26,485 research outputs found
Analysis of Modulated Multivariate Oscillations
The concept of a common modulated oscillation spanning multiple time series
is formalized, a method for the recovery of such a signal from potentially
noisy observations is proposed, and the time-varying bias properties of the
recovery method are derived. The method, an extension of wavelet ridge analysis
to the multivariate case, identifies the common oscillation by seeking, at each
point in time, a frequency for which a bandpassed version of the signal obtains
a local maximum in power. The lowest-order bias is shown to involve a quantity,
termed the instantaneous curvature, which measures the strength of local
quadratic modulation of the signal after demodulation by the common oscillation
frequency. The bias can be made to be small if the analysis filter, or wavelet,
can be chosen such that the signal's instantaneous curvature changes little
over the filter time scale. An application is presented to the detection of
vortex motions in a set of freely-drifting oceanographic instruments tracking
the ocean currents
On the absence of chiral fermions in interacting lattice theories
We consider interacting theories with a compact internal symmetry group on a
regular lattice. We show that the spectrum is necessarily vector-like provided
the following conditions are satisfied: (a)~weak form of locality,
(b)~relativistic continuum limit without massless bosons, and (c)~pole-free
effective vertex functions for conserved currents.
The proof exploits the zero frequency inverse retarded propagator of an
appropriate set of interpolating fields as an effective quadratic hamiltonian,
to which the Nielsen-Ninomiya theorem is applied.
The main results of this paper have been reported in WIS-93/56-JUNE-PH,
hep-lat/9306023.Comment: WIS-93/57-JULY-PH, LaTeX, 24 page
Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems
Harmonic inversion has already been proven to be a powerful tool for the
analysis of quantum spectra and the periodic orbit orbit quantization of
chaotic systems. The harmonic inversion technique circumvents the convergence
problems of the periodic orbit sum and the uncertainty principle of the usual
Fourier analysis, thus yielding results of high resolution and high precision.
Based on the close analogy between periodic orbit trace formulae for regular
and chaotic systems the technique is generalized in this paper for the
semiclassical quantization of integrable systems. Thus, harmonic inversion is
shown to be a universal tool which can be applied to a wide range of physical
systems. The method is further generalized in two directions: Firstly, the
periodic orbit quantization will be extended to include higher order hbar
corrections to the periodic orbit sum. Secondly, the use of cross-correlated
periodic orbit sums allows us to significantly reduce the required number of
orbits for semiclassical quantization, i.e., to improve the efficiency of the
semiclassical method. As a representative of regular systems, we choose the
circle billiard, whose periodic orbits and quantum eigenvalues can easily be
obtained.Comment: 21 pages, 9 figures, submitted to Eur. Phys. J.
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