H. S. Taylor

University of Southern California, Los Angeles, CA, United States

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Publications (22)58.55 Total impact

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    ABSTRACT: We have shown that interesting physical phenomena can be revealed in high resolution quantum recurrence spectra by application of the harmonic inversion technique, thereby circumventing the restrictions imposed by the uncertainty principle of the conventional Fourier transform. The method allows, e.g., to test the validity of semiclassical theories, to identify hidden ghost or bits in the quantum spectra, and to observe the symmetry breaking in the spectra of the hydrogen atom in crossed magnetic and electric fields. The analysis has been demonstrated here on theoretically calculated quantum spectra but can be applied to experimental spectra as well.
    08/2007: pages 215-221;
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    ABSTRACT: In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a three-dimensional system, viz. the hyperbolic four-sphere scattering system, we demonstrate the superiority of semiclassical versus quantum calculations. Semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. Comment: 10 pages, 1 figure, submitted to Phys. Lett. A
    Physics Letters A 09/2002; · 1.63 Impact Factor
  • The Journal of Physical Chemistry A 01/2001; 105:514. · 2.77 Impact Factor
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    ABSTRACT: A nonlinear parameter estimator with frequency-windowing for signal processing, called Decimated Signal Diagonalization (DSD), is presented. This method is used to analyze exponentially damped time signals of arbitrary length corresponding to spectra that are sums of pure Lorentzians. Such time signals typically arise in many experimental measurements, e.g., ion cyclotron resonance (ICR), nuclear magnetic resonance or Fourier transform infrared spectroscopy, etc. The results are compared with the standard spectral estimator, the Fast Fourier Transform (FFT). It is shown that the needed absorption spectra can be constructed simply, without any supplementary experimental work or concern about the phase problems that are known to plague FFT. Using a synthesized signal with known parameters, as well as experimentally measured ICR time signals, excellent results are obtained by DSD with significantly shorter acquisition time than that which is needed with FFT. Moreover, for the same signal length, DSD is demonstrated to exhibit a better resolving power than FFT.
    The Journal of Physical Chemistry A 11/2000; 105(2). · 2.77 Impact Factor
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    Dž. Belkić, P. A. Dando, J. Main, H. S. Taylor
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    ABSTRACT: Three novel nonlinear parameter estimators are devised and implemented for accurate and fast processing of experimentally measured or theoretically generated time signals of arbitrary length. The new techniques can also be used as powerful tools for diagonalization of large matrices that are customarily encountered in quantum chemistry and elsewhere. The key to the success and the common denominator of the proposed methods is a considerably reduced dimensionality of the original data matrix. This is achieved in a preprocessing stage called beamspace windowing or band-limited decimation. The methods are decimated signal diagonalization (DSD), decimated linear predictor (DLP), and decimated Padé approximant (DPA). Their mutual equivalence is shown for the signals that are modeled by a linear combination of time-dependent damped exponentials with stationary amplitudes. The ability to obtain all the peak parameters first and construct the required spectra afterwards enables the present methods to phase correct the absorption mode. Additionally, a new noise reduction technique, based upon the stabilization method from resonance scattering theory, is proposed. The results obtained using both synthesized and experimental time signals show that DSD/DLP/DPA exhibit an enhanced resolution power relative to the standard fast Fourier transform. Of the three methods, DPA is found to be the most efficient computationally.
    The Journal of Chemical Physics 10/2000; 113(16). · 3.12 Impact Factor
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    J. Main, P. A. Dando, Dz. Belkic, H. S. Taylor
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    ABSTRACT: We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. In a second step, the frequencies and amplitudes of the decimated signal are determined by either Decimated Linear Predictor, Decimated Pade Approximant, or Decimated Signal Diagonalization. These techniques, which would have been numerically unstable without the windowing, provide numerically more accurate semiclassical spectra than does the filter-diagonalization method. Comment: 22 pages, 3 figures, submitted to J. Phys. A
    Journal of Physics A General Physics 12/1999;
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    J. Main, P. A. Dando, Dz. Belkic, H. S. Taylor
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    ABSTRACT: Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard. Comment: 7 pages, 3 figures, submitted to Europhys. Lett
    EPL (Europhysics Letters) 09/1999; · 2.26 Impact Factor
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    ABSTRACT: We calculated all 3170 A1 and B2 (J = 0) vibronic bound states of the coupled electronic ground ( 2A1) and the first excited ( 2B2) surfaces of NO2, using a modification of the ab initio potentials of Leonardi et al. [J. Chem. Phys. 105, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated from a DVR Hamiltonian in Radau coordinates. The rms error of the eigenenergies is about 2.5 cm−1, corresponding to a relative error of 10−4 near the dissociation energy. The results are compared with the adiabatic and diabatic levels calculated from the same surfaces, with experimental data, and with some approximations for the number of states function N(E). The experimental levels are reproduced fairly well up to an energy of 12 000 cm−1 above the potential minimum while the total number of bound levels agrees to within 2% with that calculated from the phase space volume. © 1999 American Institute of Physics.
