Quantum Tomography, Wave Packets, and Solitons |
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Authors: | S. De Nicola R. Fedele M. A. Man'ko V. I. Man'ko |
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Affiliation: | 1. Istituto di Cibernetica “Eduardo Caianiello” del CNR Comprensorio “A. Olivetti,”, Fabr. 70, Via Campi Flegrei, 34, I-80078, Pozzuoli (NA), Italy 2. Dipartimento di Scienze Fisiche, Università “Federico II” di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli Complesso Universitario di Monte Sant Angelo, Via Cintia, I-80126, Napoli, Italy 3. P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Pr. 53, Moscow, 119991, Russia
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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). The quasidistributions, wavelets, and tomograms are shown to have an intrinsic connection. The analysis is extended to signals obeying to the von Neumann-like equation. For solitons (nonlinear signals) obeying the nonlinear Schrödinger equation, the tomographic probability representation is introduced. It is shown that in the probability representation the soliton satisfies a nonlinear generalization of the Fokker–Planck equation. Solutions to the Gross–Pitaevskii equation corresponding to solitons in a Bose–Einstein condensate are considered. |
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Keywords: | tomographic map phase space Wigner function solitons nonlinear Schrö dinger equation Bose– Einstein condensate |
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