Speaker:  山口 義幸 (京大情報学研究科)

Date and time: Jan.1st, 16:30-

Place: 5号館４１３号室

Title:Statistical mechanics and dynamics of long-range Hamiltonian systems

Abstract:

Long-range Hamiltonian systems consist of two-body interactions which decay algebraically at a faraway with a sufficiently small exponent. They are ubiquitous in nature: self-gravitating systems, plasmas, two-dimensional Euler fluids, certain spin systems, and so on. The long-range nature implies non-additivity, as a result, the standard statistical mechanics is not always guaranteed. Nevertheless, canonical ensemble works well in many cases and the free energy is universal because the mean-field free energy is shared. It is not the end of studies however and dynamics reveals further anomalies; An initial state does not relax to thermal equilibrium in the thermodynamic limit, and critical exponents to response take non-mean-field values. We review long-range Hamiltonian systems with highlighting mechanism of anomalies.