    The Journal of Chemical Physics 02/1999; 110(8):3756-3764. · 3.12 Impact Factor
  • D. Belkic, P.A. Dando, H.S. Taylor, J. Main
    Chemical Physics Letters 01/1999; 315(1). · 2.15 Impact Factor
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    ABSTRACT: We calculated all 2967 even and odd bound states of the adiabatic ground state of NO2, using a modification of the ab initio potential energy surface of Leonardi et al. [J. Chem. Phys. 105, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated by a DVR Hamiltonian in Radau coordinates. The relative error for the computed eigenenergies (measured from the potential minimum), is 10−4 or better, corresponding to an absolute error of less than about 2.5 cm−1. Near the dissociation threshold the average density of states is about 0.2/cm−1 for each symmetry. Statistical analysis of the states shows some interesting structure of the rigidity parameter Δ3 as a function of energy. © 1998 American Institute of Physics.
    The Journal of Chemical Physics 07/1998; 109(3):937-941. · 3.12 Impact Factor
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    ABSTRACT: We calculated all 2967 even and odd bound states of the adiabatic ground state of NO_2, using a modification of the ab initio potential energy surface of Leonardi et al. [J. Chem. Phys. 105, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated by a DVR Hamiltonian in Radau coordinates. The relative error for the computed eigenenergies is $10^{-4}$ or better. Near the dissociation threshold the density of states is about 0.3cm$^{-1}$. Statistical analysis of the states shows some interesting structure of the rigidity parameter $\Delta_3$ as a function of energy.
    01/1998;
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    ABSTRACT: In semiclassical theories for chaotic systems such as Gutzwiller's periodic orbit theory the energy eigenvalues and resonances are obtained as poles of a non-convergent series g(w)=sum_n A_n exp(i s_n w). We present a general method for the analytic continuation of such a non-convergent series by harmonic inversion of the "time" signal, which is the Fourier transform of g(w). We demonstrate the general applicability and accuracy of the method on two different systems with completely different properties: the Riemann zeta function and the three disk scattering system. The Riemann zeta function serves as a mathematical model for a bound system. We demonstrate that the method of harmonic inversion by filter-diagonalization yields several thousand zeros of the zeta function to about 12 digit precision as eigenvalues of small matrices. However, the method is not restricted to bound and ergodic systems, and does not require the knowledge of the mean staircase function, i.e., the Weyl term in dynamical systems, which is a prerequisite in many semiclassical quantization conditions. It can therefore be applied to open systems as well. We demonstrate this on the three disk scattering system, as a physical example. The general applicability of the method is emphasized by the fact that one does not have to resort a symbolic dynamics, which is, in turn, the basic requirement for the application of cycle expansion techniques. Comment: 29 pages, 4 figures, LATEX (IOP-style), revised version submitted to Nonlinearity
    Nonlinearity 09/1997; · 1.60 Impact Factor
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    J. Main, V. A. Mandelshtam, H. S. Taylor
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    ABSTRACT: Highly resolved recurrence spectra are obtained by harmonic inversion of quantum spectra of classically chaotic systems and compared in detail to the results of semiclassical {ital periodic orbit} and {ital closed orbit} theory. Our analysis is sensitive to separate orbits with nearly degenerate recurrence periods and uncovers complex ({open_quotes}ghost{close_quotes}) orbits even when they are hidden behind close-by real orbits. The method is demonstrated on an example of the hydrogen atom in external magnetic and electric fields, for both the density of states and the quantum photoabsorption cross section. {copyright} {ital 1997} {ital The American Physical Society}
    Physical Review Letters 01/1997; 78(23). · 7.73 Impact Factor
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    ABSTRACT: Two relatively new methods, the spectral projection method and the stabilization method, of implementing scattering calculations are described, and are here applied to two devices. Both methods use essentially short range spectral projection operators to produce a complete set of solutions of the wave equation that need be valid only inside the interaction region. While the spectral projection method is more generic than the stabilization method which is based on using the more difficult to compute spectral density operator, the latter becomes very efficient when narrow resonances exist. For problems of small size both methods are practical in the sense that they involve only real, symmetric matrices resulting from Hamiltonians represented onL2basis sets. For more challenging larger systems the spectral projection method lends itself to a very efficient time independent iterative procedure that obtains results simultaneously at all energies. This procedure uses modified Chebyshev recursion relations to essentially expand the operator (E−H)−1. It requires minimal storage and the resulting series converges rapidly in a manner that is uniform in energy.
