Lancaster LA1 4YB, United Kingdom

Large fluctuations are responsible for many
important physical phenomena, including e.g. stochastic resonance and
transport in Brownian ratchets. They usually proceed along *optimal
paths*. Starting from Boltzmann (1904), a huge body of theory was
developed during the last century; the modern understanding dates from
Onsager and Machlup (1953). The introduction of the prehistory
probability distribution established optimal paths as physical
observables (Dykman et al, 1992), and the corresponding optimal force
driving the fluctuations was measured for the first time by Luchinsky
(1997). Recent developments, centered on nonequilibrium systems, will
be discussed, including extensions of the work has to encompass escape
from chaotic attractors (Khovanov et al, 2000; Luchinsky et al, 2002).
In particular, it has been established that fluctuational escape from a
chaotic attractor involves the system passing between unstable saddle
cycles - thus paving the way for an analytic theory. Measurements of
the optimal force can be used to determine the energy-optimal control
function needed to effect escape in the deterministic system in the
absence of fluctuations.

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Lancaster LA1 4YB, United Kingdom

Turbulence in superfluids - e.g. the superfluid states of liquid He and He, the electron gas in superconductors, the nucleonic fluids in neutron stars, and Bose-Einstein condensates in laser-cooled gases - is quantized. It consists of a tangle of vortex lines, each element of which is identical to every other in any given system. Apart from its intrinsic scientific interest it is of importance because (a) being in some ways a very simple form of turbulence one can hope to understand in considerable detail, and (b) it is the state believed to be created during a fast passage through a second order phase transition. Two ongoing research programmes on superfluid turbulence will be reviewed and discussed. First, the initial experiments (Davis et al, 2000) on the decay of turbulence in superfluid He at mK temperatures will be considered. The vortices are created with a electrostatically-driven vibrating grid, and detected by the use of negative ions travelling near the Landau critical velocity in isotopically pure He. Preliminary results indicate that the vortex decay rate apparently becomes temperature-independent below about 70 mK. It is believed (Vinen, 2000) that the corresponding decay mechanism may involve a Kolmogorov cascade, Kelvin waves and, ultimately, phonon creation. Secondly, the status of superfluid helium experiments modelling the GUT transition in the early universe 10 s after the Big Bang (Dodd et al, 1998) will be reviewed.

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