13,693 research outputs found
The non-integrability of the Zipoy-Voorhees metric
The low frequency gravitational wave detectors like eLISA/NGO will give us
the opportunity to test whether the supermassive compact objects lying at the
centers of galaxies are indeed Kerr black holes. A way to do such a test is to
compare the gravitational wave signals with templates of perturbed black hole
spacetimes, the so-called bumpy black hole spacetimes. The Zipoy-Voorhees (ZV)
spacetime (known also as the spacetime) can be included in the bumpy
black hole family, because it can be considered as a perturbation of the
Schwarzschild spacetime background. Several authors have suggested that the ZV
metric corresponds to an integrable system. Contrary to this integrability
conjecture, in the present article it is shown by numerical examples that in
general ZV belongs to the family of non-integrable systems.Comment: 10 pages, 13 figure
Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence
The aim of this paper is to prove a Kolmogorov-type result for a
nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time
dependence. The existence of a torus with a prefixed Diophantine frequency is
shown in the forced system, provided that the perturbation is real-analytic and
(exponentially) decaying with time. The advantage consists of the possibility
to choose an arbitrarily small decaying coefficient, consistently with the
perturbation size.Comment: Several corrections in the proof with respect to the previous
version. Main statement unchange
On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators
In this note we study the approach to equilibrium of a chain of anharmonic
oscillators. We find indications that a sufficiently large system always
relaxes to the usual equilibrium distribution. There is no sign of an
ergodicity threshold. The time however to arrive to equilibrium diverges when
, being the anharmonicity.Comment: 8 pages, 5 figure
Strong-coupling behaviour in discrete Kardar-Parisi-Zhang equations
We present a systematic discretization scheme for the Kardar-Parisi-Zhang
(KPZ) equation, which correctly captures the strong-coupling properties of the
continuum model. In particular we show that the scheme contains no finite-time
singularities in contrast to conventional schemes. The implications of these
results to i) previous numerical integration of the KPZ equation, and ii) the
non-trivial diversity of universality classes for discrete models of `KPZ-type'
are examined. The new scheme makes the strong-coupling physics of the KPZ
equation more transparent than the original continuum version and allows the
possibility of building new continuum models which may be easier to analyse in
the strong-coupling regime.Comment: 21 pages, revtex, 2 figures, submitted to J. Phys.
Grover's Quantum Search Algorithm and Diophantine Approximation
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a
quantum computer can find a single marked object in a database of size N by
using only O(N^{1/2}) queries of the oracle that identifies the object. His
result was generalized to the case of finding one object in a subset of marked
elements. We consider the following computational problem: A subset of marked
elements is given whose number of elements is either M or K, M<K, our task is
to determine which is the case. We show how to solve this problem with a high
probability of success using only iterations of Grover's basic step (and no
other algorithm). Let m be the required number of iterations; we prove that
under certain restrictions on the sizes of M and K the estimation m <
(2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and
is known to be optimal up to a constant factor. Our method involves
simultaneous Diophantine approximations, so that Grover's algorithm is
conceptualized as an orbit of an ergodic automorphism of the torus. We comment
on situations where the algorithm may be slow, and note the similarity between
these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change
Energetics of positron states trapped at vacancies in solids
We report a computational first-principles study of positron trapping at
vacancy defects in metals and semiconductors. The main emphasis is on the
energetics of the trapping process including the interplay between the positron
state and the defect's ionic structure and on the ensuing annihilation
characteristics of the trapped state. For vacancies in covalent semiconductors
the ion relaxation is a crucial part of the positron trapping process enabling
the localization of the positron state. However, positron trapping does not
strongly affect the characteristic features of the electronic structure, e.g.,
the ionization levels change only moderately. Also in the case of metal
vacancies the positron-induced ion relaxation has a noticeable effect on the
calculated positron lifetime and momentum distribution of annihilating
electron-positron pairs.Comment: Submitted to Physical Review B on 17 April 2007. Revised version
submitted on 6 July 200
On the Orbit Structure of the Logarithmic Potential
We investigate the dynamics in the logarithmic galactic potential with an
analytical approach. The phase-space structure of the real system is
approximated with resonant detuned normal forms constructed with the method
based on the Lie transform. Attention is focused on the properties of the axial
periodic orbits and of low order `boxlets' that play an important role in
galactic models. Using energy and ellipticity as parameters, we find analytical
expressions of several useful indicators, such as stability-instability
thresholds, bifurcations and phase-space fractions of some orbit families and
compare them with numerical results available in the literature.Comment: To appear on the Astrophysical Journa
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