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As a result of mathematical modeling it has been shown that any closed electrical line can be interpreted as a ring waveguide where the Fermi-Pasta-Ulam recurrences of the electron and phonon currents interact with each other on the transversal and longitudinal periodical structures of the line conductor’s crystalline lattice as well as on the structures of the wire insulation. An electronic circuit simulating the mathematical model through the dynamics of magnons and phonons in a closed ferrite core with two different coils switched into the shoulders of a multivibrator has been developed. It has been demonstrated that the interacting ferromagnetic and ferroacoustic resonances excited simultaneously in a ferrite core qualitatively correspond to the dynamics of the electron and phonon currents interaction process in a closed electrical line.
The quantum model of electric current suggested by Feynman has been enlarged by n difference-differential Hamiltonian equations describing the phonon dynamics in one dimensional crystallyne lattice. The process of interaction between the electron and phonon components in a crystalline lattice of a conductor has been described by 2n parametrically coupled difference-differential Hamiltonian equations. Computer analysis of the system of these coupled equations showed that their solutions represent a form of the quantum recurrence similar to the Fermi-Pasta-Ulam recurrence. The results of the research might reconsider the existing concept of electric current and will be possibly helpful in developing an acoustic «laser».