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### Cite Details

Luis M. A. Bettencourt and C. Wetterich, "Time evolution of correlation functions for classical and quantum anharmonic oscillators", hep-ph/9805360, 1998

### Abstract

The time evolution of the correlation functions of an ensemble of anharmonic N-component oscillators with $O(N)$ symmetry is described by a flow equation, exact up to corrections of order $1/N^2$. We find effective irreversibility. Nevertheless, analytical and numerical investigation reveals that the system does not reach thermal equilibrium for large times, even when $N\rightarrow \infty$. Depending on the initial distribution, the dynamics is asymptotically stable or it exhibits growing modes which break the conditions for the validity of the 1/N expansion for large time. We investigate both classical and quantum systems, the latter being the limit of an O(N) symmetric scalar quantum field theory in zero spatial dimensions.

### BibTeX Entry

@article{bettencourt-1998-time,
author = {Luis M. A. Bettencourt and C. Wetterich},
title = {Time evolution of correlation functions for classical and quantum anharmonic oscillators},
year = {1998},
journal = {hep-ph/9805360}
}