Periodic Yukawa-potential Lorentz gas

Figure 11. Two trajectories of the periodic Yukawa-potential Lorentz gas. They start from the same position but have velocities that differ by one part in a million.

Figure 12. The diffusive modes of the periodic Yukawa-potential Lorentz gas represented by their cumulative function depicted in the complex plane ReFk,hnFk) for two different nonvanishing wavenumbers k. The horizontal straight line is the curve corresponding to the vanishing wavenumber k = 0 at which the mode reduces to the invariant microcanonical equilibrium state.

When applied to spatially extended dynamical systems, the PoUicott-Ruelle resonances give the dispersion relations of the hydrodynamic and kinetic modes of relaxation toward the equilibrium state. This can be illustrated in models of deterministic diffusion such as the multibaker map, the hard-disk Lorentz gas, or the Yukawa-potential Lorentz gas [1, 23]. These systems are spatially periodic. Their time evolution Frobenius-Perron operator... 

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