9,506 research outputs found
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 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
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