Beats in the system of three non-linear oscillators and their quantum analog

Abstract

The classical beats phenomenon is usually demonstrated for the system of two coupled oscillators. The only known realization of similar process in the short homogenous chain with more then two elements refers to the three-well quantum system with the same coupling between the wells providing the special condition on the equations describing the system. However, this condition does not appear to hold in classical homogenous coupled systems, that makes the full periodic energy exchange in the systems of three classical oscillators questionable. Here we prove that fully reciprocal periodic energy transport between the ends of a short homogenous chain of nonlinear oscillators is possible in the conservative classical system with the ‘soft’ nonlinearity. The analogy with the quantum system of the coherent (harmonic) quantum Rabi oscillations in a superposition of three quantum states helps to reveal the special condition on the effective on-site potentials, which does not exist in the classical linear system or system of more than two oscillators with ‘hard’ nonlinearity. We study the periodic energy transport and its localization with use of the regular asymptotic analysis in the reduced phase space. The reported effects can be significant for many fundamental and applied areas of sciences where the coherent energy transport is important.