Analytical Calculation of Power Flow in Three Coupled Oscillators and its Application to One Dimensional Crystal

Abstract

The motion of a system consisting of three coupled oscillators of three masses attached together by four springs is studied analytically. The system is used as a model to describe the interactions between atoms in a one dimensional crystal with spring-like forces under white noise excitations. Two different cases are considered and the frequencies of oscillations are obtained as well as the equations of motion. The equations of motions are used to determine the power flow in the systems. The power flow determined is used to describe the effects of substitution impurities in a crystal. The power flow of the two systems studied decreases exponentially with increase in frequency to an asymptotic value.

Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators

“…Coupled oscillatory quantum motions are found in almost all areas of physical sciences, ranging from nanotechnology to biology [ 4 , 5 , 6 , 7 , 8 ]. Coupled oscillatory systems can be used as a model to describe the interactions between atoms in a one-dimensional crystal with spring-like forces under white noise excitations [ 9 , 10 ]. In this regard, oscillatory motions of three masses coupled by four springs were studied analytically by Ndikilar et al [ 9 ].…”

“…Coupled oscillatory systems can be used as a model to describe the interactions between atoms in a one-dimensional crystal with spring-like forces under white noise excitations [ 9 , 10 ]. In this regard, oscillatory motions of three masses coupled by four springs were studied analytically by Ndikilar et al [ 9 ]. The dynamics of mixedness and entanglement for three coupled oscillators with arbitrary time-dependent frequencies and coupling parameters has also been investigated [ 11 ].…”