Related papers: Nonlinear Elasticity from Atomistic Mechanics
Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schr\"odinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without…
A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle…
We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities…
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is…
We introduce a theory for the absorption of electromagnetic radiation by small metal particles, which generalises the random phase approximation by incorporating both electric and magnetic dipole absorption within a unified self-consistent…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…
In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
An overview of quantum-mechanical methods to generate cross-section data for electron collisions with atoms and molecules is presented. Particular emphasis is placed on the time-independent close-coupling approach, since it is particularly…
In this article, we addressed the numerical solution of a non-linear evolutionary variational inequality, which is encountered in the investigation of quasi-static contact problems. Our study encompasses both the semi-discrete and…
In these lecture notes I review the theory of the non--linear evolution of cosmological perturbations in a self--gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian…
We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending…
It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between…
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical (2nd-Piola) stress and elastic moduli…
A physically transparent and mathematically simple semiclassical model is employed to examine dynamics in the central-spin problem. The results reproduce a number of previous findings obtained by various quantum approaches and, at the same…
This paper studies the quantum Boltzmann Nordheim equation from a Boltzmann equation for Haldane statistics. Strong solutions are obtained for the Cauchy problem with initial data in L1 and uniformly bounded on a one (resp. two or…
We study the counterpart to the multi-photon down conversion in the quantised motion of a trapped atom. The Lamb-Dicke approximation leads to a divergence of the mean motional excitation in a finite interaction time for k-quantum down…
The non autonomous Cauchy problem for time dependent 1D point interactions is considered. The regularity assumptions for the coupling parameter are accurately analyzed and show that the general results for non autonomous linear evolution…
A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the…
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…