Dynamical order in chaotic Hamiltonian system with many degrees of freedom
Tetsuro Konishir
Abstract
Classical
systems, when left isolated for long time, are believed to relax to simple
stationary state, which is called thermal equilibrium. Once we know that the
system is in thermal equilibrium (mostly coupled with another large
system called heat bath), we can
analyze the system using various methods of statistical mechanics. Although many systems are well described
by statistical mechanics, there also exist many systems
which do not monotonously relax to equilibrium. Some systems show anomalous diffusion,
some systems stick
to initial condition for long time, some show interesting order formation as transient behavior, and so on.
We show several examples of such anomalous behavior
and investigate their dynamical origins. This anomalous behavior
is generated by its own dynamics of each system driven by the Hamiltonian
itself, not caused by external force or dissipation. In other words, they
produce structure or order through chaotic dynamics. Systems to be introduced includes Hamiltonian
Mean Field (HMF) model and one-dimensional self-gravitating system.