Role of the sampling weight in evaluating classical time autocorrelation functions

We analyze how the choice of the sampling weight affects the efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phase-space density. In contrast, it is shown that the computational cost of the "standard" intuitive algorithm which samples directly from the phase-space density may scale exponentially with the number of degrees of freedom. Yet, for the stationary Gaussian distribution of harmonic systems and for the autocorrelation function of a linear function of phase-space coordinates, the computational cost of this standard algorithm is also independent of dimensionality.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data

In this paper, I propose a technique for recovering quantum dynamical information from imaginary-time data via the resolution of a one-dimensional Hamburger moment problem. It is shown that the quantum autocorrelation functions are uniquely determined by and can be reconstructed from their sequence of derivatives at origin. A general class of reconstruction algorithms is then identified, according to Theorem 3. The technique is advocated as especially effective for a certain class of quantum problems in continuum space, for which only a few moments are necessary. For such problems, it is argued that the derivatives at origin can be evaluated by Monte Carlo simulations via estimators of finite variances in the limit of an infinite number of path variables. Finally, a maximum entropy inversion algorithm for the Hamburger moment problem is utilized to compute the quantum rate of reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.

A Monte-Carlo Approach to Zero Energy Quantum Scattering

Monte-Carlo methods for zero energy quantum scattering are developed. Starting from path integral representations for scattering observables, we present results of numerical calculations for potential scattering and scattering off a schematic $^4 \rm He$ nucleus. The convergence properties of Monte-Carlo algorithms for scattering systems are analyzed using stochastic differential equation as a path sampling method.Comment: 30 pages, LaTeX, 8 (uuencoded, tared and gziped) postscript figure

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure

Lattice QCD without topology barriers

As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.Comment: Plain TeX source, 26 pages, 4 figures include

On line power spectra identification and whitening for the noise in interferometric gravitational wave detectors

In this paper we address both to the problem of identifying the noise Power Spectral Density of interferometric detectors by parametric techniques and to the problem of the whitening procedure of the sequence of data. We will concentrate the study on a Power Spectral Density like the one of the Italian-French detector VIRGO and we show that with a reasonable finite number of parameters we succeed in modeling a spectrum like the theoretical one of VIRGO, reproducing all its features. We propose also the use of adaptive techniques to identify and to whiten on line the data of interferometric detectors. We analyze the behavior of the adaptive techniques in the field of stochastic gradient and in the Least Squares ones.Comment: 28 pages, 21 figures, uses iopart.cls accepted for pubblication on Classical and Quantum Gravit

User's guide to Monte Carlo methods for evaluating path integrals

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings