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Statistical Mechanical Understanding of Two-Dimensional Point Vortex System at Negative Absolute Temperature

Statistical characteristics of two-dimensional point vortex systems in positive and negative temperature states are examined by massive numerical simulations using a special-purpose supercomputer, MDGRAPE-3. Mathematical description of the system is identical to that of a collection of charged rods, i.e., a guiding-center plasma. The characteristics of the negative temperature state is examined by a numerically obtained density of state, timeasymptotic equilibrium distributions and energy spectra at various values of temperature. The density of state has a peak and it is confirmed that the target point vortex system has the negative temperature state. In the negative temperature case, the equilibrium distribution has a dipolar structure while in the positive temperature case, the vortices spread uniformly inside the circular boundary. Slope of the energy (k−) spectrum in the intermediate k region becomes steep as energy increases.