Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Use 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 orbits in complex phase space, and the direct observation of
symmetry breaking effects. The method also solves the fundamental convergence
problems in semiclassical periodic orbit theories - for both the Berry-Tabor
formula and Gutzwiller's trace formula - and can therefore be applied as a
novel technique for periodic orbit quantization, i.e., to calculate
semiclassical eigenenergies from a finite set of classical periodic orbits. The
advantage of periodic orbit quantization by harmonic inversion is the
universality and wide applicability of the method, which will be demonstrated
in this work for various open and bound systems with underlying regular,
chaotic, and even mixed classical dynamics. The efficiency of the method is
increased, i.e., the number of orbits required for periodic orbit quantization
is reduced, when the harmonic inversion technique is generalized to the
analysis of cross-correlated periodic orbit sums. The method provides not only
the eigenenergies and resonances of systems but also allows the semiclassical
calculation of diagonal matrix elements and, e.g., for atoms in external
fields, individual non-diagonal transition strengths. Furthermore, it is
possible to include higher order terms of the hbar expanded periodic orbit sum
to obtain semiclassical spectra beyond the Gutzwiller and Berry-Tabor
approximation.

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The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin