| Contents |
| We study the problem of convergence to equilibrium for evolution equations associated to general
quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued
quadratic symbols. Under appropriate assumptions, a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven. Some applications to the study of chains of oscillators, to the generalized Langevin equation are given and to the analysis of Markov Chain Monte Carlo methods and of stochastic thermostasts for molecular dynamics simulations are given. |
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