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