Langlands duality for representations of quantum groups

We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in terms of semi-simple Lie algebras. To explain this duality, we introduce an "interpolating quantum group" depending on two parameters which interpolates between a quantum group and its Langlands dual. We construct examples of its representations, depending on two parameters, which interpolate between representations of two Langlands dual quantum groups.Comment: 37 pages. References added. Accepted for publication in Mathematische Annale

The Structure of Langevin's Memory Kernel From Lagrangian Dynamics

We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it shows some non-trivial structural features like negative correlations for some range of time separations. The system is shown to have three characteristic time scales, that control the shape of the kernel, and the transition between quadratic and linear behavior of the mean squared distance (MSD). Although the derivation of the structure in the memory kernel is obtained within a specific dynamical model, the phenomenon is shown to be quite generic.Comment: 8 pages, 5 figures, latex, include europhys.sty and euromacr.te

Efficient configurational-bias Monte-Carlo simulations of chain molecules with `swarms' of trial configurations

Proposed here is a dynamic Monte-Carlo algorithm that is efficient in simulating dense systems of long flexible chain molecules. It expands on the configurational-bias Monte-Carlo method through the simultaneous generation of a large set of trial configurations. This process is directed by attempting to terminate unfinished chains with a low statistical weight, and replacing these chains with clones (enrichments) of stronger chains. The efficiency of the resulting method is explored by simulating dense polymer brushes. A gain in efficiency of at least three orders of magnitude is observed with respect to the configurational-bias approach, and almost one order of magnitude with respect to recoil-growth Monte-Carlo. Furthermore, the inclusion of `waste recycling' is observed to be a powerful method for extracting meaningful statistics from the discarded configurations

Cubatic phase for tetrapods

We investigate the phase behavior of tetrapods, hard non-convex bodies formed by 4 rods connected under tetrahedral angles. We predict that, depending on the relative lengths of the rods these particles can form a uniaxial nematic phase, and more surprisingly they can exhibit a cubatic phase, a special case of the biaxial nematic phase. These predictions may be experimentally testable, as experimental realizations of tetrapods have recently become available.Comment: 8 pages ReVTeX 4, including 3 EPS figure

Do cylinders exhibit a cubatic phase?

We investigate the possibility that freely rotating cylinders with an aspect ratio $L/D=0.9$ exhibit a cubatic phase similar to the one found for a system of cut-spheres. We present theoretical arguments why a cubatic phase might occur in this particular system. Monte Carlo simulations do not confirm the existence of a cubatic phase for cylinders. However, they do reveal an unexpected phase behavior between the isotropic and crystalline phase.Comment: 24 pages, 12 figures, RevTex (Submitted to J. Chem. Phys.

Sampling along reaction coordinates with the Wang-Landau method

The multiple range random walk algorithm recently proposed by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)] is adapted to the computation of free energy profiles for molecular systems along reaction coordinates. More generally, we show how to extract partial averages in various statistical ensembles without invoking simulations with constraints, biasing potentials or unknown parameters. The method is illustrated on a model 10-dimensional potential energy surface, for which analytical results are obtained. It is then applied to the potential of mean force associated with the dihedral angle of the butane molecule in gas phase and in carbon tetrachloride solvent. Finally, isomerization in a small rocksalt cluster, Na4F4, is investigated in the microcanonical ensemble, and the results are compared to those of parallel tempering Monte Carlo.Comment: 6 pages, 5 figure

The role of long-range forces in the phase behavior of colloids and proteins

The phase behavior of colloid-polymer mixtures, and of solutions of globular proteins, is often interpreted in terms of a simple model of hard spheres with short-ranged attraction. While such a model yields a qualitative understanding of the generic phase diagrams of both colloids and proteins, it fails to capture one important difference: the model predicts fluid-fluid phase separation in the metastable regime below the freezing curve. Such demixing has been observed for globular proteins, but for colloids it appears to be pre-empted by the appearance of a gel. In this paper, we study the effect of additional long-range attractions on the phase behavior of spheres with short-ranged attraction. We find that such attractions can shift the (metastable) fluid-fluid critical point out of the gel region. As this metastable critical point may be important for crystal nucleation, our results suggest that long-ranged attractive forces may play an important role in the crystallization of globular proteins. However, in colloids, where refractive index matching is often used to switch off long-ranged dispersion forces, gelation is likely to inhibit phase separation.Comment: EURO-LATEX, 6 pages, 2 figure

Vapor-liquid surface tension of strong short-range Yukawa fluid

The thermodynamic properties of strong short-range attractive Yukawa fluids, k=10, 9, 8, and 7, are determined by combining the slab technique with the standard and the replica exchange Monte Carlo (REMC) methods. A good agreement was found among the coexistence curves of these systems calculated by REMC and those previously reported in the literature. However, REMC allows exploring the coexistence at lower temperatures, where dynamics turns glassy. To obtain the surface tension we employed, for both methods, a procedure that yields the pressure tensor components for discontinuous potentials. The surface tension results obtained by the standard MC and REMC techniques are in good agreement.Comment: 6 pages, 4 figure