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.
Quantum tomography, wave packets, and solitons / S., De Nicola; Fedele, Renato; M. A., Man'Ko; V. I., Man'Ko. - In: JOURNAL OF RUSSIAN LASER RESEARCH. - ISSN 1071-2836. - STAMPA. - 25:1(2004), pp. 1-29. [10.1023/B:JORR.0000012482.45444.45]
Quantum tomography, wave packets, 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). 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.