Related papers: Nonlinear Elasticity from Atomistic Mechanics
We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover…
Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on…
In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data…
We present a general method based on nonlinear response theory to obtain effective interactions between ions in an electron gas which can also be applied to other systems where an adiabatic separation of time-scales is possible. Nonlinear…
This paper extends the application of the stochastic variational method to noncentral interactions. Several examples are presented for three- and four-nucleon systems with realistic nuclear forces. The correlated Gaussians easily cope with…
Using the nonrelativistic approximation in the curved-space Dirac equation, the analog of the Pauli equation is derived for a weak gravitational field with a gauge fixing condition related to the synchronous gauge, in the presence of an…
Parametric resonance can produce particles from oscillating scalar field, where an exponential growth of the particle number density can be developed. While it has been noticed that stimulated decay in Boltzmann equations exhibits similar…
A quasi classical approximation to quantum mechanical scattering in the Moeller formalism is developed. While keeping the numerical advantage of a standard Classical--Trajectory--Monte--Carlo calculation, our approach is no longer…
In this paper we, to our knowledge, for the first time obtain the rate equations for Zeeman coherences in the broad line approximation and steady-state balance equations directly from optical Bloch equations without the use of the…
The region very close to an electron ($r << r_0 = e^2/mc^2 \approx 2.8\times 10^{-13}$ cm) is, according to quantum electrodynamics, a seething maelstrom of virtual electron-positron pairs flashing in and out of existence. To take account…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
We derive a closed set of equations for the kinetics and non-equilibrium dynamics of interacting Luttinger Liquids with cubic resonant interactions. In the presence of these interactions, the Luttinger phonons become dressed but still well…
We consider discretizations of the Einstein action of general relativity such that the resulting discrete equations of motion form a consistent constrained system. Upon ``spin foam'' quantization of the system, consistency allows a natural…
A generalized formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies for atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions…
We describe several recent results obtained in collaboration with P. Gravejat, C. Hainzl, E. S\'er\'e and J.P. Solovej, concerning a nonlinear model for the relativistic quantum vacuum in interaction with a classical electromagnetic field.
It is widely believed that classical electromagnetism is either unphysical or inconsistent, owing to pathological behavior when self-force and radiation reaction are non-negligible. We argue that there is no inconsistency as long as it is…
In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general…
We study the nonlinear mean-field dynamics of molecule formation at coherent photo- and magneto-association of an atomic Bose-Einstein condensate for the case when the external field configuration is defined by the quasi-linear level…
A formally exact relation is derived which connects thermodynamically non-equilibrium evolution of gas density distribution after its arbitrary strong spatially non-uniform perturbation and evolution of many-particle correlations between…
An approach to correlated dynamics of quantum nuclei and electrons both in dynamical interaction with external environments is presented. This stochastic quantum molecular dynamics rests on a theorem that establishes a one-to-one…