Path Integrals for (Complex) Classical and Quantum Mechanics

An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to instantons and lead to time/energy uncertainty. In practice, 'classical' particle trajectories with additional degrees of freedom have arisen in several different formulations of quantum mechanics. In this talk we compare the extended phase space of the closed time-path formalism with that of complex classical mechanics, to suggest that $\hbar$ has a role in our understanding of the latter. However, differences in the way that trajectories are used make a deeper comparison problematical. We conclude with some thoughts on quantisation as dimensional reduction.Comment: 13 pages: Published in the Proceedings of AAMP 7, (Prague) 2011. This file differs from the published version by the inclusion of extra references, with minor changes of text (which leave conclusions unaltered

Spontaneous Fluxon Formation in Annular Josephson Tunnel Junctions

It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss our experiment for measuring the Zurek-Kibble scaling exponent sigma for the production of fluxons in annular symmetric Josephson Tunnel Junctions. The predicted exponent is sigma = 0.25, and we find sigma = 0.27 +/- 0.05. Further, there is agreement with the ZK prediction for the overall normalisation

The Non-universal behaviour of Cold Fermi Condensates with Narrow Feshbach Resonances

In this paper we construct an effective field theory for a condensate of cold Fermi atoms whose scattering is controlled by a narrow Feshbach resonance. We show how, from first principles, it permits a hydrodynamic description of the BEC-BCS crossover from which the equation of state, intimately related to the speed of sound, can be derived. Specifically, we stress the non-universal behaviour of the equation of state at the unitary limit of infinite scattering length that arises when either, or both, of the range of the inter-atomic force and the scale of the molecular field become large.Comment: 7 pages, there is no differences in results between this (v2) and the older version (v1), but v2 makes the nature of the non-canonical behavior of the EOS cleare

Fluxoid formation: size effects and non-equilibrium universality

Simple causal arguments put forward by Kibble and Zurek suggest that the scaling behaviour of condensed matter at continuous transitions is related to the familiar universality classes of the systems at quasi-equilibrium. Although proposed 25 years ago or more, it is only in the last few years that it has been possible to devise experiments from which scaling exponents can be determined and in which this scenario can be tested. In previous work, an unusually high Kibble-Zurek scaling exponent was reported for spontaneous fluxoid production in a single isolated superconducting Nb loop, albeit with low density. Using analytic approximations backed up by Langevin simulations, we argue that densities as small as these are too low to be attributable to scaling, and are conditioned by the small size of the loop. We also reflect on the physical differences between slow quenches and small rings, and derive some criteria for these differences, noting that recent work on slow quenches does not adequately explain the anomalous behaviour seen here.Comment: 7 pages, 4 figures, presentation given at CMMP 201