1,563 research outputs found
Evolution equation of quantum tomograms for a driven oscillator in the case of the general linear quantization
The symlectic quantum tomography for the general linear quantization is
introduced. Using the approach based upon the Wigner function techniques the
evolution equation of quantum tomograms is derived for a parametric driven
oscillator.Comment: 11 page
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
A new representation of the 2N fold integrals appearing in various two-matrix
models that admit reductions to integrals over their eigenvalues is given in
terms of vacuum state expectation values of operator products formed from
two-component free fermions. This is used to derive the perturbation series for
these integrals under deformations induced by exponential weight factors in the
measure, expressed as double and quadruple Schur function expansions,
generalizing results obtained earlier for certain two-matrix models. Links with
the coupled two-component KP hierarchy and the two-component Toda lattice
hierarchy are also derived.Comment: Submitted to: "Random Matrices, Random Processes and Integrable
Systems", Special Issue of J. Phys. A, based on the Centre de recherches
mathematiques short program, Montreal, June 20-July 8, 200
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