Decimation and harmonic inversion of periodic orbit signals
نویسندگان
چکیده
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.
منابع مشابه
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 clo...
متن کاملUse of Harmonic Inversion Techniques in Semiclassical Quantization and Analysis of Quantum Spectra
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and to extract dynamical information from quantum spectra which has been unattainable before, such as bifurcations of orbits, the uncovering of hidden ghost orbi...
متن کاملA unified theoretical harmonic analysis approach to the cyclic wavelet transform (CWT) for periodic signals of prime dimensions
The article introduces cyclic dilation groups and finite affine groups for prime integers, and as an application of this theory it presents a unified group theoretical approach for the cyclic wavelet transform (CWT) of prime dimensional periodic signals.
متن کاملSemiclassical spectra and diagonal matrix elements by harmonic inversion of cross-correlated periodic orbit sums.
Semiclassical spectra weighted with products of diagonal matrix elements of operators A(alpha), i.e., g(alphaalpha')(E)= summation operator(n)/(E-E(n)), are obtained by harmonic inversion of a cross-correlation signal constructed of classical periodic orbits. The method provides highly resolved semiclassical spectra even in situations of nearly degenerate states, and op...
متن کامل\ expansion for the periodic orbit quantization by harmonic inversion
Semiclassical spectra beyond the Gutzwiller and Berry-Tabor approximation for chaotic and regular systems, respectively, are obtained by harmonic inversion of the \ expansion of the periodic orbit signal. The method is illustrated for the circle billiard, where the semiclassical error is reduced by one to several orders of magnitude with respect to the lowest order approximation used previously...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000