Dynamics and disorder at the Kosterlitz-Thouless transition
This thesis describes theoretical investigations into the dynamics of superfluid films and the effects of disorder on the roughening transition of crystal surfaces. The dynamic theory of superfluid helium films, due to Ambegaokar et al., is refined to improve the precision of the predictions made. A detailed comparison is made between the predictions of the modified theory and the results from experiments on helium films and on superconducting systems. It is found that, despite the modifications in the theory, agreement with experiments on helium films remains only qualitative. Consideration is then given to the effects on the roughening transition of disorder arising from screw dislocations. A crystal surface which is threaded by screw dislocation pairs may be in one of three different states depending on the temperature of the system and the way in which screw pairs are distributed. At high temperatures the interface is rough: it is not pinned to the lattice. At low temperatures the state of the interface depends on how the screw dislocations are distributed: when distributed as closely spaced pairs they lead to a faceted state with a single ground state energy; when distributed randomly they lead to a state of the interface which, though pinned to the underlying crystal lattice, has a degenerate ground state. It is then shown that the dynamic sine-Gordon formulation of the roughening transition can be used, via a Hubbard-Stratonovich transformation, to model the dynamic behaviour of superfluid systems. This method provides a re-normalization group framework within which the a.c. linear response can be studied. The ways in which the approach could be extended to study the effects of disorder and atomic layering are also discussed.