E-Book Content
Session
I"
STATISTICAL MECHANICS
EIGENMODES OF CLASSICAL FLUIDS IN THERMAL EQUILIBRIUM
E. G. D. Cohen The Rockefeller University 1230 York Avenue New York, NY 10021
Abstract The eigenmodes of a classical fluid in thermal equilibrium are discussed. wavelengths
and times, they can be computed from linear hydrodynamic
are then the hydrodynamic diffusion
modes,
in particular,
the heat mode,
of heat in the fluid and two sound modes.
For long
equations.
which
For short wavelengths
they can be derived from linear kinetic operators.
For low densities,
extensions of the kinetic analogues of the heat and sound modes.
the e x t e n d e d extensions
of the Boltzmann operator
heat mode,
while
next
of the sound modes.
is used.
the
and times
the linear
Boltzmann operator can be employed and the three most important eigenmodes
a generalization
They
describes
are direct
For high densities,
The most important eigenmode
in i m p o r t a n c e
come
two e i g e n m o d e s
These three extended hydrodynamic
that
is are
modes can be used
to obtain the light and neutron spectra of fluids and vice versa.
I.
Introduction
In this
paper,
classical particles. the one
I am c o n c e r n e d
statistical
with
mechanics
the t r a n s i t i o n
for m a c r o s c o p i c
The basic question then is:
hand,
the d y n a m i c s
from
classical
systems,
mechanics
consisting
how does one make a c o n n e c t i o n
of the many
particles
between,
here
liquids, The most
to a d i s c u s s i o n
of this question for classical fluids,
familiar
macroscopic
properties
properties.
Thus
description
of a system
the o b s e r v e d
with
local
involves the identification statistically
averaged
is c o n n e c t e d
but also
distribution with
function,
and
time
velocity
equilibrium
therefore systems,
kinetic equations.
or the
of p a r t i c l e s
~n thermal equilibrium, and
A finer
uses distribution
description
functions,
which gives the average number
average number of pairs systems
properties.
velocities
a certain
microscopic
or the local
with the average momentum density at this point and similarly
for other local thermodynamic positions
of observed
number density at a particular point in the
fluid is identified with the average number of particles at this point
point
I restrict
i.e., gases and
and what follows has been written with these systems in mind.
macroscopic
velocity
on
in the system, and on the other
hand, the physically observed properties of the system in the laboratory? myself
to
of very many
their
they
pair
of p a r t i c l e s
distribution
at two points
involving
with
not
only
like the single particle at a p a r t i c u l a r
function, certain
that gives the
velocities.
In