7 J an 2 00 4 Relaxation to a Perpetually Pulsating Equilibrium
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چکیده
Paper in honour of Freeman Dyson on the occasion of his 80th birthday. Normal N-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2kT , but, when inter-particle forces are an inverse cubic repulsion together with a linear (simple harmonic) attraction, the system pulsates for ever. In spite of this pulsation in scale, r(t), other degrees of freedom relax to an ever-changing Maxwellian distribution. With a new time, τ , defined so that r 2 d/dt = d/dτ it is shown that the remaining degrees of freedom evolve with an unchanging reduced Hamiltonian. The distribution predicted by equilibrium statistical mechanics applied to the reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature pulsates like r −2. Numerical simulation with 1000 particles demonstrate a rapid relaxation to this pulsating equilibrium .
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تاریخ انتشار 2004