Physical consequences of P≠\neqNP and the DMRG-annealing conjecture

Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and, thus, these theorems do not apply directly to it. But {\em classical simulations} of physical processes are programs running on Turing machines and, as such, are subject to them. In this work, computational complexity theory is applied to classical simulations of systems performing an adiabatic quantum computation (AQC), based on an annealed extension of the density matrix renormalization group (DMRG). We conjecture that the computational time required for those classical simulations is controlled solely by the {\em maximal entanglement} found during the process. Thus, lower bounds on the growth of entanglement with the system size can be provided. In some cases, quantum phase transitions can be predicted to take place in certain inhomogeneous systems. Concretely, physical conclusions are drawn from the assumption that the complexity classes {\bf P} and {\bf NP} differ. As a by-product, an alternative measure of entanglement is proposed which, via Chebyshev's inequality, allows to establish strict bounds on the required computational time.Comment: Accepted for publication in JSTA

Distortion of Globular Clusters by Galactic Bulges

One of the external fields that influences the population of globular clusters is that due to galactic bulges. In extreme situations, perigalactic distances $r_p \le 100$ pc, globular clusters could suffer total disruption in a single passage. A more common scenario is that for cluster orbits with $r_p \ge 200$ pc. We investigate the effects of tidal forces from a bulge on the shape of globular clusters for this type of encounters. We find distortions characterized by ``twisting isophotes'' and consider the potential for observability of this effect. In the Milky Way, a typical globular cluster must pass within several hundred pc of the center to experience substantial distortion, and it is possible that this has happened recently to one or two present day clusters. We estimate that this distortion could be observed even for globulars in dense fields toward the bulge. In more extreme environments such as giant ellipticals or merger products with newly formed globulars, this effect could be more common, extending out to orbits that pass within 1 kpc of the bulge center. This would lead to a substantial shift in the eccentricity distribution of globulars in those galaxies.Comment: 12 pages, 8 figure

Why, when, and how fast innovations are adopted

When the full stock of a new product is quickly sold in a few days or weeks, one has the impression that new technologies develop and conquer the market in a very easy way. This may be true for some new technologies, for example the cell phone, but not for others, like the blue-ray. Novelty, usefulness, advertising, price, and fashion are the driving forces behind the adoption of a new product. But, what are the key factors that lead to adopt a new technology? In this paper we propose and investigate a simple model for the adoption of an innovation which depends mainly on three elements: the appeal of the novelty, the inertia or resistance to adopt it, and the interaction with other agents. Social interactions are taken into account in two ways: by imitation and by differentiation, i.e., some agents will be inclined to adopt an innovation if many people do the same, but other will act in the opposite direction, trying to differentiate from the "herd". We determine the conditions for a successful implantation of the new technology, by considering the strength of advertising and the effect of social interactions. We find a balance between the advertising and the number of anti-herding agents that may block the adoption of a new product. We also compare the effect of social interactions, when agents take into account the behavior of the whole society or just a part of it. In a nutshell, the present model reproduces qualitatively the available data on adoption of innovation.Comment: 11 pages, 13 figures (with subfigures), full paper (EPJB 2012) on innovation adoption mode

An ADM 3+1 formulation for Smooth Lattice General Relativity

A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve three basic steps. First, the coordinate quantities such as the Riemann and extrinsic curvatures are extracted from the lattice. Second, the 3+1 ADM equations are used to evolve the coordinate data, and finally, the coordinate data is used to update the scalar data on the lattice (such as the leg lengths). The scheme will be presented only for the case of vacuum spacetime though there is no reason why it could not be extended to non-vacuum spacetimes. The scheme allows any choice for the lapse function and shift vectors. An example for the Kasner $T^3$ cosmology will be presented and it will be shown that the method has, for this simple example, zero discretisation error.Comment: 18 pages, plain TeX, 5 epsf figues, gzipped ps file also available at http://newton.maths.monash.edu.au:8000/preprints/3+1-slgr.ps.g

