H. S. Taylor
University of Southern California, Los Angeles, CA, USA

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Publications (10)6.67 Total impact

  • Chapter: Analysis of Quantum Spectra by Harmonic Inversion
    J. Main, G. Wunner, V. A. Mandelshtam, H. S. Taylor
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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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    Article: Classical, semiclassical, and quantum investigations of the 4-sphere scattering system
    J. Main, E. Atilgan, H. S. Taylor, G. Wunner
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    ABSTRACT: A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional 3-disk system. While in systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods, this situation can be reversed with increasing dimension of the problem. For the 4-sphere system with large separations between the spheres, we demonstrate the superiority of semiclassical versus quantum calculations, i.e., semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. The 4-sphere system with touching spheres is a challenging problem for both quantum and semiclassical techniques. Here, semiclassical resonances are obtained via harmonic inversion of a cross-correlated periodic orbit signal. Comment: 12 pages, 5 figures, submitted to Phys. Rev. E
    11/2003;
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    Article: Superiority of semiclassical over quantum mechanical calculations for a three-dimensional system
    J. Main, G. Wunner, E. Atilgan, H. S. Taylor, P. A. Dando
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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
    09/2002;
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    Article: Decimated Signal Diagonalization for Fourier Transform Spectroscopy
    Dž. Belkić, P. A. Dando, J. Main, H. S. Taylor, S. K. Shin
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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.
    11/2000;
  • Article: Decimation and Harmonic Inversion of Periodic Orbit Signals
    J. Main, D Z Belki C, 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 Pad e 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. 1. Introduction The semiclassical quantization of systems with an underlying chaotic classical dynamics is a nontrivial problem due to the fact that Gutzwiller's trace formula [1, 2] does not usually converge in those regions where the eigenenergies or resonances are located. Various techniques ...
    03/2000;
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    Article: Decimation and Harmonic Inversion of Periodic Orbit Signals
    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
    12/1999;
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    Article: Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums
    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
    09/1999;
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    Article: Harmonic inversion as a general method for periodic orbit quantization
    J. Main, V. A. Mandelshtam, G. Wunner, H. S. Taylor
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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
    09/1997;
  • Article: Extraction of dynamics from the resonance structure of HeH2+ spectra
    V. A. Mandelshtam, H. S. Taylor, Christof Jung, H. F. Bowen, Donald J. Kouri
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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. · 3.33 Impact Factor
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    Article: Resonance positions and widths by complex scaling and modified stabilization methods: van der Waals complex NeICl
    Victor Ryaboy, Nimrod Moiseyev, V. A. Mandelshtam, H. S. Taylor
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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. · 3.33 Impact Factor

Institutions

  • 1994–2007
    • University of Southern California
      • Department of Chemistry
      Los Angeles, CA, USA
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