Intermediate dynamics between Newton and Langevin

Abstract

A dynamics between Newton and Langevin formalisms is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding a vanishing zero-frequency friction the corresponding non-Markovian Brownian dynamics exhibits anomalous behavior which is characterized by ballistic diffusion and accelerated transport. We also investigate the role of a possible initial correlation between the system degrees of freedom and the heat-bath degrees of freedom for the asymptotic long-time behavior of the system dynamics. As two test beds we investigate (i) the anomalous energy relaxation of free non-Markovian Brownian motion that is driven by a harmonic velocity noise and (ii) the phenomenon of a net directed acceleration in noise-induced transport of an inertial rocking Brownian motor.

7 pages, 2 figures, Physical Review E (in press)

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• Markovian embedding of fractional superdiffusion
• Analytical results for long time behavior in anomalous diffusion
• Quantum Langevin equation of a charged oscillator in a magnetic field and coupled to a heat bath through momentum variables
• Non-universal power law distribution of intensities of the self-excited Hawkes process: a field-theoretical approach
• Localized Mode and Nonergodicity of a Harmonic Oscillator Chain
• Field master equation theory of the self-excited Hawkes process
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• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments
• Quantum Brownian Motion of a charged oscillator in a magnetic field coupled to a heat bath through momentum variables
• Effective Hamiltonian of topologically stabilized polymer states