Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations

Many alternative formulations of Einstein's evolution have lately been examined, in an effort to discover one which yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations, we instead develop analytic tools to discover which formulations are particularly ill-behaved. Specifically, we examine the growth of approximate (geometric-optics) solutions, studied only in the future domain of dependence of the initial data slice (e.g. we study transients). By evaluating the amplification of transients a given formulation will produce, we may therefore eliminate from consideration the most pathological formulations (e.g. those with numerically-unacceptable amplification). This technique has the potential to provide surprisingly tight constraints on the set of formulations one can safely apply. To illustrate the application of these techniques to practical examples, we apply our technique to the 2-parameter family of evolution equations proposed by Kidder, Scheel, and Teukolsky, focusing in particular on flat space (in Rindler coordinates) and Schwarzchild (in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

Experimental study of vapor-cell magneto-optical traps for efficient trapping of radioactive atoms

We have studied magneto-optical traps (MOTs) for efficient on-line trapping of radioactive atoms. After discussing a model of the trapping process in a vapor cell and its efficiency, we present the results of detailed experimental studies on Rb MOTs. Three spherical cells of different sizes were used. These cells can be easily replaced, while keeping the rest of the apparatus unchanged: atomic sources, vacuum conditions, magnetic field gradients, sizes and power of the laser beams, detection system. By direct comparison, we find that the trapping efficiency only weakly depends on the MOT cell size. It is also found that the trapping efficiency of the MOT with the smallest cell, whose diameter is equal to the diameter of the trapping beams, is about 40% smaller than the efficiency of larger cells. Furthermore, we also demonstrate the importance of two factors: a long coated tube at the entrance of the MOT cell, used instead of a diaphragm; and the passivation with an alkali vapor of the coating on the cell walls, in order to minimize the losses of trappable atoms. These results guided us in the construction of an efficient large-diameter cell, which has been successfully employed for on-line trapping of Fr isotopes at INFN's national laboratories in Legnaro, Italy.Comment: 9 pages, 7 figures, submitted to Eur. Phys. J.

Entanglement of two blocks of spins in the critical Ising model

We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and L=2. In the general case, the critical entropy is shown to be additive when d goes to infinity. Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d. This formula is in excellent agreement with numerical results.Comment: published versio

The role of initial conditions in the ageing of the long-range spherical model

The kinetics of the long-range spherical model evolving from various initial states is studied. In particular, the large-time auto-correlation and -response functions are obtained, for classes of long-range correlated initial states, and for magnetized initial states. The ageing exponents can depend on certain qualitative features of initial states. We explicitly find the conditions for the system to cross over from ageing classes that depend on initial conditions to those that do not.Comment: 15 pages; corrected some typo

Entanglement properties of quantum spin chains

We investigate the entanglement properties of a finite size 1+1 dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure

Exact boundary conditions in numerical relativity using multiple grids: scalar field tests

Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy code with an exterior characteristic code connected across a time-like interface, is a promising technique for the generation and extraction of gravitational waves. While it provides a tool for the exact specification of boundary conditions for the Cauchy evolution, it also allows to follow gravitational radiation all the way to infinity, where it is unambiguously defined. We present a new fourth order accurate finite difference CCM scheme for a first order reduction of the wave equation around a Schwarzschild black hole in axisymmetry. The matching at the interface between the Cauchy and the characteristic regions is done by transfering appropriate characteristic/null variables. Numerical experiments indicate that the algorithm is fourth order convergent. As an application we reproduce the expected late-time tail decay for the scalar field.Comment: 14 pages, 5 figures. Included changes suggested by referee

Quantum Quench from a Thermal Initial State

We consider a quantum quench in a system of free bosons, starting from a thermal initial state. As in the case where the system is initially in the ground state, any finite subsystem eventually reaches a stationary thermal state with a momentum-dependent effective temperature. We find that this can, in some cases, even be lower than the initial temperature. We also study lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor change

Dynamic crossover in the global persistence at criticality

We investigate the global persistence properties of critical systems relaxing from an initial state with non-vanishing value of the order parameter (e.g., the magnetization in the Ising model). The persistence probability of the global order parameter displays two consecutive regimes in which it decays algebraically in time with two distinct universal exponents. The associated crossover is controlled by the initial value m_0 of the order parameter and the typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo simulations of the two-dimensional Ising model with Glauber dynamics display clearly this crossover. The measured exponent of the ultimate algebraic decay is in rather good agreement with our theoretical predictions for the Ising universality class.Comment: 5 pages, 2 figure

Entanglement entropy of two disjoint intervals in conformal field theory

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any integer n is calculated as the four-point function of a particular type of twist fields and the final result is expressed in a compact form in terms of the Riemann-Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos corrected and refs adde