66 research outputs found
On the selection of the classical limit for potentials with BV derivatives
We consider the classical limit of the quantum evolution, with some rough
potential, of wave packets concentrated near singular trajectories of the
underlying dynamics. We prove that under appropriate conditions, even in the
case of BV vector fields, the correct classical limit can be selected
Mean-field evolution of fermions with singular interaction
We consider a system of N fermions in the mean-field regime interacting
though an inverse power law potential , for
. We prove the convergence of a solution of the many-body
Schr\"{o}dinger equation to a solution of the time-dependent Hartree-Fock
equation in the sense of reduced density matrices. We stress the dependence on
the singularity of the potential in the regularity of the initial data. The
proof is an adaptation of [22], where the case is treated.Comment: 16 page
Higher-order nonlinear electron-acoustic solitary excitations in partially degenerate quantum electron-ion plasmas
Propagation of dressed solitary excitations are studied in a partially
degenerate quantum plasma in the framework of quantum-hydrodynamics (QHD) model
using multiple scales technique. The evolution equation together with a linear
inhomogeneous differential equation is solved using Kodama-Taniuti
renormalizing technique. It is shown that the type of solitary excitations
(bright or dark) is defined by two critical plasma parameter values.Comment: To appear in Indian Journal of Physic
Time scales and exponential trends to equilibrium: Gaussian model problems
We review results on the exponential convergence of multi- dimensional Ornstein-Uhlenbeck processes and discuss related notions of characteristic timescales with concrete model systems. We focus, on the one hand, on exit time distributions and provide ecplicit expressions for the exponential rate of the distribution in the small noise limit. On the other hand, we consider relaxation timescales of the process to its equi- librium measured in terms of relative entropy and discuss the connection with exit probabilities. Along these lines, we study examples which il- lustrate specific properties of the relaxation and discuss the possibility of deriving a simulation-based, empirical definition of slow and fast de- grees of freedom which builds upon a partitioning of the relative entropy functional in conjuction with the observed relaxation behaviour
Using perturbed underdamped langevin dynamics to efficiently sample from probability distributions
In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics. We show that appropriate choices of the perturbations can lead to samplers that have improved properties, at least in terms of reducing the asymptotic variance. We present a detailed analysis of the new Langevin sampler for Gaussian target distributions. Our theoretical results are supported by numerical experiments with non-Gaussian target measures
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