Equilibrium Distribution of Microscopic Energy Flux
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.