1) Interaction effects in chaotic systems.

Funded by the BSF

__Abstract__

One of the outstanding challenges in condensed
mater physics is to understand

the manifestations of many body interactions
in systems with quenched disorder.

Akin to this area of research is the field of
mesoscopic physics and quantum

dots. Unlike disordered systems, the quasiparticle
dynamics in these systems

is usually ballistic. However, being chaotic,
it shares common features

with the diffusive motion of electrons in disordered
systems. In the last few

years a large amount of puzzling experimental
data has been accumulated in this

field. For example, the symmetric Coulomb-Blockade
peak spacing distribution,

the absence of even/odd effects due to the spin
of the electron, the relative

insensitivity to magnetic field, and the bunching
in the addition spectra of

quantum dots. This data, apparently, contradicts
our physical picture of these

systems, which was borrowed from random matrix
theory and disorder perturbation

theory. The main goals of this research are:
(1) to improve our understanding of

the interplay among many-body interactions, quantum
interference effects, and

the chaotic dynamics in ballistic systems; (20
To clarify the differences

between ballistic and disordered systems; (3)
To explain results of experiments

in the field, and suggest new predictions.

2) Weak localization effects in ballistic systems.

Funded by The Israel Academy of Sciences and Humanities

__Abstract__

Recent advances in nanostructure technology have
opened the possibility of

experimental studies of clean chaotic systems,
systems in which electrons travel

ballistically, and the effects of impurity scattering
are weak. Such systems

nowadays are realized in quantum dots,
aluminum nanoparticles, and integrated

systems of superconductors and normal metals.
However, despite the vast number

of experiments in the field, the theoretical
understanding of interference

effects in ballistic systems is unsatisfactory.
The main problem is the lack of

a systematic perturbation theory, analogous to
the impurity diagrammatic

technique in disordered systems. In particular,
we do not understand the

mechanism of weak localization in ballistic systems.
Such understanding is the

main goal of this research. We focus our
attention on three problems:

(1) To extend the disorder diagrammatic technique
to the regime of nearly

ballistic systems; (2) To use variational calculations
for characterization of

relaxation processes in chaotic systems; (3)
To construct a new non-linear sigma

model with an effective action which describes
the evolution only on a subspace

of the full phase space. The results will be
used to understand existing

experimental data.

3) Effects of discterization in diffusion-reaction systems.

__Abstract__

Nonequilibrium systems of diffusing reactants
are very common in nature.

In chemistry almost any chemical reaction is
a reaction-diffusion system.

In physics, the standard examples are annihilation
of electrons and holes

moving in a disordered media, or vortices and

antivortices in type two superconductors. Examples
from other fields include:

Population dynamics in biology, spread of epidemics
in health science, and

group decision dynamics in social science. The
simplest description of

reaction-diffusion dynamics employs the densities
of the reactants as

the basic ingredients of the equations
of motion. However, it turns out that

these equations fail to describe these systems
in low dimensions.

The discretized nature of the reactants leads
to a scenario similar to quantum

phase transition. In this research project we
investigate the

Lotka-Volterra system using renormalization group
procedure, as well as

Bethe anzats solution for the 1-d case.

**KEY WORDS**: Chaos, Mesoscopic systems,
Semiclassics, Nonequilibrium,

Reaction-Diffusion.