1) Interaction effects in chaotic systems.
Funded by the BSF
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
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
3) Effects of discterization in diffusion-reaction systems.
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,