[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] ABSTRACT: The many-body Green's function theory of Yarlagadda and Taylor (1975) is applied in the lowest order to the coincident ionization of the helium atom. Significant agreement is obtained with the experimental results of Ehrhardt and coworkers (1972). The success of the two-time model of inelastic processes is demonstrated.
Journal of Physics B Atomic and Molecular Physics 01/2001; 9(5):829. DOI:10.1088/0022-3700/9/5/025
[Show abstract][Hide abstract] ABSTRACT: The stabilisation method is used to compute the resonant states of HCl -. Resonant states of HCl- that dissociate to H -+Cl and Cl-+H are found as well as those that dissociate to H+Cl+e. The totality of these states explain all the known qualitative and threshold features of vibrational excitation, dissociative attachment and associative detachment without doing rigorous electron-polar-molecule scattering computations. The computations were carried out using Gaussian orbitals and SCF+CI methods.
Journal of Physics B Atomic and Molecular Physics 01/2001; 10(11):2253. DOI:10.1088/0022-3700/10/11/025
[Show abstract][Hide abstract] 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). DOI:10.1063/1.1310612 · 2.95 Impact Factor
[Show abstract][Hide abstract] 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 Padé 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.
Journal of Physics A General Physics 12/1999; 33(6). DOI:10.1088/0305-4470/33/6/311
[Show abstract][Hide abstract] 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
[Show abstract][Hide abstract] ABSTRACT: A procedure based on the rotated-coordinate method (RCM) is proposed to obtain widths for the decay of resonance into individual channels and it is demonstrated for a simple model potential.
Journal of Physics B Atomic and Molecular Physics 12/1998; 13(12):L377. DOI:10.1088/0022-3700/13/12/005
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] ABSTRACT: New methods of high resolution spectral analysis of short time signals are presented. These methods utilize the filter-diagonalization approach of Wall and Neuhauser [J. Chem. Phys. 102, 8011 (1995)] that extracts the complex frequencies w k and amplitudes d k from a signal C(t) = Σ kd ke -itωk in a small frequency interval by recasting the harmonic inversion problem as the one of a small matrix diagonalization. The present methods are rigorously adapted to the conventional case of the signal available on a sparse equidistant time grid and use a more efficient boxlike filter. Various applications are discussed, such as iterative diagonalization of large Hamiltonian matrices for calculating bound and resonance states, scattering calculations in the presence of narrow resonances, etc. For the scattering problem the harmonic inversion is directly applied to the signal c n=(X fT n(Ĥ)X i), generated by the dynamical system governed by a modified Chebyshev recursion, avoiding the usual recasting the problem to the time domain. Some challenging numerical examples are presented. The general filter-diagonalization method is shown to be stable and efficient for the extraction of thousands of complex frequencies ω k and amplitudes d k from a signal. When the model signal is "spoiled" by a moderate amount of an additive Gaussian noise the obtained spectral estimate is still superior to the conventional Fourier spectrum.
[Show abstract][Hide abstract] 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. DOI:10.1006/spmi.1996.0053 · 2.10 Impact Factor
[Show abstract][Hide abstract] 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 11/1994; 101(10):8792-8799. DOI:10.1063/1.468072 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An alternative formalism that diagonalizes the system Hamiltonian in ever larger boxes is shown to yield, for any Hermitian Hamiltonian and in particular a time-periodic Hamiltonian, all the observables sought by generic non-scrL2 full-scattering and half-scattering methods. No complex potential, coordinate rotations, or solutions of coupled equations are necessary. All observable quantities are computed from the same set of diagonalizations. A model Floquet problem is treated.
Physical Review A 11/1994; 50(4):3276-3284. DOI:10.1103/PhysRevA.50.3276 · 2.81 Impact Factor
[Show abstract][Hide abstract] 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. DOI:10.1103/PhysRevA.50.2764 · 2.81 Impact Factor
[Show abstract][Hide abstract] 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. DOI:10.1063/1.467354 · 2.95 Impact Factor
[Show abstract][Hide abstract] 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. DOI:10.1103/PhysRevA.48.818 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A new conceptually simple and computationally economic method of evaluating the spectral density is presented. The spectral density is then used to compute the microcanonical rate constant by a procedure that uses only the eigenfunctions and real eigenvalues of the system in a series of finite enclosures. Absorbing potentials or dilatation analytic methods are not needed. Thermal rates at low temperatures are obtained to high accuracy using very small basis sets. Examples are presented for single symmetric and asymmetric barriers fit to the potential for H+H2→H2+H and Cl+H2→HCl+H 1D reactions. An asymmetric double barrier is also studied so as to include a problem where narrow resonances contribute to the low temperature thermal rate constant. The method presented here should also be of great use in modeling electronic mesoscopic devices.
The Journal of Chemical Physics 07/1993; 99(1):222-227. DOI:10.1063/1.466183 · 2.95 Impact Factor