1,052 research outputs found

### Conformal Field Theory of Critical Casimir Interactions in 2D

Thermal fluctuations of a critical system induce long-ranged Casimir forces
between objects that couple to the underlying field. For two dimensional (2D)
conformal field theories (CFT) we derive an exact result for the Casimir
interaction between two objects of arbitrary shape, in terms of (1) the free
energy of a circular ring whose radii are determined by the mutual capacitance
of two conductors with the objects' shape; and (2) a purely geometric energy
that is proportional to conformal charge of the CFT, but otherwise
super-universal in that it depends only on the shapes and is independent of
boundary conditions and other details.Comment: 5 pages, 3 figure

### Renormalization Group Approach to Interacting Crumpled Surfaces: The hierarchical recursion

We study the scaling limit of a model of a tethered crumpled D-dimensional
random surface interacting through an exclusion condition with a fixed impurity
in d-dimensional Euclidean space by the methods of Wilson's renormalization
group. In this paper we consider a hierarchical version of the model and we
prove rigorously the existence of the scaling limit and convergence to a
non-Gaussian fixed point for $1 \leq D0$ sufficiently
small, where $\epsilon = D - (2-D) {d\over 2}$.Comment: 47 pages in simple Latex, PAR-LPTHE 934

### Non-equilibrium forces following quenches in active and thermal matter

Non-equilibrium systems are known to exhibit long-ranged correlations due to
conservation of quantities like density or momentum. This, in turn, leads to
long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a
variety of non-equilibrium settings. Here, we study such forces, which arise
transiently between parallel plates or compact inclusions in a gas of
particles, following a change ("quench") in temperature or activity of the
medium. Analytical calculations, as well as numerical simulations of passive or
active Brownian particles, indicate two distinct forces: (i) The immediate
effect of the quench is adsorption or desorption of particles of the medium to
the immersed objects, which in turn initiates a front of relaxing (mean)
density. This leads to time-dependent {\it density-induced forces}. (ii) A
long-term effect of the quench is that density fluctuations are modified,
manifested as transient (long-ranged) (pair-)correlations that relax
diffusively to their (short-ranged) steady-state limit. As a result, transient
{\it fluctuation-induced forces} emerge. We discuss the properties of
fluctuation-induced and density-induced forces as regards universality,
relaxation as a function of time, and scaling with distance between objects.
Their distinct signatures allow us to distinguish the two types of forces in
simulation data. Finally, we propose several scenarios for their experimental
observation.Comment: - Added Journal reference and DOI - Modified title - Fixed minor
typos - Added plot of Eq. (32) [16 pages, 11 figures

### Renormalization and Hyperscaling for Self-Avoiding Manifold Models

The renormalizability of the self-avoiding manifold (SAM) Edwards model is
established. We use a new short distance multilocal operator product expansion
(MOPE), which extends methods of local field theories to a large class of
models with non-local singular interactions. This validates the direct
renormalization method introduced before, as well as scaling laws. A new
general hyperscaling relation for the configuration exponent gamma is derived.
Manifolds at the Theta-point, and long range Coulomb interactions are briefly
discussed.Comment: 10 pages + 1 figure, TeX + harvmac & epsf (uuencoded file),
SPhT/93-07

### Optimal paths on the road network as directed polymers

We analyze the statistics of the shortest and fastest paths on the road
network between randomly sampled end points. To a good approximation, these
optimal paths are found to be directed in that their lengths (at large scales)
are linearly proportional to the absolute distance between them. This motivates
comparisons to universal features of directed polymers in random media. There
are similarities in scalings of fluctuations in length/time and transverse
wanderings, but also important distinctions in the scaling exponents, likely
due to long-range correlations in geographic and man-made features. At short
scales the optimal paths are not directed due to circuitous excursions governed
by a fat-tailed (power-law) probability distribution.Comment: 5 pages, 7 figure

### Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables

Dynamical heterogeneities -- strong fluctuations near the glass transition --
are believed to be crucial to explain much of the glass transition
phenomenology. One possible hypothesis for their origin is that they emerge
from soft (Goldstone) modes associated with a broken continuous symmetry under
time reparametrizations. To test this hypothesis, we use numerical simulation
data from four glass-forming models to construct coarse grained observables
that probe the dynamical heterogeneity, and decompose the fluctuations of these
observables into two transverse components associated with the postulated
time-fluctuation soft modes and a longitudinal component unrelated to them. We
find that as temperature is lowered and timescales are increased, the time
reparametrization fluctuations become increasingly dominant, and that their
correlation volumes grow together with the correlation volumes of the dynamical
heterogeneities, while the correlation volumes for longitudinal fluctuations
remain small.Comment: v4: Detailed analysis of transverse and longitudinal parts. One
figure removed, two added. v3: Explicit decomposition into transverse and
longitudinal parts, discussion of correlation volumes. One more figure v2:
Modified introduction and forma

### First order wetting of rough substrates and quantum unbinding

Replica and functional renormalization group methods show that, with short
range substrate forces or in strong fluctuation regimes, wetting of a
self-affine rough wall in 2D turns first-order as soon as the wall roughness
exponent exceeds the anisotropy index of bulk interface fluctuations. Different
thresholds apply with long range forces in mean field regimes. For
bond-disordered bulk, fixed point stability suggests similar results, which
ultimately rely on basic properties of quantum bound states with asymptotically
power-law repulsive potentials.Comment: 11 pages, 1 figur

### First Passage Distributions in a Collective Model of Anomalous Diffusion with Tunable Exponent

We consider a model system in which anomalous diffusion is generated by
superposition of underlying linear modes with a broad range of relaxation
times. In the language of Gaussian polymers, our model corresponds to Rouse
(Fourier) modes whose friction coefficients scale as wavenumber to the power
$2-z$. A single (tagged) monomer then executes subdiffusion over a broad range
of time scales, and its mean square displacement increases as $t^\alpha$ with
$\alpha=1/z$. To demonstrate non-trivial aspects of the model, we numerically
study the absorption of the tagged particle in one dimension near an absorbing
boundary or in the interval between two such boundaries. We obtain absorption
probability densities as a function of time, as well as the position-dependent
distribution for unabsorbed particles, at several values of $\alpha$. Each of
these properties has features characterized by exponents that depend on
$\alpha$. Characteristic distributions found for different values of $\alpha$
have similar qualitative features, but are not simply related quantitatively.
Comparison of the motion of translocation coordinate of a polymer moving
through a pore in a membrane with the diffusing tagged monomer with identical
$\alpha$ also reveals quantitative differences.Comment: LaTeX, 10 pages, 8 eps figure

### Patterns in the Kardar-Parisi-Zhang equation

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang
equation for the kinetic growth of an interface in higher dimensions. The weak
noise approach provides a many body picture of a growing interface in terms of
a network of localized growth modes. Scaling in 1d is associated with a gapless
domain wall mode. The method also provides an independent argument for the
existence of an upper critical dimension.Comment: 8 pages revtex, 4 eps figure

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