@statphys23

Equilibrium Distribution of Microscopic Energy Flux

, , and . Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)

Abstract

Recent studies on reproducing heat conduction in Hamilton systems revealed that anomalous thermal conductivity is ubiquitous in wide variety of systems even if those have strong mixing property, especially in those the total momentum is conserved$^1)-3)$. What is typical in those systems is that the thermal conductivity diverges with system size while the temperature profile has well-scaled normal form. Those facts indicate that there are both diffusive and ballistic transport processes in such systems. Microscopic description and understanding for such non-diffusive energy transport is expected together with its evaluation from the anomaly of the macroscopic transport coefficient or long-time tailes of correlation functions. In this study we focus on the distribution function $P(j)$ of the microscopic energy flux carried by a single particle $i$, equation $j$ = p_i^2 \mbox$p$_i2m^2 + \sum_j łeft\ U_ij $p$_i2m - łeft( $q$_i - $q$_j \right) łeft( U_ij$q$_i \mbox$p$_im \right) \right\, equation in equilibrium state. It is observed in Lennard-Jones particle system that $P(j)$ has a broad peak in small $j$ regime and a stretched-exponential decay for large $j$. The peak structure originates in a potential advection term and energy transfer term between the particles. The stretched exponential tail comes from the momentum energy advection term$^4)$. There are many ways to transport the energy microscopically. Asymmetry in the higher order cumulant of $P(p)$ and correlations among momentum variables and coordinate variables will be possible candidates. For local, not microscopic, heat flux, spatial correlations among particles is also essential for anomalous behaviors and that should be detected as the deviation from the independent sum of the single particle distribution. The normal distribution obtained here gives good basis for considering how energy flows in each system. 1) S. Lepri, R. Livi, and A. Politi, Physics Reports 377 (2003) 1., 2) T. Shimada, T. Murakami, S. Yukawa, K. Saito, and N. Ito, J. Phys. Soc. Jpn. 69 (2000) 3150. 3) T. Murakami, T. Shimada, S. Yukawa, and N. Ito, J. Phys. Soc. Jpn. 72 (2003) 1049. 4) T. Shimada, F. Ogushi, and N. Ito, submitted to J. Phys. Soc. Jpn.

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