscreened Coulomb interaction in a one-dimensional electron system at low-energy. We use renormalization group methods and a GW approximation, in order to analyze the model. This yields both a strong wavefunction…

The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…

We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant…

An Ewald decomposition of the two-dimensional Yukawa potential and its derivative is presented for both the periodic and the free-space case. These modified Bessel functions of the second kind of zeroth and first degrees are used e.g. when…

We present results of Monte-Carlo simulations for finite 2D single and bilayer systems. Strong Coulomb correlations lead to arrangement of particles in configurations resembling a crystal lattice. For binary layers, there exists a…

A Monte Carlo computer simulation algorithm in classical phase space is given for the treatment of quantum systems. The non-commutativity of position and momentum is accounted for by a mean field approach and instantaneous effective…

A new Riemann solver is built to address numerical resolution of complex flow models. The research direction is closely linked to a variant of the Baer and Nunziato (1986) model developed in Saurel et al. (2017a). This recent model provides…

We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of quantum dots defined in a semiconductor two-dimensional electron gas system. Bands with energies above the lowest energy band…

In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The…

Quantum Monte Carlo methods are used to calculate various ground state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at $r_s\simeq…

Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and continues to attract significant international attention. This…

Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…

Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…

The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the…

The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the Monte-Carlo technique. A new melting criterion…

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…

Model reduction methods for bilinear control systems are compared by means of practical examples of Liouville-von Neumann and Fokker--Planck type. Methods based on balancing generalized system Gramians and on minimizing an H2-type cost…

Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…