Lattice gas with ``interaction potential''

We present an extension of a simple automaton model to incorporate non-local interactions extending over a spatial range in lattice gases. {}From the viewpoint of Statistical Mechanics, the lattice gas with interaction range may serve as a prototype for non-ideal gas behavior. {}From the density fluctuations correlation function, we obtain a quantity which is identified as a potential of mean force. Equilibrium and transport properties are computed theoretically and by numerical simulations to establish the validity of the model at macroscopic scale.Comment: 12 pages LaTeX, figures available on demand ([email protected]

Mean field and corrections for the Euclidean Minimum Matching problem

Consider the length $L_{MM}^E$ of the minimum matching of N points in d-dimensional Euclidean space. Using numerical simulations and the finite size scaling law $= \beta_{MM}^E(d) N^{1-1/d}(1+A/N+... )$, we obtain precise estimates of $\beta_{MM}^E(d)$ for $2 \le d \le 10$. We then consider the approximation where distance correlations are neglected. This model is solvable and gives at $d \ge 2$ an excellent ``random link'' approximation to $\beta_{MM}^E(d)$. Incorporation of three-link correlations further improves the accuracy, leading to a relative error of 0.4% at d=2 and 3. Finally, the large d behavior of this expansion in link correlations is discussed.Comment: source and one figure. Submitted to PR

Statistical mechanics of error exponents for error-correcting codes

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.Comment: 32 pages, 13 figure

Conformal diagrams for the gravitational collapse of a spherical dust cloud

We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of the radial null geodesics and a local analysis of their behavior close to the singularity. As an application, we consider a collapsing spherical dust cloud, generate the corresponding conformal diagram and analyze the structure of the resulting singularity. A new bound on the initial data which guarantees that the singularity is visible from future null infinity is also obtained.Comment: added a new subsection with a phase space analysis, 23 pages, 8 figure

Kerr non-linearity in a superconducting Josephson metamaterial

We present a detailed experimental and theoretical analysis of the dispersion and non-linear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 SQUIDs in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalisation of the bare frequencies and the long-range nature of the island charge screening by a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measured Kerr coefficients with theory and find good agreement

Quantum interference of ultrastable twin optical beams

We report the first measurement of the quantum phase-difference noise of an ultrastable nondegenerate optical parametric oscillator that emits twin beams classically phase-locked at exact frequency degeneracy. The measurement illustrates the property of a lossless balanced beam-splitter to convert number-difference squeezing into phase-difference squeezing and, thus, provides indirect evidence for Heisenberg-limited interferometry using twin beams. This experiment is a generalization of the Hong-Ou-Mandel interference effect for continuous variables and constitutes a milestone towards continuous-variable entanglement of bright, ultrastable nondegenerate beams.Comment: 4 pages, 4 figs, accepted by Phys. Rev. Let

Star Formation Near Photodissociation Regions: Detection of a Peculiar Protostar Near Ced 201

We present the detection and characterization of a peculiar low-mass protostar (IRAS 22129+7000) located ~0.4 pc from Ced 201 Photodissociation Region (PDR) and ~0.2 pc from the HH450 jet. The cold circumstellar envelope surrounding the object has been mapped through its 1.2 mm dust continuum emission with IRAM-30m/MAMBO. The deeply embedded protostar is clearly detected with Spitzer/MIPS (70 um), IRS (20-35 um) and IRAC (4.5, 5.8, and 8 um) but also in the K_s band (2.15 um). Given the large "near- and mid-IR excess" in its spectral energy distribution, but large submillimeter-to-bolometric luminosity ratio (~2%), IRAS 22129+7000 must be a transition Class 0/I source and/or a multiple stellar system. Targeted observations of several molecular lines from CO, 13CO, C18O, HCO+ and DCO+ have been obtained. The presence of a collimated molecular outflow mapped with the CSO telescope in the CO J=3-2 line suggests that the protostar/disk system is still accreting material from its natal envelope. Indeed, optically thick line profiles from high density tracers such as HCO+ J=1-0 show a red-shifted-absorption asymmetry reminiscent of inward motions. We construct a preliminary physical model of the circumstellar envelope (including radial density and temperature gradients, velocity field and turbulence) that reproduces the observed line profiles and estimates the ionization fraction. The presence of both mechanical and (non-ionizing) FUV-radiative input makes the region an interesting case to study triggered star formation

Finite geometries and diffractive orbits in isospectral billiards

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.Comment: 10 page