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Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball II: the 3d case

Jean Bourgain, Aynur Bulut (2014)

Journal of the European Mathematical Society

We extend the convergence method introduced in our works [8–10] for almost sure global well-posedness of Gibbs measure evolutions of the nonlinear Schrödinger (NLS) and nonlinear wave (NLW) equations on the unit ball in d to the case of the three dimensional NLS. This is the first probabilistic global well-posedness result for NLS with supercritical data on the unit ball in 3 . The initial data is taken as a Gaussian random process lying in the support of the Gibbs measure associated to the equation,...

Asymptotic Feynman–Kac formulae for large symmetrised systems of random walks

Stefan Adams, Tony Dorlas (2008)

Annales de l'I.H.P. Probabilités et statistiques

We study large deviations principles for N random processes on the lattice ℤd with finite time horizon [0, β] under a symmetrised measure where all initial and terminal points are uniformly averaged over random permutations. That is, given a permutation σ of N elements and a vector (x1, …, xN) of N initial points we let the random processes terminate in the points (xσ(1), …, xσ(N)) and then sum over all possible permutations and initial points, weighted with an initial distribution. We prove level-two...

Computer simulation of the atomic behaviour in condensed phases.

Antoni Giró Roca, Joan Angel Padró (1987)


Molecular dynamics simulation method for the study of condensed phases of matter is described in this paper. Computer programs for the simulation of atomic motion have been developed. Time-saving techniques, like the cellular method have been incorporated in order to optimize the available computer resources. We have applied this method to the simulation of Argon near its melting point. Differences in the structure, thermodynamic properties and time correlation functions of solid and liquid phases...

From Planck to Ramanujan : a quantum 1 / f noise in equilibrium

Michel Planat (2002)

Journal de théorie des nombres de Bordeaux

We describe a new model of massless thermal bosons which predicts an hyperbolic fluctuation spectrum at low frequencies. It is found that the partition function per mode is the Euler generating function for unrestricted partitions p ( n ). Thermodynamical quantities carry a strong arithmetical structure : they are given by series with Fourier coefficients equal to summatory functions σ k ( n ) of the power of divisors, with k = - 1 for the free energy, k = 0 for the number of particles and k = 1 for the internal energy. Low...

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