Enigma of probability amplitudes in Hamiltonian formulation of integrable semidiscrete nonlinear Schrödinger systems.
An attempt to find a probability-amplitude-based Hamiltonian representation of the symmetrical version of integrable semidiscrete multicomponent nonlinear Schrödinger systems is made. Thus the on-cell locality of the general point transformation in combination with the model multicomponentness is shown to contradict the concept of canonical Hamiltonian representation in terms of probability amplitudes. Nevertheless, the above concept can be realized in a slightly adjusted semidiscrete multicomponent nonlinear Schrödinger system that preserves some physically valuable solutions of the original (either symmetric or asymmetric) integrable model. The advantages of the adjusted Hamiltonian model for the analysis of real physical systems are formulated. Examples of longitudinal and lateral soliton dynamics on multichain tubular lattices subjected to uniform electric and magnetic fields are given.
Vakhnenko
Oleksiy O
OO
Department of Quantum Electronics, Bogolyubov Institute for Theoretical Physics, 14-B Metrologichna Street, Kyïv 03143, Ukraine.