Entanglement and particle correlations of Fermi gases in harmonic traps

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.Comment: 15 pages, 22 fig

The uniformly frustrated two-dimensional XY model in the limit of weak frustration

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array, in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behaviour of the XY model for T <= T_{KT}, where T_{KT} is the Kosterlitz-Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behaviour of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations.Comment: 12 page

Probing for local activity-related modulation of the infrared backscattering of the brain cortex

The possibility to measure the metabolic activity of the brain cortex, with submillimeter spatial and subsecond temporal resolution, would open up enticing scenarios in addressing basic issues on the relation between different structural components of brain signal processing, and in providing an operational pathway to interaction with (dis)functional signal patterns. In the present article, we report the description of a simple system that allows the detection of the minute changes that occur in the optical backscattering of the cortex as a metabolic response to external stimuli. The simplicity of the system is compatible with scalability to an implantable probe. We validate the system on an animal model, and we propose an algorithm to extract meaningful data from the measured signal. We thus show the detection of individual haemodynamic cortical responses to individual stimulation events, and we provide operational considerations on the signal structure

Static and dynamic structure factors in three-dimensional randomly diluted Ising models

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.Comment: 43 page

Large-N phase transition in lattice 2-d principal chiral models

We investigate the large-N critical behavior of 2-d lattice chiral models by Monte Carlo simulations of U(N) and SU(N) groups at large N. Numerical results confirm strong coupling analyses, i.e. the existence of a large-N second order phase transition at a finite $\beta_c$.Comment: 12 pages, Revtex, 8 uuencoded postscript figure

The critical behavior of 3D Ising glass models: universality and scaling corrections

We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin-glass models: the +-J Ising model for two values of the disorder parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for bond-occupation probability p_b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent omega related to the leading irrelevant operator, omega=1.0(1). We also determine the critical exponents nu and eta. Taking into account the scaling corrections, we obtain nu=2.53(8) and eta=-0.384(9).Comment: 9 pages, published versio

Crossover scaling from classical to nonclassical critical behavior

We study the crossover between classical and nonclassical critical behaviors. The critical crossover limit is driven by the Ginzburg number G. The corresponding scaling functions are universal with respect to any possible microscopic mechanism which can vary G, such as changing the range or the strength of the interactions. The critical crossover describes the unique flow from the unstable Gaussian to the stable nonclassical fixed point. The scaling functions are related to the continuum renormalization-group functions. We show these features explicitly in the large-N limit of the O(N) phi^4 model. We also show that the effective susceptibility exponent is nonmonotonic in the low-temperature phase of the three-dimensional Ising model.Comment: 5 pages, final version to appear in Phys. Rev.

Strong coupling expansion of chiral models

A general precedure is outlined for an algorithmic implementation of the strong coupling expansion of lattice chiral models on arbitrary lattices. A symbolic character expansion in terms of connected values of group integrals on skeleton diagrams may be obtained by a fully computerized approach.Comment: 2 pages, PostScript file, contribution to conference LATTICE '9