    Superlattices and Microstructures 06/1996; 20(1):87–104. · 1.98 Impact Factor
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    ABSTRACT: For the reaction of He with H2+, starting with accurate theoretically computed reactive, elastic, and inelastic scattering data that reveals many complex unassignable narrow resonances, the detailed motions governing the dynamics of the tight transition state are extracted. Methods ranging from scattering theory, the stabilization theory of dynamics, nonlinear dynamic periodic orbit theory, and hierarchical smoothing theory which was developed to study complex ‘‘chaotic’’ spectra, are all used in the analysis. Relationships between the doorway model of nuclear physics, aspects of transition state theory, and models of nonlinear chaotic dynamics are pointed out and used to shed light on the fact that the complex resonance structure observed is one quantum manifestation of classical transient chaos in scattering processes. The transition (or doorway) state corresponds to the only populous and robust periodic orbit or set of similar periodic orbits whose motion allows the types of energy transfers necessary to go from reactants to products. Wave packet motion and quantum eigenfunctions are influenced by these periodic orbits. © 1995 American Institute of Physics.
    The Journal of Chemical Physics 05/1995; 102(20):7988-8000. · 3.12 Impact Factor
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    ABSTRACT: For the purposes of computing resonance parameters an alternative version of the stabilization method is used in a simpler way than previously reported [V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, Phys. Rev. Lett. 70, 1932 (1993)]. The method is based on the calculation of the eigenphase sum, which, as is shown, can be extracted easily from a stabilization diagram.
    Physical Review A 10/1994; 50(3):2764-2766. · 3.04 Impact Factor
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    ABSTRACT: The discrete variable representation (DVR) formulation of the complex coordinate method as has been used for calculating several resonances of NeICl [J. Chem. Phys. 98, 1888 (1993)], and a modified version of the recent developed stabilization method [Phys. Rev. Lett. 70, 1932 (1993)] are used for calculating all 30 isolated narrow resonances of NeICl (B, ν=2). The two L2 methods require a similar computational effort. The modified stabilization method requires the calculations of eigenvalues of real and symmetric Hamiltonian matrices in a sequence of ever larger enclosing boxes. The complex DVR method requires the use of complex arithmetic and calculations of eigenvalues of complex symmetrical matrices.
    The Journal of Chemical Physics 09/1994; 101(7):5677-5682. · 3.12 Impact Factor
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    ABSTRACT: A new method of doing scattering calculations is presented and illustrated. Reactive state‐to‐state transition amplitudes, microcanonical rate, resonance parameters, and related quantities are computed for the collinear H+H2→H2+H exchange reaction. The method only involves diagonalizations of a real symmetric system Hamiltonian placed in a series of enclosing boxes.
    The Journal of Chemical Physics 01/1994; 101:8792-8799. · 3.12 Impact Factor
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    ABSTRACT: A conceptually simple and computationally economical, scrL2-discrete-basis-set stabilization method of computing a spectral density as a function of energy is presented. Photoabsorbtion to the continuum is emphasized in examples of model problems. The use of the method for computing rates and state-dependent cross sections is sketched. Traditional scattering solutions are avoided, as are dilatation analytic, imaging, and absorbing-potential techniques.
    Physical Review A 08/1993; 48(1):818-821. · 3.04 Impact Factor
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    ABSTRACT: The stabilization method is used to calculate the density of resonance states and when applied to isolated resonances yields a most simple method for extracting the resonance energy and width.
    Physical Review Letters 04/1993; 70(13):1932-1935. · 7.73 Impact Factor