The authors have declared that no competing interests exist.

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».

According to the quantum concept suggested by Feynman

Where n -is the number of atoms in a crystallyne lattice,

The system (1) has solutions corresponding to the states of a certain energy:

Feynman has shown

If to consider the density probability

On the other hand the crystalline lattice is filled with a gas of phonons whose energy distribution along the chain of atoms can be also represented by the system (1) and the phonon current can be written like follows:

Where

So for a full description of an electric current it is necessary to take into account a process of interaction between electrons and phonons (it is not only scattering but a resonant interaction as well). Such interaction has to result in appearance of a product

By analogy with the system (1) the dynamics of the phonon energy disribution along the chain of atoms in one dimensional crystalline lattice (

Where n - is the number of the atom in a crystalline lattice,

A computer study of the systems of equations (1) and (6) shows two different types of their solutions depending on the boundary conditions that correspond to the fixed ends of the chain or open ones. In particular, for the open ends the solutions of (1) and (6) look strongly non linear at the beginning and at the end of the chain while they don't change considerably along all n points.

The system describing an interaction between electrons and clusters of phonons in a crystalline lattice can be given as a result of parametric coupling of (1) and (6):

………… (7)

Where _{1}is the energy of the heat vibrations of the lattice.

The system (7) describes the interaction process between electrons and clusters of phonons in the crystalline lattice. The solutions of (7) represent a sophisticated energy distribution along the lattice. Since the system (7) represents in fact one of the quantum recurrence forms

The first members in (8) represent the Fourier sequences and the second members - sums of nonequidistant harmonics formed as a result of dispersion in a lattice

Computer study of the system (7) solutions shows an intermittency process typical for the recurrence mode similar to the Fermi-Pasta-Ulam recurrence

The coupled system (7) can simulate a physical functioning of a simple electric transformer for example an ingnition coil. As a first step of applying the computer model for a desciption of this electrical device the system's boundary conditions were chosen to simulate two coils of an electric transformer for example, an ingnition coil. For that purpose the boundary conditions of the first (electron) equation of (7) corresponded to the open ends of the chain and for the second (phonon) equation for half fixed ends (the beginning of the chain had fixed ends but the end had open ones). The solutions in this case show that despite an equal number of points in both difference-differential equations in (7) the amplitude in the electron chain was by an order larger than that in the phonon chain. It allows to speak out in favor of a quantum mechanical basis for the describing the physics of a simple electric transformer. The transformer mode of the system (7) is shown in

The results of the transformer mode simulation within the proposed model suggest a quantum mechanical basis for the description of its physical functioning. That is an exchange of energy between the two electron and phonon quantum recurrences (8) in accordance with the general properties of the resonant interaction between the recurrences

Next step of the computer simulation was to visualize the general dynamics of the interaction between electron and phonon amplitudes described by the equations (7) in case of the open ends mode of the boundary conditions for both chains in (7).

Computer solutions of the electric current model (7) given in

The solutions of the system (7) (

Enlarging of the quantum model of electric current suggested by R.Feynman resulted in widening of the general concept of electric current and hammering out the electron-phonon interaction mathematical model of electrical current . Proposed model shows another essential property of electric current - the presence of the phonon component in the conductor's crystalline lattice possessing a considerable amount of energy. According to the suggested model any electric current represents a quantum recurrence between the energies of electron and phonon components. That brings a new possible usage of the conductor's crystalline lattice energy as a huge reserve for saving electrical energy since all transmission lines materials represent crystalline lattice phonon energy containers. Beside that, a new concept of the electrical current reveals the ways for some possible modifications of such electrical devices as transformers, motors, heaters etc to enhance their efficiency. The results of the suggested model computer study display reasons for possible happening of large scale blackouts in electrical networks as a result of formation of a long distance spatial selfparametric excitation expressed in increasing of the amplitude voltage oscillations damaging the network devices. To crown it all the selfparametric excitation mode found during the study of the model puts forward a concept for developing of a phonon laser.