UK Nonlinear News, November 2000

International Workshop on Fluctuations and Superfluidity (Lancaster University)

Peter McClintock (

The primary aim of this conference was to bring together fluctuational nonlinear dynamicists and superfluid physicists in a context where they could communicate and exchange ideas and information easily. It seemed to be generally agreed that this aim was successfully achieved.

Fluctuations play a key role in many physical processes. But it is a role that in many cases is not yet properly understood. Over the last few years, there have been increasing efforts to develop fluctuation theory in application to a wide range of scientific problems. Gratifying progress has already been made, but a huge amount remains to be done and the activity is burgeoning. Recent examples include the investigation of stochastic phase switching of a parametrically driven electron in a Penning trap; studies of thermally activated transitions in a bistable optical trap; and the observation and measurement of the dynamics of activated escape in a semiconductor laser.

In low temperature physics and superfluidity, however, fluctuations are usually treated on the assumption that the system remains in thermal equilibrium, or quasiequilibrium. But deviations from equilibrium may change very dramatically, not only the prefactors, but also the exponents in the nucleation rates, because the notion of free energy barriers for given thermodynamic conditions no longer applies. For thermally activated processes, the whole phase equilibrium curve can become completely different, as illustrated by the Landauer blowtorch theorem. Dramatic changes occur also for quantum tunnelling rates, because the systems of interest then lack time reversibility, and the notion of tunnelling through a static potential barrier is inapplicable.

Although proven to work successfully in other areas, these ideas had not yet become widely appreciated within the the low temperature community. At the same time, it seemed that there are many observed LT phenomena that may be accounted for, or at least illuminated by, ideas from fluctuation theory. Examples include: nonequilibrium phase transitions in the liquid heliums; creation of quantized vortices by ions in superfluid He-4, which has been shown to occur via a form of macroscopic tunnelling clearly involving the quantum analogue of a classical large rare fluctuation; orifice flow, where the vortex creation and unpinning processes apparently involve tunnelling and where stochastic effects are clearly evident in many of the published data; nucleation of He-3 B-phase from the A-phase through the influence of cosmic rays, resulting in the so-called "baked Alaska" scenario, representing a perfect example of the kind of nonequilibrium situation to which some of the theoretical techniques recently developed by the fluctuational dynamics community may be applicable.

The idea of the small workshop was to make it possible for some of the leading researchers in superfluidity and fluctuational dynamics to meet each other and to exchange ideas and experiences. A major aim was thus to bring together what had hitherto been two distinct communities. In particular, we hoped to make the low temperature community aware of recent events and discoveries in the nonequilibrium fluctuational dynamics that may help to enhance their understanding of low temperature phenomena, and we hoped to appraise the fluctuational dynamics community of some of the challenging problems in low temperature physics to which their techniques might fruitfully be applied. A second aim of the workshop was to broaden perspectives generally by inclusion of a few carefully chosen researchers who are already applying fluctuation theory successfully to a diverse range of problems in different scientific, engineering, and medical disciplines. A third aim was educational: to include some young researchers from the low temperature and other areas, able to benefit from the debate and, we hoped, make significant contributions to it.

The workshop spanned 2 full days, over the week-end 2-3 September 2000, with participation restricted to 36 carefully selected scientists. The opening talk by Brage Golding (East Lansing) on activated escape in a driven system - and how it can be understood in terms of large fluctuations - set the scene. He was followed by Hermann Grabert (Freiburg) discussing quantum phase fluctuations in Josephson junctions, and Dmitri Luchinsky explaining how the recently introduced "logarithmic susceptibility" solves several long-standing problems in the treatment of periodically driven fluctuating systems. The other 20 talks also dealt with extremely important problems related to superfluidity and fluctuational nonlinear dynamics. They included Wojciech Zurek (Los Alamos) on defect creation during symmetry-breaking phase transitions in superfluids and at the GUT transition of the early universe; George Pickett on the Kibble mechanism in He-3 and nucleation across the superfluid A/B boundary; discussions of fluctuations in superfluid and classical turbulence by Joe Vinen (Birmingham), Eric Varoquaux (Orsay), Shaun Fisher (Lancaster), Gary Williams (UCLA) and Charlie Doering (Michigan). Philip Stamp (Utrecht) discussed quantum tunnelling in both superfluids and magnetic systems, and Mark Dykman (East Lansing) discussed tunnelling in many electron systems. Roger Bowley (Nottingham) recounted the remarkable tale of how his analysis of quantized vortex nucleation in superfluid He-4 had led directly to improvements in MRI design and multi-million pound patents. Feodor Kusmartsev (Loughborough) discussed parallels between vortex nucleation in helium and in small superconductors, and Mike Lea (Royal Holloway) presented arguments for a non-equilibrium phase transition in electronic microchannels on the He-4 surface; Charles Williams (Exeter) described recent results on quantum evaporation/condensation on the surface. Robert Maier (Arizona), Martin Van Exter (Leiden) and Stanislav Soskin (Kiev) considered different forms of fluctuational escape; Pierre Thibault (Grenoble) discussed order parameter fluctuations for He-4 in disordered media; and Nigel Stocks (Warwick) reported the new phenomenon of suprathreshold stochastic resonance. Finally, Aneta Stefanovska (Ljubljana) described fluctuations and phase transitions in the cardiovascular system, closely analogous to phenomena seen earlier in lasers.

Posters were presented by Manuel Arrayas (Leiden), Alexander Balanov (Lancaster), Sergei Dzhosyuk (Harvard), Philip Hendry (Lancaster), Natalia Igosheva (Saratov), Nata Janson (Lancaster), Richard Lee (NPL), Hamish Nichol (Lancaster) and Sergei Timashev (Moscow).

The (memorable) after dinner speech was by Riccardo Mannella (Pisa).

Mark Dykman (East Lansing) was Programe Chairman and the conference was organised by a committee chaired by Dmitri Luchinsky (Lancaster), with web (and other) support from Elena Luchinskaya; the overall chairman was Peter McClintock (Lancaster). The meeting was supported by the EC and by EPSRC. The full programme and other details can be accessed on the conference website:

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