Displaying similar documents to “Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups”

Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics

Othmar Koch, Christof Neuhauser, Mechthild Thalhammer (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for exponential operator splitting methods of (nonstiff) order applied to the multi-configuration...

The continuous Coupled Cluster formulation for the electronic Schrödinger equation

Thorsten Rohwedder (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the . Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis to obtain existence and uniqueness...

Discrete time markovian agents interacting through a potential

Amarjit Budhiraja, Pierre Del Moral, Sylvain Rubenthaler (2013)

ESAIM: Probability and Statistics

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A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the ‘gradient’ of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active...

Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift

David J. Knezevic, Endre Süli (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential that is equal to +∞ along the boundary ∂ of the computational domain . Using...

Discrete Spectrum of the Periodic Schrödinger Operator with a Variable Metric Perturbed by a Nonnegative Potential

M. Sh. Birman, V. A. Sloushch (2010)

Mathematical Modelling of Natural Phenomena

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We study discrete spectrum in spectral gaps of an elliptic periodic second order differential operator in (ℝ) perturbed by a decaying potential. It is assumed that a perturbation is nonnegative and has a power-like behavior at infinity. We find asymptotics in the large coupling constant limit for the number of eigenvalues of the perturbed operator that have crossed a given point inside the gap or the edge of the gap. The...

The mixed regularity of electronic wave functions multiplied by explicit correlation factors

Harry Yserentant (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The electronic Schrödinger equation describes the motion of electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3 variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, 2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons, the decay behavior...