β Scribed by Ch. Gruber; Ph. Martin
No coin nor oath required. For personal study only.
It is shown that equilibrium states of classical systems of point particles are translation invariant whenever they have integrable clustering. Equilibrium states are defined by correlation functions obeying the BBGKY hierarchy. The result holds for two-body forces which may have locally integrable singularities as well as a long-range part including the Coulomb force. Under the same clustering assumptions, jellium systems (with uniform charged background) are also translation invariant in dimension greater than one.
π SIMILAR VOLUMES
Fluctuations in classical continuous systems are studied. In the low activity high temperature regime for these fluctuations a central limit theorem is proven and the space of macroscopic fluctuations is constructed. Furthermore, it is shown that the generator of the microscopic stochastic dynamics
Attempts are made to construct exact invariants for a variety of time-dependent classical dynamical systems in three dimensions. We make use of the dynamical algebraic method for this purpose and explore several new systems admitting the invariants. In particular, systems involving both momentum and