Polarized Fermi fluids: My research interests are in quantum fluids and solids. In particular my collaborators and I have studied transport and equilibrium properties of fluid polarized Fermi systems, including pure liquid 3He, 3He gas, and dilute solutions of 3He in liquid 4He. These substances are polarized by high magnetic fields or by optical pumping techniques. A particular feature of these systems is the mean-field effect known as "identical particle spin rotation," a forward-scattering exchange effect analogous to mean-fields in Landau Fermi liquid theory. This effect gives rise, for example, to transvers spin waves, even in gases obeying Boltzmann statistics and to reactive terms in the spin diffusion equation (Leggett-rice effect). Transport in these systems is interesting because of the strong dependence that coefficients such as spin diffusion, thermal conductivity, and viscosity have on the degree of polarization. We have developed a computational method, using a generalization of the Boltzmann kinetic equation, that can be used for dilute systems over temperatures ranging all the way from degeneracy at low temperatures to Boltzmann statistics at high temperatures. This is important because many experiments involve the intermediate range between these two extremes. There are a variety of magnetic phenomena to be studied including the Leggett-Rice effect, spin waves, spin echoes, non-linear magnetic phenomena, spin relaxation times, and anisotropic spin diffusion, a field that recently has become controversial. New experiments on spin transport in dilute solutions at very high polarizations and low temperatures have recently been completed and we are providing theoretical support for these.
Polarized Heisenberg Paramagnets: Recently we have extended our studies of polarized systems to solid paramagnets, including solid 3He. The methods used for the fluid cases, based on the kinetic equation, do not work in this case and we must compute transport properties via Kubo theory. We find the remarkable result that longitudinal and transverse spin diffusion coefficients are not the same in this system, a feature reminiscent of what happens in the liquid. Indeed it seems that the Leggett-Rice effect should occur in this system. This result implies interesting non-linear effects will exist in the highly polarized magnetic solid paramagnetic systems.
Bose-Einstein Condensation: The discovery of Bose-Einstein condensation (BEC) in alkali gases held in magnetic traps has caused great excitment among researchers in the area of quantum systems. In these gases particles avalanche into the lowest quantum state below a certain transition temperature which can be as low as nanokelvin for a small number of particles. The MIT atomic physics group under the direction of W. Ketterle is among those studying such systems. We have been studying what happens in these systems when they are restricted to just two-dimensions. A curious feature of the 2D system is that the ideal gas does have a phase transition, which is removed as soon as the least interaction is turned on. While there can be no real phase transition to a Bose-condensed state in only dimensions, there is some sort of phase transition, possibly a Kosterlitz-Thouless transition at a given temperature. We are continuing the study of this system by analytic means and by path-integral Monte Carlo techniques.
An analog of the Leggett-Rice effect occurs in the trapped alkali gases. When two hyperfine states are trapped, they can act like a pseudo-spin-1/2 system and have the same kind of identical spin-rotation effects that occur in a spin-1/2 Fermi system. Indeed an oscillatoy segregation of the two hyperfine states occurs as an analog of a spin wave in the Fermi system. [For the experiment: see H. J. Lewandowski et al, Phys. Rev. Letters 88, 070403 (2002) cond-mat/0204182; for a theoretical treatment see J. N. Fuchs, D. M. Gangardt, and F. Laloë, Phys. Rev. Letters 88, 230404 (2002) cond-mat/0112228.] We are collaborating on work in this area with the Robert Ragan from Univertsity of Wiscosin/La Crosse.