Stochastic dynamics with a mesoscopic bath

Plyukhin, A. V.; Schofield, Jeremy

doi:10.1103/physreve.64.041103

Cited by 20 publications

(35 citation statements)

References 21 publications

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“…In the theory of open systems, the deterministic dynamics of particles in the system is replaced by the stochastic Langevin equation in the classical limit. The problem has been investigated with the use of various models in which a single particle (the system) is attached at the center (or edge) of a linear chain [2,3], or it is coupled to a bath consisting of a collection of harmonic oscillators [4]- [13]. Many studies have been made for open systems by using the Caldeira-Leggett (CL) model given by [4][5][6] …”

Section: Introductionmentioning

confidence: 99%

Classical small systems coupled to finite baths

Hasegawa

2011

Phys. Rev. E

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We have studied the properties of a classical N S -body system coupled to a bath containing N Bbody harmonic oscillators, employing an (N S + N B ) model which is different from most of the existing models with N S = 1. We have performed simulations for N S -oscillator systems, solving 2(N S + N B ) first-order differential equations with N S ≃ 1 − 10 and N B ≃ 10 − 1000, in order to calculate the time-dependent energy exchange between the system and the bath. The calculated energy in the system rapidly changes while its envelope has a much slower time dependence.Detailed calculations of the stationary energy distribution of the system f S (u) (u: an energy per particle in the system) have shown that its properties are mainly determined by N S but weakly depend on N B . The calculated f S (u) is analyzed with the use of the Γ and q-Γ distributions: the latter is derived with the superstatistical approach (SSA) and microcanonical approach (MCA) to the nonextensive statistics, where q stands for the entropic index. Based on analyses of our simulation results, a critical comparison is made between the SSA and MCA. Simulations have been performed also for the N S -body ideal-gas system. The effect of the coupling between oscillators in the bath has been examined by additional (N S + N B ) models which include baths consisting of coupled linear chains with periodic and fixed-end boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Classical small systems coupled to finite baths

Hasegawa

2011

Phys. Rev. E

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“…If one applies a similar analysis to the primary correlations C i (t), Eq. (14), one gets a familiar approximate relation for the left side of the chain [5,8,10]…”

Section: Relation To Primary Correlationsmentioning

confidence: 99%

Correlations of correlations: Secondary autocorrelations in finite harmonic systems

Plyukhin

2015

Phys. Rev. E

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The momentum or velocity autocorrelation function C(t) for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the autocorrelation function of the long-time noisy tail of C(t) ("a correlation of the correlation"), which characterizes the distribution of recurrence times. Remarkably, for harmonic systems with same-mass particles this secondary correlation may coincide with the primary correlation C(t) (when both functions are normalized) either exactly, or over a significant initial time interval. When the tagged particle is heavier than the rest, the equality does not hold, correlations show nonrandom long-time scale pattern, and higher-order correlations converge to the lowest normal mode.

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“…where recall ω 0 = k/m, k is the force constant, m is the mass of an atom [10]. The ratio of the diffusion coefficients for carrier hopping along a static chain (2) to that for atomic diffusion (3) can be written as…”

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confidence: 99%

“…All atoms have the same mass m, the harmonic force constant is k, so the highest oscillation mode has the frequency 2ω 0 , with ω 0 = k/m. Using a normal mode transformation one can show (see for instance [10]) that for finite temperature T the mean square displacement (MSD) of an atom is proportional to its distance from the chain's end, and that the relative displacement of two atoms linearly increases with their separation,…”

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confidence: 99%

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Hitchhiking transport in quasi–one-dimensional systems

Plyukhin¹

2005

Europhys. Lett.

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Abstract. -In the conventional theory of hopping transport the positions of localized electronic states are assumed to be fixed, and thermal fluctuations of atoms enter the theory only through the notion of phonons. On the other hand, in 1D and 2D lattices, where fluctuations prevent formation of long-range order, the motion of atoms has the character of the large scale diffusion. In this case the picture of static localized sites may be inadequate. We argue that for a certain range of parameters, hopping of charge carriers among localization sites in a network of 1D chains is a much slower process than diffusion of the sites themselves. Then the carriers move through the network transported along the chains by mobile localization sites jumping occasionally between the chains. This mechanism may result in temperature independent mobility and frequency dependence similar to that for conventional hopping.Introduction. -Systems consisting of weakly coupled one-dimensional (1D) chains are ubiquitous and important. Anisotropic organic solids, polymers, columnar liquid crystals are just a few examples of quasi 1D systems important for applications. Biomaterials like DNA and proteins in many respects behave as topologically 1D systems. Because of structural and dynamic disorder, the charge transport in these materials is often due to incoherent phonon-assisted hopping of charge carriers between localized sites. Most theoretical models of hopping transport in quasi-1D systems predict a strong temperature dependence for the carrier mobility of the form µ ∼ e

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Stochastic dynamics with a mesoscopic bath

Cited by 20 publications

References 21 publications

Classical small systems coupled to finite baths

Classical small systems coupled to finite baths

Correlations of correlations: Secondary autocorrelations in finite harmonic systems

Hitchhiking transport in quasi–one-dimensional systems

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