8,429 research outputs found
Data analysis of gravitational-wave signals from spinning neutron stars. V. A narrow-band all-sky search
We present theory and algorithms to perform an all-sky coherent search for
periodic signals of gravitational waves in narrow-band data of a detector. Our
search is based on a statistic, commonly called the -statistic,
derived from the maximum-likelihood principle in Paper I of this series. We
briefly review the response of a ground-based detector to the
gravitational-wave signal from a rotating neuron star and the derivation of the
-statistic. We present several algorithms to calculate efficiently
this statistic. In particular our algorithms are such that one can take
advantage of the speed of fast Fourier transform (FFT) in calculation of the
-statistic. We construct a grid in the parameter space such that
the nodes of the grid coincide with the Fourier frequencies. We present
interpolation methods that approximately convert the two integrals in the
-statistic into Fourier transforms so that the FFT algorithm can
be applied in their evaluation. We have implemented our methods and algorithms
into computer codes and we present results of the Monte Carlo simulations
performed to test these codes.Comment: REVTeX, 20 pages, 8 figure
Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
Recent advances in Random Matrix Theory enable one to determine the
pseudoscalar decay constant from the response of eigenmodes of quenched
fermions to an imaginary isospin chemical potential. We perform a pilot test of
this idea, from simulations with two flavors of dynamical overlap fermions.Comment: 11 pages, 7 figures, Revte
Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
Folding of the triangular lattice in a discrete three-dimensional space is
investigated by means of the transfer-matrix method. This model was introduced
by Bowick and co-workers as a discretized version of the polymerized membrane
in thermal equilibrium. The folding rule (constraint) is incompatible with the
periodic-boundary condition, and the simulation has been made under the
open-boundary condition. In this paper, we propose a modified constraint, which
is compatible with the periodic-boundary condition; technically, the
restoration of translational invariance leads to a substantial reduction of the
transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the
singularities of the crumpling transitions for a wide range of the bending
rigidity K. We observe a series of the crumpling transitions at K=0.206(2),
-0.32(1), and -0.76(10). At each transition point, we estimate the latent heat
as Q=0.356(30), 0.08(3), and 0.05(5), respectively
Randomizing multi-product formulas for Hamiltonian simulation
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of quantum simulation algorithms are deterministic, a recent surge of ideas has shown that randomization can greatly benefit algorithmic performance. In this work, we introduce a scheme for quantum simulation that unites the advantages of randomized compiling on the one hand and higher-order multi-product formulas, as they are used for example in linear-combination-of-unitaries (LCU) algorithms or quantum error mitigation, on the other hand. In doing so, we propose a framework of randomized sampling that is expected to be useful for programmable quantum simulators and present two new multi-product formula algorithms tailored to it. Our framework reduces the circuit depth by circumventing the need for oblivious amplitude amplification required by the implementation of multi-product formulas using standard LCU methods, rendering it especially useful for early quantum computers used to estimate the dynamics of quantum systems instead of performing full-fledged quantum phase estimation. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth. To corroborate their functioning, we prove rigorous performance bounds as well as the concentration of the randomized sampling procedure. We demonstrate the functioning of the approach for several physically meaningful examples of Hamiltonians, including fermionic systems and the Sachdev–Ye–Kitaev model, for which the method provides a favorable scaling in the effort
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