2012/03/30 by Yevgeny Krivolapov, Shmuel Fishman · 7 citations
Computer Science · Mathematics · Physics and Astronomy · #Anomalous diffusion #Fourier transform #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Renormalization group #Scaling #Spectral density #Statistical physics #Statistics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.86.030103
published in Physical Review E 86(3), 030103 (American Physical Society) · 5 pages, 3 figures
arxiv created 2012/03/30 · openalex publication_date 2012/09/24 · arxiv updated 2013/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small velocities uniform acceleration takes place, and at a later stage fluctuations of the potential are encountered, resulting in a regime of anomalous diffusion. This regime was studied in the framework of the Fokker-Planck approximation. The diffusion coefficient in velocity was expressed in terms of the average power spectral density, which is the Fourier transform of the potential correlation function. This enabled to establish a scaling form for the Fokker-Planck equation and to compute the large and small velocity limits of the diffusion coefficient. A classification of the random potentials into universality classes, characterized by the form of the diffusion coefficient in the limit of large and small velocity, was performed. It was shown that one-dimensional systems exhibit a large variety of universality classes, contrary to systems in higher dimensions, where only one universality class is possible. The relation to Chirikov resonances, which are central in the theory of chaos, was demonstrated. The general theory was applied and numerically tested for specific physically relevant examples.