Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions

We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed.Comment: 4 pages, one figure, revised versio

Numerical indications of a q-generalised central limit theorem

We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called $q$-product with $q \le 1$. We show that, in the large $N$ limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are $q_e$-Gaussians, i.e., $p(x) \propto [1-(1-q_e) \beta(N) x^2]^{1/(1-q_e)}$, with $q_e=2-\frac{1}{q}$, and with coefficients $\beta(N)$ approaching finite values $\beta(\infty)$. The particular case $q=q_e=1$ recovers the celebrated de Moivre-Laplace theorem.Comment: Minor improvements and corrections have been introduced in the new version. 7 pages including 4 figure

Local entanglement generation in the adiabatic regime

We study entanglement generation in a pair of qubits interacting with an initially correlated system. Using time independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theory. We then apply these results to the case of qubits interacting with a scalar quantum field. We study three different variations of this setup; a quantum field subject to Dirichlet boundary conditions, a quantum field interacting with a classical potential and a quantum field that starts in a thermal state.Comment: 9 pages, 6 figures. v2: reference [14] adde

Universality in Random Walk Models with Birth and Death

Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions $D\neq 2,~4$. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. Implications for the adsorption transition of polymers at curved interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure

Percolation model for nodal domains of chaotic wave functions

Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolation-like model for description of these nodal domains which permits to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way of deeper understanding of the structure of chaotic wave functions.Comment: 4 pages, 6 figures, Late

MODELLING THE ELECTRON WITH COSSERAT ELASTICITY

Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body–fluid interaction holding for the case of many bodies