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Volumn 76, Issue 6, 2007, Pages

Dynamic correlations of macroscopic quantities

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; ONE DIMENSIONAL; THERMODYNAMIC PROPERTIES; TIME MEASUREMENT;

EID: 36749002149     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.062601     Document Type: Article
Times cited : (3)

References (17)
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    • Since dynamics is linear and stable, the evolution from an arbitrary initial condition will be the sum of the decay of this initial condition and the evolution from a flat initial condition.
    • Since dynamics is linear and stable, the evolution from an arbitrary initial condition will be the sum of the decay of this initial condition and the evolution from a flat initial condition.
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    • note
    • For arbitrary times, using the Schwarz inequality, for any t, and t′: Gδ Qp (t, t′) 8 π2 La [G xp ζ (t, t′)] 2, where a is a microscopic cutoff.
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    • note
    • Formally, m=1/2 corresponds to the case where G eq xm ζ (0) diverges logarithmically, in an extended definition of G eq xm ζ (τ) based on Eq. 6.
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    • note
    • In order to obtain explicit analytic formulas, we approximate the sum over k with a continuous integration, and the size L is here simply introduced by considering a cutoff at k=2π/L. While this approach gives the correct scaling behavior, the numerical prefactors may not be accurate.
  • 12
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    • note
    • Nevertheless, the diffusive behavior of the TCFs must be distinguished from the diffusion of the center of mass of the system. The position of the center of mass is hk=0 (t) /L. Its diffusion results from the fact that i ωk=0 =0, so that t hk=0 = ηk=0. Solving this equation, one finds [hk=0 (t+τ) - hk=0 (t)] 2 = Bk=0 τ, so that Bk=0 is the diffusion constant of the center of mass. Using Eq. 14, Bk=0 = (4πA kB T/σ) for n=0, and Bk=0 =0 for n>1. Taking the example of atomic steps, we recover the fact that the center of mass of a straight step should diffuse for n=0 (nonconserved, or Glauber dynamics), and cannot move due to mass conservation for n=2 (conserved, or Kawasaki dynamics). Since ζ -defined in Eq. (4)-does not contain the mode k=0, the quantities Qp, which are functionals of ζ, also do not account for this mode. (In order to be more explicit, we may define R0 = dx h2 by analogy with Q0. We then find Fδ R0 (τ) = Fδ Q0 (τ) + B k=0 2 (2t+τ) τ. Hence, we see explicitly the consequences of the diffusion of the center of mass in the term B k=0 2 (2t+τ) τ.)
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