From Order to Disorder: Superfluidity, Stochastic Processes, and the Dynamics of Life—Dedicated to Professor Peter McClintock on the Occasion of His 85th Birthday

Dear Colleagues,

This special issue in honour of Prof Peter McClintock focuses on fields in which he has made groundbreaking contributions. This most notably includes work on the superfluidity and quantum vortices of He-4, and on fluctuations in nonlinear systems.

The superfluidity of He-4 remains a fascinating and controversial topic in condensed matter physics – the easy questions were answered long ago,  leaving behind more fundamental questions which are still outstanding. For many decades, most work on superfluid and superconducting vortices has treated their dynamics classically, with classical forces (Magnus, Iordanski, etc.) acting on them. Some authors (notably D.J. Thouless and collaborators) strongly objected, arguing that the true dynamics was quantum-mechanical. That this must be so is clear from vortex tunneling experiments, starting with pioneering experiments using ions (McClintock et al), followed by annular superflow experiments (J.C.S. Davis, E. Varoquaux, and others).  And yet, as Thouless emphasized, there is an air of mystery here. What is the effective mass of a superfluid vortex (estimates range from zero to infinity!)? How does vortex nucleation work, both microscopically (where it begins), and macroscopically (since a macroscopic flow field is created with the vortex)? What is the equation of motion for a superfluid vortex (the classical Hall/Vinen/Iordanski equations, or the quantum equations of Thouless et al., or of Thompson and Stamp)? Why are vortex nucleation experiments (quantum and thermal) so poorly explained by theory? What causes the genesis and growth of quantum turbulence (and of quantum cavitation)?  And what about quantum vortices and vortex nucleation in 2-d superfluids (where tunneling must cross over to classical Kosterlitz-Thouless physics)? And how does dissipation affect all of this? None of this is well understood.

Talk of dissipation leads naturally to more general questions about random processes as formulated by Boltzmann. However, the very notion still remains puzzling. Classical randomness comes either from averaging over many environmental degrees of freedom, from dynamical chaos for even a few degrees of freedom (as in the Solar System), or from nonautonomous dynamics either with a few degrees of freedom, or in networks.  An interesting example, to which Peter McClintock has made a major contribution, concerns rare events in dynamical systems caused by the decrease of entropy in thermal reservoirs coupled to them. This is related to larger questions–eg., how diffusion of interacting classical particles occurs in a random landscape, how thermalization occurs in classical systems, and how couplings govern their dynamics. Quantum mechanics of course adds further complexity to the mix, and changes the questions – the physics of quantum chaos is quite different from classical chaos, and disorder has a radically different effect on a quantum system (leading, to, e.g., localization). And the role of dissipation is fundamentally different in quantum systems, first pointed out in the classic work of Caldeira and Leggett - this is a topic of great current interest.

Life adds another huge dimension to these discussions. Recent works on brain and cardiovascular dynamics point to a need to focus on the role of mutual interactions between dynamical systems (like those between the heart and the lungs). They happen on many time scales inviting a time-localised approach rather than averaging. The seeming disorder may unwind as highly ordered multiscale dynamics  if the time-scale of entropy production is carefully considered. The lessons from living systems can sometimes be useful in solving problems in seemingly very different areas, like the dynamics of electrons on the surface of liquid helium, to which Peter McClintock recently contributed.

These are all very active current research topics.

Finally, it is worth noting that Professor Peter McClintock's extensive contributions extend far beyond the topics mentioned above, encompassing a wide range of scientific phenomena, including stochastic resonance and its deterministic counterpart, vibrational resonance, both of which are integral to his research in nonlinear dynamics.

Prof. Dr. Aneta Stefanovska
Prof. Dr. Philip C.E. Stamp
Prof. Dr. Mark Dykman
Prof. Dr. Laszlo B. Kish
Prof. Dr. Ladislav Skrbek
Guest Editors

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