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- W2950061342 abstract "We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear Schrodinger equation with a focusing nonlinearity of order $p<6$. Key properties of these Gibbs measures, in particular absence of phase transitions and regularity properties of field samples, are established. We then study a time evolution of this system given by the Hamiltonian evolution perturbed by a stochastic noise term that mimics effects of coupling the system to a heat bath at some fixed temperature. The noise is of Ornstein-Uhlenbeck type for the Fourier modes of the field, with the strength of the noise decaying to zero, as the frequency of the mode tends to $infty$. We prove exponential approach of the state of the system to a grand-canonical Gibbs measure at a temperature and chemical potential determined by the stochastic noise term." @default.
- W2950061342 created "2019-06-27" @default.
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- W2950061342 date "2014-09-08" @default.
- W2950061342 modified "2023-09-27" @default.
- W2950061342 title "Exponential Relaxation to Equilibrium for a One-Dimensional Focusing Non-Linear Schrodinger Equation with Noise" @default.
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