1. SPONTANEOUS
SYMMETRY BREAKING, TOPOLOGICAL DEFECTS
AND TYPE II SUPERCONDUCTIVITY
Superconductivity brings an example of spontaneous symmetry
breaking,
motivated by real physics. The project involves a study
of the
Ginzburg-Landau theory [1] and its extantion to type
II
superconductivity [2], acquaintance with the concept
of the
topologic defect - Abrikosov vortex. A number of problems
could form
the mini-projects associated with this Literature review.
Different relevant problems of quantum mechanics are
considered
together
with a toy problem about a drunkard in a city full of
policemen.
3.
FUNCTIONAL INTEGRAL, PHASE TRANSITIONS AND
TYPE
I SPONTANEOUS SYMMETRY BREAKING
This project reviews a number of concepts: phase transitions
of type I
and type II, spontaneous symmetry breaking, functional
integral, scaling,
catastrophe theory, etc. It involves a study of
a seminal paper [6], which
shows that, in a compressible solids, any type II phase
transition is
transformed into a type I transition. A mini-project
on material of this review
is available.
4. RATE OF DEPHASING FOR ELECTRONS IN METALS
The aim of this project to study the paper [17] about
electron in a metal,
which interacts with the other electrons. Such
interaction leads, at finite
temperatures, to relaxation of the phase of the
wave function of electron.
Finally, the rate of this relaxation as function
of temperature and the
propertices of the sample is calculated.
Meanwhile, the student should
learn about the way such a rate is measured
(weak localisation), about
electromagnetic noise, Feynman path integral and
other things.
5. MOESSBAUER EFFECT AND ORTHOGONALITY CATASTROPHE
Project involves a review of two phenomena
associated with a reaction of a
coupled system to a sudden pertirbation [11].
It involves a study of a two
classical many-body problems about the recoil-less emition
of gamma-rays and
the motion of an external heavy particle in electron
gas and X-ray absorption
6. PHASE-SLIP-CENTRES,
THERMALLY ACTIVATED DESTRUCTION OF
SUPERCONDUCTIVITY AND
RESISTANCE OF SUPERCONDUCTING WIRES
Superconductivity means zero resistance. The resistance
would vanish if
not the thermal fluctuations, which lead to temporary
and local
destruction of superconductivity. As the result, a superconducting
wire
obtains a finite resistance, which decreases exponentially
with
decreasing the temperature. Theoretical consideration
of this problem [19]
involves a study of several basic ingredient, characteristic
for modern
theory: order parameter and its time evolution; nucleation
of the defects,
activation energy, rate of nucleation. This is a pretty
demanding but
hugely rewarding project.
7. HOT ELECTRONS IN SEMICONDUCTORS
The aim of this project is to introduce the student to
several basic notions of
Physical Kinetics [20]: Boltzmann equation, its
transformation into Fokker-Planck
equation, stationary solution. All this
could be seen while discussing electrons in
semiconductors, interacting
with each other and with phonons.
8. ANOMALOUS SKIN-EFFECT AND CYCLOTRON RESONANCE
This project is introducing the student into kinetics of
electrons in clean metals
in presence of high frequency electromagnetic filed. Two cases are
under
consideration: zero magnetic field
(skin-effect) and non-zero constant magnetic
field parallel to the surface of the sample. A further development of
the subject
is also possible: a selective
transparency; waves, etc.
9. BOLTZMAN EQUATION AND COLLECTIVE MODES IN PLASMAS
This review allows to the student to get acquainted with
several concenpts: Boltzmann
Equation,
collective motion and plasma oscillations, their dispersion and
attenuation,
plasma instabilities, echo.
REFERENCES
1. V.L.Ginzburg and L.D.Landau, in L.D.Landau Collected Papers.
2. A.A.Abrikosov, JETP (1957)
3. J.S.Langer and J.H. Zittartz Phys Rev (1966)
4. B.I. Halperin and M. Lax, Phys Rev (1966)
5. E. Brezin and G. Parisi, J.Phys. C (1982)
6. A.I. Larkin and S.A. Pikin, First
- nearly second order transiition.
JETP
33, (1969).
7. L. Gunther, D. Bergman and Y. Imry
,
Renormalized critical
behavior or first order phase transitions?
Phys Rev Lett
27, 558 (1971).
8. Y. Imry. Tricritical points in compressible magnetic systems. Phys Rev Lett. 33, 1304 (1974).
10. N.D. Mermin, Reviews of Modern Physics
11. H.Lipkin, Quntim Mechanics
12. P.W. Anderson Phys. Rev. (1965)
13. P. Nozieres and C. de Dominicis Phys. Rev. (1970)
14. L. Cooper, Phys. Rev. (1956)
15. J. Bardeen, L. Cooper and J.R. Schrieffer, Phys. Rev. (1957)
16. A.A. Abrikosov, L.P. Gorkov, I.E.
Dzyaloshinskii
Methods of
Quantum Field Theory in Statistical Physics
17. L.D. Landau and E.M.Lifshits, Statistical Physics. Part I
18. B.L. Altshuler, A.G.Aronov
and D.E.Khmelnitskii
Effect of electron-electron
collisions with small energy transfer
on Quantum
Localisation, J.Phys. C15, p7367 (1982)
19. L.S. Langer and
V. Ambegaokar,
Intrinsic
Resistive Transition in Narrow Superconducting
Channels.
Phys.
Rev. 164, 498 (1967)
20.
E.M.Lifsits
and L.P.Pitaevskii,
Physical Kinetics,
Pergamon Press
21.
Niels Berglund and Turgay Uzer,
Foundation of Physuics, vol 31, p.283 (2001)
Contact D.E.Khmelnitskii
Mott 521
tel: 37 289
e-mail: DEK12@cam.ac.uk