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.