The wave packets both linear and nonlinear like solitons (signals) described by a complex time-dependent function are mapped onto positive probability distributions (tomograms). Quasidistributions, wavelets and tomograms are shown to have an intrinsic connection. Analysis is extended to signals obeying to the von Neumann-like equation. For solitons (nonlinear signals) obeying to the nonlinear Schroedinger equation, the tomographic probability representation is introduced. It is shown that in the probability representation the soliton satisfies to a nonlinear generalization of the Fokker-Planck equation. Solutions to the Gross-Pitaevskii equation corresponding to solitons in Bose-Einstein condensate are considered.

Quantum tomography, wavepackets and solitons

FEDELE, RENATO;
2004

Abstract

The wave packets both linear and nonlinear like solitons (signals) described by a complex time-dependent function are mapped onto positive probability distributions (tomograms). Quasidistributions, wavelets and tomograms are shown to have an intrinsic connection. Analysis is extended to signals obeying to the von Neumann-like equation. For solitons (nonlinear signals) obeying to the nonlinear Schroedinger equation, the tomographic probability representation is introduced. It is shown that in the probability representation the soliton satisfies to a nonlinear generalization of the Fokker-Planck equation. Solutions to the Gross-Pitaevskii equation corresponding to solitons in Bose-Einstein condensate are considered.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/7048
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