24 research outputs found
Metastable Dynamics above the Glass Transition
The element of metastability is incorporated in the fluctuating nonlinear
hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass
transition. This is achieved through the introduction of the defect density
variable into the set of slow variables with the mass density and
the momentum density . As a first approximation, we consider the case
where motions associated with are much slower than those associated with
. Self-consistently, assuming one is near a critical surface in the MCT
sense, we find that the observed slowing down of the dynamics corresponds to a
certain limit of a very shallow metastable well and a weak coupling between
and . The metastability parameters as well as the exponents
describing the observed sequence of time relaxations are given as smooth
functions of the temperature without any evidence for a special temperature. We
then investigate the case where the defect dynamics is included. We find that
the slowing down of the dynamics corresponds to the system arranging itself
such that the kinetic coefficient governing the diffusion of the
defects approaches from above a small temperature-dependent value .Comment: 38 pages, 14 figures (6 figs. are included as a uuencoded tar-
compressed file. The rest is available upon request.), RevTEX3.0+eps
Non-Linear Stochastic Equations with Calculable Steady States
We consider generalizations of the Kardar--Parisi--Zhang equation that
accomodate spatial anisotropies and the coupled evolution of several fields,
and focus on their symmetries and non-perturbative properties. In particular,
we derive generalized fluctuation--dissipation conditions on the form of the
(non-linear) equations for the realization of a Gaussian probability density of
the fields in the steady state. For the amorphous growth of a single height
field in one dimension we give a general class of equations with exactly
calculable (Gaussian and more complicated) steady states. In two dimensions, we
show that any anisotropic system evolves on long time and length scales either
to the usual isotropic strong coupling regime or to a linear-like fixed point
associated with a hidden symmetry. Similar results are derived for textural
growth equations that couple the height field with additional order parameters
which fluctuate on the growing surface. In this context, we propose
phenomenological equations for the growth of a crystalline material, where the
height field interacts with lattice distortions, and identify two special cases
that obtain Gaussian steady states. In the first case compression modes
influence growth and are advected by height fluctuations, while in the second
case it is the density of dislocations that couples with the height.Comment: 9 pages, revtex
Nonequilibrium critical dynamics of the relaxational models C and D
We investigate the critical dynamics of the -component relaxational models
C and D which incorporate the coupling of a nonconserved and conserved order
parameter S, respectively, to the conserved energy density rho, under
nonequilibrium conditions by means of the dynamical renormalization group.
Detailed balance violations can be implemented isotropically by allowing for
different effective temperatures for the heat baths coupling to the slow modes.
In the case of model D with conserved order parameter, the energy density
fluctuations can be integrated out. For model C with scalar order parameter, in
equilibrium governed by strong dynamic scaling (z_S = z_rho), we find no
genuine nonequilibrium fixed point. The nonequilibrium critical dynamics of
model C with n = 1 thus follows the behavior of other systems with nonconserved
order parameter wherein detailed balance becomes effectively restored at the
phase transition. For n >= 4, the energy density decouples from the order
parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime
(z_S <= z_rho) entire lines of genuine nonequilibrium model C fixed points
emerge to one-loop order, which are characterized by continuously varying
critical exponents. Similarly, the nonequilibrium model C with spatially
anisotropic noise and n < 4 allows for continuously varying exponents, yet with
strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium
perturbations leads to genuinely different critical behavior with softening
only in subsectors of momentum space and correspondingly anisotropic scaling
exponents. Similar to the two-temperature model B the effective theory at
criticality can be cast into an equilibrium model D dynamics, albeit
incorporating long-range interactions of the uniaxial dipolar type.Comment: Revtex, 23 pages, 5 eps figures included (minor additions), to appear
in Phys. Rev.
Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
A systematic analysis of the Burgers--Kardar--Parisi--Zhang equation in
dimensions by dynamic renormalization group theory is described. The fixed
points and exponents are calculated to two--loop order. We use the dimensional
regularization scheme, carefully keeping the full dependence originating
from the angular parts of the loop integrals. For dimensions less than
we find a strong--coupling fixed point, which diverges at , indicating
that there is non--perturbative strong--coupling behavior for all .
At our method yields the identical fixed point as in the one--loop
approximation, and the two--loop contributions to the scaling functions are
non--singular. For dimensions, there is no finite strong--coupling fixed
point. In the framework of a expansion, we find the dynamic
exponent corresponding to the unstable fixed point, which describes the
non--equilibrium roughening transition, to be ,
in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly,
our result for the correlation length exponent at the transition is . For the smooth phase, some aspects of the
crossover from Gaussian to critical behavior are discussed.Comment: 24 pages, written in LaTeX, 8 figures appended as postscript,
EF/UCT--94/3, to be published in Phys. Rev. E
Stochastic Growth Equations and Reparametrization Invariance
It is shown that, by imposing reparametrization invariance, one may derive a
variety of stochastic equations describing the dynamics of surface growth and
identify the physical processes responsible for the various terms. This
approach provides a particularly transparent way to obtain continuum growth
equations for interfaces. It is straightforward to derive equations which
describe the coarse grained evolution of discrete lattice models and analyze
their small gradient expansion. In this way, the authors identify the basic
mechanisms which lead to the most commonly used growth equations. The
advantages of this formulation of growth processes is that it allows one to go
beyond the frequently used no-overhang approximation. The reparametrization
invariant form also displays explicitly the conservation laws for the specific
process and all the symmetries with respect to space-time transformations which
are usually lost in the small gradient expansion. Finally, it is observed, that
the knowledge of the full equation of motion, beyond the lowest order gradient
expansion, might be relevant in problems where the usual perturbative
renormalization methods fail.Comment: 42 pages, Revtex, no figures. To appear in Rev. of Mod. Phy
Many body physics from a quantum information perspective
The quantum information approach to many body physics has been very
successful in giving new insight and novel numerical methods. In these lecture
notes we take a vertical view of the subject, starting from general concepts
and at each step delving into applications or consequences of a particular
topic. We first review some general quantum information concepts like
entanglement and entanglement measures, which leads us to entanglement area
laws. We then continue with one of the most famous examples of area-law abiding
states: matrix product states, and tensor product states in general. Of these,
we choose one example (classical superposition states) to introduce recent
developments on a novel quantum many body approach: quantum kinetic Ising
models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of
correlated electron systems". Improved version new references adde
Nonlinear fluctuating hydrodynamics and sequence of time scales of relaxation in supercooled liquids
QCD CORRECTIONS TO INCLUSIVE JET PHOTOPRODUCTION VIA DIRECT PHOTONS
Bödeker D. QCD CORRECTIONS TO INCLUSIVE JET PHOTOPRODUCTION VIA DIRECT PHOTONS. Zeitschrift für Physik C. 1993;59(3):501-510.The calculation of the QCD corrections to jet photoproduction in electron proton collisions is described. We consider the case of a direct (pointlike) photon and use the Weizsacker-Williams approximation to describe the spectrum of the (quasi-) real photons. We list expressions for the calculation of one and two jet inclusive cross section and present numerical results for the ep collider HERA