1.MANY-VALLEY EFFECTS IN 2D SYSTEMS (T)
 

Active areas in many semiconducting devices confine current carriers (electrons and holes) in 2D plane.
In many cases, the energy spectrum of these carriers has several minima in 2D Brillouine zone - valleys -
and kinetics of the carriers is determines by the fast relaxation within single valley and a slow relaxation
between the valleys. This could lead to a number of specific non-equilibrium phenomena. While these
phenomena in the bulk semiconcunctors were a subject of extensive research, vey little is known about
specifics of the many-valley properties of 2D systems. The aim of the proposed project is to feel
the mentioned gap and to study the many-valley phenomena in 2D systems.
 
 

2. INTERFACE OF A SUPER-SOLID AND A SUPR-FLUID.
MELTING WAVES. (T)

Super-solid is a hypotetical substance, which unifies properties of a elastic body and that of a super-fluid.
The project suggests to study the properties of of the interface of a super-solid and a super-fluid, kinetics
of growth of super-solid from the melt and meltig waves.
 
 

3. VIRIAL EXPANSION FOR WEAKLY DOPED p-TYPE SEMICONDUCTORS.

The valence band in many cubic semiconductors has a peculiar structure which
gives rise to two branches of excitations: the heavy and the light holes. Masses of
these excitation may be very different. Under this condition, an aceptor has two radii
r_h and r_l. Two very different radii make the effect of finite concentration of
acceptors a new problem, which has several domain of conditions depending on
ratios of mean distance between acceptors and these radii. All this requires a new
theory of the Metal-Insulator Transition in these substances.
The purpose of this project is to study effects of finite concentration of acceptors,
calculate the density of states and see the precursors of the Metal-Insulator Transition
 
 

4. DEPHASING OF ELECTRONS IN A METAL
DUE TO INTERACTION WITH FLUCTUATIONS OF PAIRNG (T).

Electrons in a normal metal are quatum particles characterised by both the
occupation numbers and the phase. Phase relaxation (dephasing) is an important
characteristics measured experimentally. The leading contribution to rate of
dephasing comes from the electron-electron interaction. At the temperature T
approuching critical temperature Tc of the transition into superconducting state,
the interaction leading to formation of the Cooper pairs is especially strong and
leads to efficient and temperature dependent dephasing.
The aim of the project is to calculate the rate of dephasing due to this mechanism
and find out its dependence on temperature and magnetic field.
 

5. LIFSHITS POINT IN A COMPRESSIBLE SOLID (T).

The Lifshits point is a point at the phase transition line on the phase diagramme, at which
the transition into an uniformly ordered phase is transformed into the transition into a
phase with periodically modulated order parameter. The period of modulation goes to
infnity at approuching the Lifshits point. The subject of this project is a study of effects
of elastic deformation on shape of the phase diagram.
approuching critical temperature Tc of the transition into superconducting state,
the interaction leading to formation of the Cooper pairs is especially strong and
leads to efficient and temperature dependent dephasing.
The aim of the project is to calculate the rate of dephasing due to this mechanism
and find out its dependence on temperature and magnetic field.
 

6. CROSSING OF DISCONTINUITIES IN MHD (T).

This project relates to Magnetic Hydrodynamics (MHD): Dynamics of a conducting
fluid in presence of magnetic field. Analogously to conventional Fluid Mechanics,
MHD has diffent kind of discontinuities: sound lines, shock waves, etc. The aim of
this project is to study the shape of these lines near their crossing points.

7. SCATTERING AT THE TIP OF A POTENTIAL (T).

The subject of this project is a problem of the quantum scattering theory: a potential U(r)
has a maximum at r = 0. Find the differential and total scattering cross-sections at energies
E close to the tip U(0) of this potential.

8. SINAI DIFFUSION (T).

It is suggested to solve a problem of a one-diensional random walk in presence of an independent random
"wind", which would drag the walker either forward or backward. The solution requires a knowledge of the
modern methods of the theory: supersymmetry, transfer-matrix - which will be acquired in the process of the
work on the project.

9. GEOMETRY OF KOHN'S SURFACES AND ITS IMPLICATION (T).

Kohn's Surfaces consists of points q in the reciprical space, at which the polarization of the electron gas X(q)
has a singularity. The aim of this project is to study evolution of the shape of the Kohn's Surface when the
shape of the Fermi Surface changes (Geometry of Kohn's Surface). Another question is to look at implcation
of the shape of the Kohn's Surface on Fermi Surface of the carriers.

10.SHOENBERG MAGNETISM, CURRENT-CURRENT INTERACTION
AND MARGINAL FERMI LIQUID (T).

David Shoenberg [1] was first to point out that the electrons in a normal metal under conditions of de Haas - van Alphen effect
feel the induction B rather than applied field H. Brian Pippard [2] wen further and came to conclusion that this phenomenon
which he called The Shoenberg Magnetism, leads to the first order transition with the two phase regions on the phase diagram
and areas of meta-stability. T.Holstein et al [3] re-interpreted the whole phenomenon as a result of interaction between electrons
mediated by transverse electromagnetic field and suggested to take into account not only the static but also the dynamic - i.e.
time dependent - part of this interaction. They have found that, despite the mentioned interaction is very weak, it could lead to
the strong effect at very low tempratures. They show that, under mentioned condition, the Landau's theory of Fermi Liquid is not
valid. Unfortunately, these authors did not study the effect om the mentioned interaction on de Haas - van Alphen effect itself and
did not estimate how the value of the non-Fermi-liquid effects varied across the phase diagram. This task is the subject of proposed
project.
[1] D.Shoenberg, Phil Trans. Roy Soc, A255, 85 (1962)
[2] A.B.Pippad, Proc Roy Soc, A272, 192 (1963)
[3] T.Holstein, R.E.Norton, P.Pincus, Phys Rev, B8, 2649 (1973)