Condensed Matter Physics is arguably the broadest, most loosely defined discipline in Physics. My work is, in that sense, quintessential condensed matter theory, ranging from studies of transport in disordered superconductors to models for the motion of flocks of birds. The unifying theme of this work, to the extent that there is one, is the study of long distance and long time properties of strongly fluctuating systems with many degrees of freedom. The topics I am currently most actively studying are:

1) Birds; or, the theory of flocking: in 1995, with Yuhai Tu, I developed a set of continuum equations of motion to describe the collective behavior of large numbers of self-propelled entities all moving together. The most common type of such entity is, of course, living creatures; as a result, the equations we propsed should be quite generally applicable to the motions of herds of wildebeest, schools of fish, flocks of birds, singular of rhinoceri, and swarms of bacteria. Indeed, it should describe the collective motions of any organisms – or self-propelled automata – that follow their neighbors. Our model combines features of the Navier-Stokes equation for a simple compressible fluid and a simple relaxational model for spins in a ferromagnet. In addition, it exhibits the unusual phenomenon known as the breakdown of linearized hydrodynamics: the failure of the linearized equations of motion to correctly predict even the scaling of response and correlations. This breakdown is induced by strong fluctuations; despite it, we are able to predict exactly the scaling exponents characterizing the long wavelength behavior of the flock. Our most surprising result is that although a million physicists, all standing in a plain and able to see only a few of their neighbors, could not manage to all point in the same direction, a million wildebeest can quite easily all move in the same direction.

These equations are now considered a sort of “standard model” for flocking, and have been re-derived from kinetic theory for a wide variety of different microscopic models by many authors.

Just as the Navier-Stokes equations of ordinary fluid mechanics describe the liquid phase of water, but not its solid phase (ice), so to the equations Tu and I developed only describe one of many possible “phases” of a flock.

Many of my current projects in this area involve predicting what other sorts of phases might occur in flocks, and providing a continuum description of them as well. My most recent project in this area has been the development of a theory of smectics “P”, a new “liquid crystal” phase that has been observed in simulations of some flocking models, in which the “flock” organizes into liquid-like layers, along which it flies.

Another project involves studying “incompressible” flocks, whose density is fixed. This proves to map on to an equilibrium smectic liquid crystal, which in turn can be mapped onto the “KPZ” equation, which is a model for the growth of interfaces.

I’ve also worked on the behavior of flocks moving over disordered surfaces, or through disordered media, and on the response of flocks to external guiding fields.