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Derivation of Hartree’s theory for mean-field Bose gases

Mathieu Lewin (2013)

Journées Équations aux dérivées partielles

This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of N bosons with an interaction of intensity 1 / N (mean-field regime). In the limit N , we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation in these...

Diamagnetic behavior of sums Dirichlet eigenvalues

László Erdös, Michael Loss, Vitali Vougalter (2000)

Annales de l'institut Fourier

The Li-Yau semiclassical lower bound for the sum of the first N eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.

Diffusion Monte Carlo method: Numerical Analysis in a Simple Case

Mohamed El Makrini, Benjamin Jourdain, Tony Lelièvre (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove...

Dynamical entropy of a non-commutative version of the phase doubling

Johan Andries, Mieke De Cock (1998)

Banach Center Publications

A quantum dynamical system, mimicking the classical phase doubling map z z 2 on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.

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