Publication Numbers: 42.

In this project we examine the glassy properties
of

strongly disordered systems of localized electrons,

interacting via the Coulomb interaction.

These studies are motivated by recent experimental

results obtained by the group of Zvi Ovadyahu
in

Jerusalem, who observed very slow relaxation
times

characteristic of glassy dynamics.

Theoretical studies have shown

the existence of multiple low energy minima in
such models,

which is typical in glassy systems.

The glassy behavior sets in gradually as the
temperature is

lowered without evidence for

a finite temperature glass transition.

Theoretical studies and computer simulations
have

shown that there is a gap in the density

of states (DS) around the Fermi level, known
as the

Coulomb gap.

The statistical physics of Coulomb Glass systems
is

poses challenging problems since one needs to
include

the long range Coulomb interaction

while constraining the motion of electrons by

variable range hopping considerations.

Introducing a set of suitable correlation functions

we have recently studied the equilibrium dynamics

of the Coulomb glass at low temperatures [42].

We found

that the configuration of occupied sites within
the

Coulomb gap persistently changes at temperatures
much

lower than the width of the gap itself,

while the shape of the density of states

remains essentially unchanged.

We interpret these results in terms of drift
of the

system between multiple energy minima, which
may also

imply that interacting electrons may be effectively

delocalized within the Coulomb gap.

**Future Plans**:

We now focus on

extending our approach to non-equilibrium conditions

in which the challenge is to calculate the conductivity.

Without the Coulomb interaction, the conductivity
can

be described as a percolation problem.

However, the Coulomb interaction introduces a
varying

energy landscape, deviating from the percolation
picture,

while the variable range hopping introduces a
vast

increase in the number of possible hopping paths.

A direct calculation of the conductivity will
help

us to develop a theoretical framework for the

understanding of the experimental results, in
which

the system is driven out of equilibrium and

the conductivity is measured during the equilibration

process.