Can the Velocity Autocorrelation Function Decay Exponentially?

Lee, M. Howard

doi:10.1103/physrevlett.51.1227

Cited by 91 publications

(54 citation statements)

References 20 publications

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“…Following the same line of thought, we arrive at the conclusion that R(t) is even. Lee [25] has also shown that both the memory and the correlation function must be even functions for any Hamiltonian system. Consequently, we can write with a 0 = R(0) = 1 and,…”

Section: Memory Correlation Functions and Noisementioning

confidence: 99%

Non-exponential relaxation for anomalous diffusion

et al. 2006

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We study the relaxation process in normal and anomalous diffusion regimes for systems described by a generalized Langevin equation (GLE). We demonstrate the existence of a very general correlation function which describes the relaxation phenomena. Such function is even; therefore, it cannot be an exponential or a stretched exponential. However, for a proper choice of the parameters, those functions can be reproduced within certain intervals with good precision. We also show the passage from the non-Markovian to the Markovian behaviour in the normal diffusion regime. For times longer than the relaxation time, the correlation function for anomalous diffusion becomes a power law for broadband noise.

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Section: Memory Correlation Functions and Noisementioning

confidence: 99%

Non-exponential relaxation for anomalous diffusion

et al. 2006

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“…This is so because we know [17] that, in accordance with the work of Ref. [18,19], the relaxation process of a variable made unstable by a bath with a bounded spectrum, cannot be exactly exponential. At long times, after the completion of the exponential decay of the macroscopic variable, non-exponential tails appear [17].…”

Section: Markov Approximation To Friction In the Zero-temperaturementioning

confidence: 92%

The Markov approximation revisited: Inconsistency of the standard quantum Brownian motion model

Rocco

Grigolini

1999

Physics Letters A

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“…They must correspond to what has been termed "admissible" functions [8] (see section 3). The D,, being the lengths of the basis vectors, denote some excitable dynamic modes.…”

Section: Continued Fractionsmentioning

confidence: 99%

The topology of Hilbert spaces and the dynamics of molecular processes

Lee

Kim

Cummings

et al. 1995

Journal of Molecular Structure: THEOCHEM

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The transfer of energy from one mode to another whether within a molecule or between molecules is a fundamental process in nature. The delocalization of energy which encompasses energy transfer is closely related to time evolution in a system. The recently developed method of recurrence relations shows that the time evolution and the topology of a particular Hilbert space structure are equivalent. In this work a number of different topological shapes of infinitedimensional Hilbert spaces obtained from microscopic models are summarized to illustrate a variety of admissible time-evolution functions.

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Can the Velocity Autocorrelation Function Decay Exponentially?

Cited by 91 publications

References 20 publications

Non-exponential relaxation for anomalous diffusion

Non-exponential relaxation for anomalous diffusion

The Markov approximation revisited: Inconsistency of the standard quantum Brownian motion model

The topology of Hilbert spaces and the dynamics of molecular processes

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