Time dependent correlation functions and mode-mode coupling theories

Pomeau, Yves; Résibois, Pierre

doi:10.1016/0370-1573(75)90019-8

Cited by 503 publications

(348 citation statements)

References 114 publications

Supporting

Mentioning

333

Contrasting

Order By: Relevance

“…it oscillates with a power-law envelope. Accordingly, its Laplace trasform has branch-cut singularities of the form q 2 /(z ± q) 1 3 . This finding is not consistent with the heuristic assumption made in [14,15] and the result of [17], where simplified MCT equations were solved with the Ansatz Fourier transform of the memory function Γ(q, ω) for the same parameter values as in figure 1 and for three wavenumbers, namely, π/100 (solid line), 2π/100 (dashed line), and 3π/100 (dotted line).…”

Section: Numerical Analysismentioning

confidence: 99%

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

et al. 2007

View full text Add to dashboard Cite

Abstract. We study the dynamics of long-wavelength fluctuations in onedimensional (1D) many-particle systems as described by self-consistent modecoupling theory. The corresponding nonlinear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depends on the order of the leading nonlinear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.

show abstract

Section: Numerical Analysismentioning

confidence: 99%

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

et al. 2007

View full text Add to dashboard Cite

show abstract

“…Subscript int in the first integral in (14) means that the integral is taken over the interval where the integrand is real. This interval consists of two segments: from 0 to l 1 (k) and from l 2 (k) to 2π, where l 1 (k) and l 2 (k) are the two solutions of the transcendental equation for k ′…”

Section: The Peierls Equationmentioning

confidence: 99%

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

2003

View full text Add to dashboard Cite

The Peierls equation is considered for the Fermi-Pasta-Ulam β lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal mode energy as a function of wave vector k is estimated to be proportional to k 5/3 . This leads to the t −3/5 long time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained through the mode coupling theory our estimations give the same k dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam β lattice may lead to finite heat conductivity in this model.

show abstract

“…Since the diffusion coefficient is thought to be the integral of this function, we were forced to the reluctant conclusion that the self diffusion coefficient does not exist for two dimensional systems. It is presently believed that each of the Navier-Stokes transport coefficients diverge in two dimensions (Pomeau and Resibois, 1975). …”

Section: Introductionmentioning

confidence: 99%

Statistical Mechanics of Nonequilbrium Liquids

Morriss¹,

Evans²

2007

View full text Add to dashboard Cite

Time dependent correlation functions and mode-mode coupling theories

Cited by 503 publications

References 114 publications

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Statistical Mechanics of Nonequilbrium Liquids

Contact Info

Product

Resources

About