IRREVERSIBLE EVOLUTION TOWARDS EQUILIBRIUM OF COUPLED QUANTUM HARMONIC-OSCILLATORS - A COARSE-GRAINED APPROACH

The dynamics of an integrable linear set of a very great number N (10( 2) to 10(5)) of quantum harmonic oscillators coupled linearly in the r otating wave approximation and subject to the initial condition that o nly one oscillator is in an excited coherent state whereas the other o nes are in the ground state, is numerically studied in the framework o f a coarse grained approach. It appears that the coarse grained statis tical entropy of this integrable system increases during a certain tim e characteristic of the system, and then fluctuates around some consta nt average value which depends on the energy cell width DELTAepsilon o f the analysis. Then, a study of the energy distribution of the oscill ators inside these energy cells shows that this distribution is expone ntially decreasing as for ergodic systems. The Boltzmann-like paramete r B of the exponential distribution is found to fluctuate around a con stant value that is inversely proportional to the initial excitation e nergy. Again, the relative fluctuations of the B parameter of this mic rocanonical system, appear to be inversely proportional to the square root of N, as for a canonical ensemble. All properties for this system are those of a statistical equilibrium.