8,487 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
Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model
We investigate the potential energy surface of a phi^4 model with infinite
range interactions. All stationary points can be uniquely characterized by
three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_-
= 1, provided that the interaction strength mu is smaller than a critical
value. The saddle index n_s is equal to alpha_0 and its distribution function
has a maximum at n_s^max = 1/3. The density p(e) of stationary points with
energy per particle e, as well as the Euler characteristic chi(e), are singular
at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu)
\neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per
particle at the thermodynamic phase transition point T_c. This proves that
previous claims that the topological and thermodynamic transition points
coincide is not valid, in general. Both types of singularities disappear for H
\neq 0. The average saddle index bar{n}_s as function of e decreases
monotonically with e and vanishes at the ground state energy, only. In
contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is
given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 >
upsilon_0, the ground state energy.Comment: 9 PR pages, 6 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
Microscopic Dynamics of Hard Ellipsoids in their Liquid and Glassy Phase
To investigate the influence of orientational degrees of freedom onto the
dynamics of molecular systems in its supercooled and glassy regime we have
solved numerically the mode-coupling equations for hard ellipsoids of
revolution. For a wide range of volume fractions and aspect ratios
we find an orientational peak in the center of mass spectra
and about one decade
below a high frequency peak. This orientational peak is the counterpart of a
peak appearing in the quadrupolar spectra and
. The latter peak is almost insensitive on
for close to one, i.e. for weak steric hindrance, and broadens strongly
with increasing . Deep in the glass we find an additional peak between
the orientational and the high frequency peak. We have evidence that this
intermediate peak is the result of a coupling between modes with and
, due to the nondiagonality of the static correlators.Comment: 6 figures, 12 page
Affine crystal structure on rigged configurations of type D_n^(1)
Extending the work arXiv:math/0508107, we introduce the affine crystal action
on rigged configurations which is isomorphic to the Kirillov-Reshetikhin
crystal B^{r,s} of type D_n^(1) for any r,s. We also introduce a representation
of B^{r,s} (r not equal to n-1,n) in terms of tableaux of rectangular shape r x
s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial analogue of
the type A column splitting procedure) to construct a bijection between
elements of a tensor product of Kirillov-Reshetikhin crystals and rigged
configurations.Comment: 26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26
pages; examples added; introduction revised; final version. (v1) 24 page
Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution
We investigate hard ellipsoids of revolution in a parameter regime where no
long range nematic order is present but already finite size domains are formed
which show orientational order. Domain formation leads to a substantial slowing
down of a collective rotational mode which separates well from the usual
microscopic frequency regime. A dynamic coupling of this particular mode into
all other modes provides a general mechanism which explains an excess peak in
spectra of molecular fluids. Using molecular dynamics simulation on up to 4096
particles and on solving the molecular mode coupling equation we investigate
dynamic properties of the peak and prove its orientational origin.Comment: RevTeX4 style, 7 figure
- …