Department of Theoretical Physics
Research School of Physical Science and Engineering
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Department of Theoretical Physics
Research School of Physical Science and Engineering
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Postgraduate and Honours Projects Level of project: Honours or PhB undergraduate with
good physics, maths and computational background. Bose-Einstein Condensation in Presence of Confinement
and Interaction Description: Recently Bose-Einstein condensation(BEC) in dilute atomic gases in traps have been established in several laboratories. This has inspired the theorists to examine the role of confinement and/or interactions for the formation of BEC. At the mean field level there has been conflicting results on how the BEC is affected by both. In this proposal we plan to make a systematic study of the critical temperature of BEC and how it is dependent on the confinement and/or interactions. Level of project: Research students with very good
physics, maths,and computational background. Electronic, Transport and Optical Properties of Broken-Gap
Semiconductor Quantum Well Structures Description of project: We know that in conventional condensed matter materials the conduction band is always higher than the vanlence band. However, it has been realised recently that in InAs/GaSb-based quantum well systems, the top of the vanlence-band in the GaSb layer can be significantly higher than the bottom of the conduction-band in the InAs layer. Thus, advanced electronic and optical devices (eg, high-mobility and high-frequency transistors, terahertz laser generators and photon detectors, etc.) can be realised on the basis of these broken-gap semiconductor structures. In this project, the electronic, transport and optical properties of these novel systems will be studied theoretically in collaboration with an experimental group from the US Army Research Laboratory. Level of project: Research students (PhD, Honours, Summer Vacation, PhB undergrad) with good physics (electronics, optics and optoelectronics), maths and computational background. Excitation Spectrum of Spin Lattice Description of the project: The spin lattice is a
dimensional generalization of a spin chain. It is a lattice of an arbitrary
shape and size. Each vertex of the lattice carries a local triplet of
Pauli matrices (they form the algebra of observables) and some extra
numerical parameters. It is known how to produce the set of operators
with the following features: Level of the project: PhD Excitonic Superfluidity in Quantum Hall Bilayers Description: Very recently semiconductor quantum Hall bilayer systems have provided clear evidence of excitonic superfludity. A few years ago we have investigated electron and hole bilayer superconductivity. Now this proposal is made to study theoretically various aspects of coupled electron and hole bilayers including the novel results of excitonic superfluidity. Level of project: Research students with very good
physics, maths,and computational background. Finite Dimensional Representations of Quantum Affine
Algebras Quantum affine algebras are deformations of affine Lie algebras (central extensions of loop algebras). Understanding their representation theory is of utmost importance in the study of, e.g., integrable models of statistical mechanics. As yet, however, even the finite dimensional irreducible representations are poorly understood except in the simplest cases. The aim of this project is to formulate a conjecture on the general structure of finite dimensional irreducible representations of quantum affine algebras consistent with what is known already. Generalized Geometry, T-duality and Mirror Symmetry T-duality, in its simplest form, is the R to 1/R symmetry of String Theory compactified on a circle of radius R. It can be generalized to manifolds which admit circle actions (e.g. circle bundles) or, more generally, torus actions. In the case of nontrivial torus bundles, and in the background of H-flux, T-duality relates manifolds of different topology and can even map to noncommutative geometries. The purpose of this project is to study these phenomena (as well as the closely related “mirror symmetry”) in the context of Hitchin’s `generalized geometry’. High Temperature Superconductivity At present the nature of high-temperature superconductivity remains elusive in spite of the fact that many novel models have been proposed. We study this problem by using an exact technique based on an infinite order unitary transformation. The transformation applied to the high temperatrure superconductors show that an attractive interaction at the oxygen ion sites appear due to oxygen-copper virtual charge excitations. The project will determine the physical properties of this newly discovered attractive force and provide determine the pairing mechanism which results from this attrcation. Physics of Membrane Ion Channels Description of project: The field of biological ion channels has entered into a rapid phase of development in the past few years, partly due to the breakthroughs in determination of the crystal structures of membrane proteins and advances in computer simulations of bio-molecules. These advances have finally enabled the long-dreamed goal of relating function of a channel to its underlying molecular structure. In this project, theoretical models of several different types of biological ion channels will be constructed and then tested using various computational tools, such as molecular dynamics calculations and stochastic dynamics simulations. Level of project: Research students with good physics,
maths, or computational background. Quasi-Classical Expansion of Schroedinger Equation
and Conformal Field Theory Description of project: A separation of variables (SoV) originally appeared in the classical papers of 19th century scientists. During last decades it was recognized that, properly generalized, this method can be the most universal approach in the analysis of dynamics in integrable systems. One of the challenging problems is to apply SoV to a dynamical system of relativistic one-dimensional particles with a special interaction (trigonometric Ruijsenaars model). This model has deep connections with both physics and mathematics. From one side it describes the system of particles with fractional statistics. From another side its eigenfunctions are given by Macdonald symmetric polynomials in many variables. In this project the properties of this system will be studied via a reduction to a set of dynamical systems in one variable. Level of Project: PhD Statistics of Quasiparticles Collective excitations in quantum many body systems (as, e.g., in the fractional quantum Hall effect) often exhibit statistics different from the usual boson or fermion statistics. A particular form of these more general 'exclusion statistics' has been introduced by Haldane. The aim of this project is to investigate aspects of these more general exclusion statistics using techniques from algebraic geometry. String Theory and Integrable Systems This project aims to develop and employ the full power of the theory
of integrable quantum systems to new models of quantum many-body spin
systems with long-range interactions. These models have been placed
at the international centre-stage of developments in string theory in
a series of recent surprising and unexpected mathematical connections,
which relate spectra of free strings in the AdS5/S5 curved background
to the spectra of the Heisenberg type spin Hamiltonians with non-local
interactions. Several student projects of various complexity are available
at the honours Strongly Correlated Electron Systems The central problem posed by heavy fermion and collosal magneto-resistance
materials is to understand the interplay of localized moments and conduction
electrons. In low dimensional strongly correlated electron systems this
problem can be addressed using Abelian bosonization technique. The project
will determine the magnetic phase diagram of ...strength of the double-exchange
ferromagnetic interaction in the Periodic Anderson model. The effect
of phonons and of the Topics in String Theory String theory is, at present, the only candidate for a consistent unification
of all four fundamental forces. Many important advances in String Theory
have been made in the last couple of years. These include: String dualities,
a microscopic derivation of the Bekenstein-Hawking black-hole entropy,
a concrete manifestation of the holographic principle, the emergence
of noncommutative geometry as a candidate for the quantum geometry of
spacetime and the classification of D-brane changes in terms of K-theory. Transport in Mesoscopic Systems Description: In mesoscopic physics study of electronic transport is one of the prominent areas. During past two decades a vast amount of research has been made on the ballistic,duffusive and tunnelling transport. In this area experiment is well ahead of the theory. The only theory in common use is the "Landauer-Büttiker formalism", which has demonstrated considerable success. In the current proposal we intend to examine a general microscopic linear response approach to deal with the electronic transport in a variety of physical situations with and without a magnetic field. A careful analysis is necessary to compare linear response and Landauer-Büttiker theories. Level of project: Research students with very good
physics, maths,and computational background. Turbulence, Transitions, and Transport in Flatland Level of project: Research students with good physics,
maths, or computational Theoretical Plasma Physics Condensed Matter Theory |
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