5,541 research outputs found
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
Microscopic theory of glassy dynamics and glass transition for molecular crystals
We derive a microscopic equation of motion for the dynamical orientational
correlators of molecular crystals. Our approach is based upon mode coupling
theory. Compared to liquids we find four main differences: (i) the memory
kernel contains Umklapp processes, (ii) besides the static two-molecule
orientational correlators one also needs the static one-molecule orientational
density as an input, where the latter is nontrivial, (iii) the static
orientational current density correlator does contribute an anisotropic,
inertia-independent part to the memory kernel, (iv) if the molecules are
assumed to be fixed on a rigid lattice, the tensorial orientational correlators
and the memory kernel have vanishing l,l'=0 components. The resulting mode
coupling equations are solved for hard ellipsoids of revolution on a rigid
sc-lattice. Using the static orientational correlators from Percus-Yevick
theory we find an ideal glass transition generated due to precursors of
orientational order which depend on X and p, the aspect ratio and packing
fraction of the ellipsoids. The glass formation of oblate ellipsoids is
enhanced compared to that for prolate ones. For oblate ellipsoids with X <~ 0.7
and prolate ellipsoids with X >~ 4, the critical diagonal nonergodicity
parameters in reciprocal space exhibit more or less sharp maxima at the zone
center with very small values elsewhere, while for prolate ellipsoids with 2 <~
X <~ 2.5 we have maxima at the zone edge. The off-diagonal nonergodicity
parameters are not restricted to positive values and show similar behavior. For
0.7 <~ X <~ 2, no glass transition is found. In the glass phase, the
nonergodicity parameters show a pronounced q-dependence.Comment: 17 pages, 12 figures, accepted at Phys. Rev. E. v4 is almost
identical to the final paper version. It includes, compared to former
versions v2/v3, no new physical content, but only some corrected formulas in
the appendices and corrected typos in text. In comparison to version v1, in
v2-v4 some new results have been included and text has been change
Beautiful Baryons from Lattice QCD
We perform a lattice study of heavy baryons, containing one () or
two -quarks (). Using the quenched approximation we obtain for the
mass of
The mass splitting between the and the B-meson is found to increase
by about 20\% if the light quark mass is varied from the chiral limit to the
strange quark mass.Comment: 11 pages, Figures obtained upon request from [email protected]
Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids
When non-adsorbing polymers are added to an isotropic suspension of rod-like
colloids, the colloids effectively attract each other via depletion forces. We
performed Monte Carlo simulations to study the phase diagram of such
rod-polymer mixture. The colloidal rods were modelled as hard spherocylinders;
the polymers were described as spheres of the same diameter as the rods. The
polymers may overlap with no energy cost, while overlap of polymers and rods is
forbidden.
Large amounts of depletant cause phase separation of the mixture. We
estimated the phase boundaries of isotropic-isotropic coexistence both, in the
bulk and in confinement. To determine the phase boundaries we applied the grand
canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120,
10925 (2004)], and we performed a finite-size scaling analysis to estimate the
location of the critical point. The results are compared with predictions of
the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento
D 16, 949 (1994)]. We also give estimates for the interfacial tension between
the coexisting isotropic phases and analyse its power-law behaviour on approach
of the critical point
Renormalization and Quantum Scaling of Frenkel-Kontorova Models
We generalise the classical Transition by Breaking of Analyticity for the
class of Frenkel-Kontorova models studied by Aubry and others to non-zero
Planck's constant and temperature. This analysis is based on the study of a
renormalization operator for the case of irrational mean spacing using
Feynman's functional integral approach. We show how existing classical results
extend to the quantum regime. In particular we extend MacKay's renormalization
approach for the classical statistical mechanics to deduce scaling of low
frequency effects and quantum effects. Our approach extends the phenomenon of
hierarchical melting studied by Vallet, Schilling and Aubry to the quantum
regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy
Test of the semischematic model for a liquid of linear molecules
We apply to a liquid of linear molecules the semischematic mode-coupling
model, previously introduced to describe the center of mass (COM) slow dynamics
of a network-forming molecular liquid. We compare the theoretical predictions
and numerical results from a molecular dynamics simulation, both for the time
and the wave-vector dependence of the COM density-density correlation function.
We discuss the relationship between the presented analysis and the results from
an approximate solution of the equations from molecular mode-coupling theory
[R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].Comment: Revtex, 10 pages, 4 figure
Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study
We perform a comparative study of the free energies and the density
distributions in hard sphere crystals using Monte Carlo simulations and density
functional theory (employing Fundamental Measure functionals). Using a recently
introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009))
we obtain crystal free energies to a high precision. The free energies from
Fundamental Measure theory are in good agreement with the simulation results
and demonstrate the applicability of these functionals to the treatment of
other problems involving crystallization. The agreement between FMT and
simulations on the level of the free energies is also reflected in the density
distributions around single lattice sites. Overall, the peak widths and
anisotropy signs for different lattice directions agree, however, it is found
that Fundamental Measure theory gives slightly narrower peaks with more
anisotropy than seen in the simulations. Among the three types of Fundamental
Measure functionals studied, only the White Bear II functional (Hansen-Goos and
Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for
the equilibrium vacancy concentration and a physical behavior of the chemical
potential in crystals constrained by a fixed vacancy concentration.Comment: 17 pages, submitted to Phys. Rev.
Molecular mode-coupling theory for supercooled liquids: Application to water
We present mode-coupling equations for the description of the slow dynamics
observed in supercooled molecular liquids close to the glass transition. The
mode-coupling theory (MCT) originally formulated to study the slow relaxation
in simple atomic liquids, and then extended to the analysis of liquids composed
by linear molecules, is here generalized to systems of arbitrarily shaped,
rigid molecules. We compare the predictions of the theory for the -vector
dependence of the molecular nonergodicity parameters, calculated by solving
numerically the molecular MCT equations in two different approximation schemes,
with ``exact'' results calculated from a molecular dynamics simulation of
supercooled water. The agreement between theory and simulation data supports
the view that MCT succeeds in describing the dynamics of supercooled molecular
liquids, even for network forming ones.Comment: 22 pages 4 figures Late
Heavy-light baryonic mass splittings from the lattice
We present lattice estimates of the mass of the heavy-light baryons
and obtained using propagating heavy quarks. For
our result is GeV, after
extrapolation to the continuum limit and in the quenched approximation.Comment: 3 pages postscript, Contribution to Lattice'9
Scaling Study of the Leptonic Decay Constants of Heavy-Light Mesons: A Consumers Report on Improvement Factors
A high statistics calculation, performed at and ,
enables us to study the variation of the leptonic decay constants of
heavy pseudoscalar mesons with the lattice spacing . We observe only a weak
dependence when the standard normalization is used for the
quark fields, whereas application of the Kronfeld-Mackenzie normalization
induces a stronger variation with . Increasing the meson mass from
to this situation becomes even more pronounced.Comment: Lattice 93, 3 pages Latex, 2 postscript figures (epsf style
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