Condensed Matter Theory

Abstract:

Solutions of interacting linear polymers are mapped onto a system of "soft" spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only the center of mass (c.m.) of the polymer coils. The effective pair potentials are derived by inverting the c.m. pair distribution function, generated in Monte Carlo simulations, using the hypernetted chain closure. The method, previously devised for the self-avoiding walk model of polymers in good solvent, is extended to the case of polymers in solvents of variable quality by adding a finite nearest-neighbor monomer-monomer attraction to the previous model and varying the temperature. The resulting effective pair potential is found to depend strongly on temperature and polymer concentration. At low concentration the effective interaction becomes increasingly attractive as the temperature decreases, eventually violating thermodynamic stability criteria. However, as polymer concentration is increased at fixed temperature, the effective interaction reverts to mostly repulsive behavior. These issues help to illustrate some fundamental difficulties encountered when coarse-graining complex systems via effective pair potentials.

Abstract:

The slow dynamics of granular flow is studied as an extension of static granular problems, which, as a consequence of shaking or related regimes, can be studied by the methods of statistical mechanics. For packed (i.e. 'jammed'), hard and rough objects, kinetic energy is a minor and ignorable quantity, as is strain. Hence, in the static case, the stress equations need supplementing by 'missing equations' depending solely on configurations. These are in the literature; this paper extends the equilibrium studies to slow dynamics, claiming that the strain rate (which is a consequence of flow, not of elastic strain) takes the place of stress, and as before, the analogue of Stokes's equation has to be supplemented by new 'missing equations' which are derived and which depend only on configurations.

Abstract:

We calculate the low-temperature spectral function of one-dimensional incommensurate charge density wave states and half filled Mott insulators. At T=0 there are two dispersing features associated with the spin and charge degrees of freedom, respectively. We show that already at very low temperatures (compared to the gap) one of these features gets severely damped. We comment on implications of this result for photoemission experiments.

Abstract:

Lattice models with N = 2 supersymmetry are introduced. It is shown that the continuum limit of the simplest of these models is a well known (1 + 1)-dimensional quantum field theory with N = (2,2) superconformal symmetry. The close connections with models of current interest in the study of strongly correlated electrons is noted. Furthermore, it is demonstrated how supersymmetry can be useful in studying their properties.