The H=xp model revisited and the Riemann zeros

Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, in average, as the non trivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this paper, we show that the Hamiltonian H = x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet L-functions using different self-adjoint extensions of H. We discuss the relation of our work to Polya's fake zeta function and suggest an experimental realization in terms of the Landau model.Comment: 5 pages, 3 figure

Winding up by a quench: vortices in the wake of rapid Bose-Einstein condensation

A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. We use quantum kinetic theory to show that this mechanism, originally postulated in the cosmological context, and analysed so far only on the mean field classical level, should allow spontaneous generation of vortex lines in trapped Bose-Einstein condensates of simple topology, or of winding number in toroidal condensates.Comment: 4 pages, 2 figures; misprint correcte

Quantification of Linear and Nonlinear Cardiorespiratory Interactions under Autonomic Nervous System Blockade

This paper proposes a methodology to extract both linear and nonlinear respiratory influences from the heart rate variability (HRV), by decomposing the HRV into a respiratory and a residual component. This methodology is based on least-squares support vector machines (LS-SVM) formulated for nonlinear function estimation. From this decomposition, a better estimation of the respiratory sinus arrhythmia (RSA) and the sympathovagal balance (SB) can be achieved. These estimates are first analyzed during autonomic blockade and an orthostatic maneuver, and then compared against the classical HRV and a model that considers only linear interactions. Results are evaluated using surrogate data analysis and they indicate that the classical HRV and the linear model underestimate the cardiorespiratory interactions. Moreover, the linear and nonlinear interactions appear to be mediated by different control mechanisms. These findings will allow to better assess the ANS and to improve the understanding of the interactions within the cardiorespiratory system

Three dimensional numerical relativity: the evolution of black holes

We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing this code, and its performance on massively parallel and vector supercomputers. As a test case, we present evolutions for the first 3D black hole spacetimes. We identify a number of difficulties in evolving 3D black holes and suggest approaches to overcome them. We show how special treatment of the conformal factor can lead to more accurate evolution, and discuss techniques we developed to handle black hole spacetimes in the absence of symmetries. Many different slicing conditions are tested, including geodesic, maximal, and various algebraic conditions on the lapse. With current resolutions, limited by computer memory sizes, we show that with certain lapse conditions we can evolve the black hole to about $t=50M$, where $M$ is the black hole mass. Comparisons are made with results obtained by evolving spherical initial black hole data sets with a 1D spherically symmetric code. We also demonstrate that an ``apparent horizon locking shift'' can be used to prevent the development of large gradients in the metric functions that result from singularity avoiding time slicings. We compute the mass of the apparent horizon in these spacetimes, and find that in many cases it can be conserved to within about 5\% throughout the evolution with our techniques and current resolution.Comment: 35 pages, LaTeX with RevTeX 3.0 macros. 27 postscript figures taking 7 MB of space, uuencoded and gz-compressed into a 2MB uufile. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ and mpeg simulations at http://jean-luc.ncsa.uiuc.edu/Movies/ Submitted to Physical Review

A Wormhole at the core of an infinite cosmic string

We study a solution of Einstein's equations that describes a straight cosmic string with a variable angular deficit, starting with a $2 \pi$ deficit at the core. We show that the coordinate singularity associated to this defect can be interpreted as a traversible wormhole lodging at the the core of the string. A negative energy density gradually decreases the angular deficit as the distance from the core increases, ending, at radial infinity, in a Minkowski spacetime. The negative energy density can be confined to a small transversal section of the string by gluing to it an exterior Gott's like solution, that freezes the angular deficit existing at the matching border. The equation of state of the string is such that any massive particle may stay at rest anywhere in this spacetime. In this sense this is 2+1 spacetime solution.Comment: 1 tex file and 5 eps files. To be Published in Nov. in Phys.Rev.