We consider a two-dimensional Lorentz gas with infinite horizon. This paradigmatic model consists of pointlike particles undergoing elastic collisions with fixed scatterers arranged on a periodic lattice. It was rigorously shown that when t→∞, the distribution of particles is Gaussian. However, the convergence to this limit is ultraslow, hence it is practically unattainable. Here, we obtain an analytical solution for the Lorentz gas' kinetics on physically relevant timescales, and find that the density in its far tails decays as a universal power law of exponent -3. We also show that the arrangement of scatterers is imprinted in the shape of the distribution.
We study, both analytically and numerically, the phenomenon of energy dissipation in single-domain ferromagnetic nanoparticles driven by an alternating magnetic field. Our interest is focused on the power loss resulting from the Landau-Lifshitz-Gilbert equation, which describes the precessional motion of the nanoparticle magnetic moment. We determine the power loss as a function of the field amplitude and frequency and analyze its dependence on different regimes of forced precession induced by circularly and linearly polarized magnetic fields. The conditions to maximize the nanoparticle heating are also analyzed.
We consider transport in two billiard models, the infinite horizon Lorentz gas and the stadium channel, presenting analytical results for the spreading packet of particles. We first obtain the cumulative distribution function of traveling times between collisions, which exhibits non-analytical behavior. Using a renewal assumption and the Lévy walk model, we obtain the particles' probability density. For the Lorentz gas, it shows a distinguished difference when compared with the known Gaussian propagator, as the latter is valid only for extremely long times. In particular, we show plumes of particles spreading along the infinite corridors, creating power-law tails of the density. We demonstrate the slow convergence rate via summation of independent identically distributed random variables on the border between Lévy and Gauss laws. The renewal assumption works well for the Lorentz gas with intermediately sized scattering centers, but fails for the stadium channel due to strong temporal correlations. Our analytical results are supported with numerical samplings. arXiv:1908.02053v2 [cond-mat.stat-mech]
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