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 FokkerPlanck equation. Solutions to the GrossPitaevskii equation corresponding to solitons in a BoseEinstein condensate are considered.
Quantum tomography, wavepackets and solitons
S De Nicola;
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 FokkerPlanck equation. Solutions to the GrossPitaevskii equation corresponding to solitons in a BoseEinstein condensate are considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.