## PHYS4014 Physics Honours Coursework B

## Lecturer(s):

**Statistical Mechanics**

Prof Oleg Sushkov

Dr Dimitrie Culcer

**Quantum Field Theory**

Prof Oleg Sushkov

**Advanced Condensed Matter Physics**

Dr Dimitrie Culcer

Prof Michelle Simmons

**Cosmology and the Interstellar Medium**

Dr Jan Hamman

Dr Maria Cunningham

## Course Description :

Advanced physics in statistical mechanics and a selection of topics including; condensed matter physics; quantum field theory; cosmology and the interstellar medium; and stellar astrophysics. Not all topics may be available every year.

**Statistical Mechanics**

Interaction in classical fluids: Cluster expansions for an imperfect gas; the product theorem; Ursell cluster functions, articulation and nodal circles; introduction to theories of liquids; distribution functions; Orstein Zernike equations; the HNC and PY approximations; the virial expansion and equations of state; comparison with molecular dynamics simulations;

Phase Transitions and Critical Phenomena: Phenomenology of first order phase transitions; critical points and critical exponents; the Ising model and applications, approximate and exact solutions.

Approach to Equilibrium, Transport Phenomena, and Irreversibility: Brownian motion; Boltzmann transport equation, approximate solutions; the H theorem and the problem of irreversibility; Liouville equation, time correlation functions, Linear response theory; The fluctuation theorem.**Quantum Field Theory**

The subject is introduced by addressing several phenomena, including the following ones:

Casimir effect

Lamb shift - splitting of atomic energy levels, which from the first glance should be degenerate

Vacuum polarization

Heizenerg-Euler problem, behaviour of the vacuum in strong magnetic field

Schwinger phenomenon, production of electron - positron pairs in static electric field

Their general properties as well as relations with phenomena that take place at low energies (say, in atomic and condensed matter physics, or astrophysics) are outlined.**Advanced Condensed Matter Physic**s

Conduction in 3D and 2D semiconductors;

band structure and density of states in 2D, including quantum Hall effect;

quantum wires (1D systems);

quantum dots (0D systems)*Magnetism*

Ferromagnets and Antiferromagnets; Heisenberg Model, exchange; Ground state of the Heisenberg antiferromagnetic; Low temperature behaviour of the Heisenberg ferromagnetic; Spin waves/ Calculation of the magnon dispersion law; Magnetism in Metals; Indirect exchange and RKKY interaction; Magnetic frustration and Spin glasses; Magnetic structures of rare earth metals; Mean field theory of itinerant electron magnetism; Band Magnetism – Stoner Criterion; Measurement of magnetic properties and structure*Superconductivity*

Electron-phonon interaction; Type I and II superconductors; The Cooper problem; The BCS theory of Superconductivity/ BCS Hamiltonian; Flux quantization and vortices; Ginzburg-Landau theory; High temperature superconductors; Predictions and comparisons with experiment**Cosmology and the Interstellar Medium**

Basics of General Relativity: equivalence principle, curved spacetime, geodesic equation, Einstein equations; Applications of General Relativity: Schwarzschild geometry, gravitational lensing, gravitational waves, FLRW cosmology

The Interstellar Medium: the ISM, radiative transfer; local thermodynamic equilibrium, ionization and recombination; emission lines; dynamics; shock waves; HII regions; supernova remnants.

**Astrophysics**

Stellar radiation, spectra classification. Hertzsprung Russell diagrams, determination of stellar masses and radii. Equations of stellar structure, energy sources in stars, nuclear reaction cycles energy transport, equations of state, degeneracy, opacity. Properties of main sequence stars, stellar evolution, structure of red giants and white dwarfs. The solar atmosphere

## Semester(s) Offered:

Semester 2 only