Infinite Invariant Density Determines Statistics of Time Averages for Weak Chaos

Weakly chaotic non-linear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and non-integrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of non-integrable observables, for example the time average position of the particle. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem.Comment: 5 pages, 3 figure

The Computational Power of Minkowski Spacetime

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.Comment: 6 pages, LaTeX, feedback welcom

The relationship between quality of life (EORTC QLQ-C30) and survival in patients with gastro-oesopohageal cancer

It remains unclear whether any aspect of quality of life has a role in predicting survival in an unselected cohort of patients with gastro-oesophageal cancer. Therefore the aim of the present study was to examine the relationship between quality of life (EORTC QLQ-C30), clinico-pathological characteristics and survival in patients with gastro-oesophageal cancer. Patients presenting with gastric or oesophageal cancer, staged using the UICC tumour node metastasis (TNM) classification and who received either potentially curative surgery or palliative treatment between November 1997 and December 2002 (n=152) participated in a quality of life study, using the EORTC QLQ-C30 core questionnaire. On univariate analysis, age (P < 0.01), tumour length (P < 0.0001), TNM stage (P<0.0001), weight loss (P<0.0001), dysphagia score (P<0.001), performance status (P<0.1) and treatment (P<0.0001) were significantly associated with cancer-specific survival. EORTC QLQ-C30, physical functioning (P<0.0001), role functioning (P<0.001), cognitive functioning (P<0.01), social functioning (P<0.0001), global quality of life (P<0.0001), fatigue (P<0.0001), nausea/vomiting (P<0.01), pain (P<0.001), dyspnoea (P<0.0001), appetite loss (P<0.0001) and constipation (P<0.05) were also significantly associated with cancer-specific survival. On multivariate survival analysis, tumour stage (P<0.0001), treatment (P<0.001) and appetite loss (P<0.0001) were significant independent predictors of cancer-specific survival. The present study highlights the importance of quality of life (EORTC QLQ-C30) measures, in particular appetite loss, as a prognostic factor in these patients

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

Spatial search by quantum walk

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fail

The Bulk Motion of Flat Edge-On Galaxies Based on 2MASS Photometry

We report the results of applying the 2MASS Tully-Fisher (TF) relations to study the galaxy bulk flows. For 1141 all-sky distributed flat RFGC galaxies we construct J, H, K_s TF relations and find that Kron $J_{fe}$ magnitudes show the smallest dispersion on the TF diagram. For the sample of 971 RFGC galaxies with V_{3K} < 18000 km/s we find a dispersion $\sigma_{TF}=0.42^m$ and an amplitude of bulk flow V= 199 +/-61 km/s, directed towards l=301 degr +/-18 degr, b=-2 degr +/-15 degr. Our determination of low-amplitude coherent flow is in good agreement with a set of recent data derived from EFAR, PSCz, SCI/SCII samples. The resultant two- dimensional smoothed peculiar velocity field traces well the large-scale density variations in the galaxy distributions. The regions of large positive peculiar velocities lie in the direction of the Great Attractor and Shapley concentration. A significant negative peculiar velocity is seen in the direction of Bootes and in the direction of the Local void. A small positive peculiar velocity (100 -- 150 km/s) is seen towards the Pisces-Perseus supercluster, as well as the Hercules - Coma - Corona Borealis supercluster regions.Comment: 10 pages, 5 figures. A&A/2003/3582 accepted 15.05.200

Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.Comment: 4 pages, 3 eps figure

Quantum Algorithm for Molecular Properties and Geometry Optimization

It is known that quantum computers, if available, would allow an exponential decrease in the computational cost of quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.Comment: 6 page

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