Rectification of acoustic phonons in harmonic chains with nonreciprocal spring defects

Abstract

The scattering of acoustic phonons by nonreciprocal spring defects inserted in an harmonic chain is investigated. The degree of nonreciprocity of the forces mediated by the defect springs is parameterized by a single quantity Δ that effectively takes into account the interaction of the coupled masses with hidden degrees of freedom of an underlying nonequilibrium system. We demonstrate a pronounced rectification effect with transmission having a preferential direction. Nonreciprocity also allows energy exchange between the system and the medium. Further, we show a cooperative action between defects mediated by resonant cavity modes. The influence of damping forces is also explored and shown to promote the rectification of the reflected vibrational wave component.

Asymmetric acoustic wave scattering by a nonreciprocal and position-dependent mass defect

“…As demonstrated in [52], the nonreciprocal medium can lead to energy gain or loss of the harmonic vibrations, being conservative only in the limit k = π. For the nonlinear case, the sum of the transmission and reflection coefficients is plotted for |I| 2 = 10 in figure 5 together with the corresponding result in the linear regime.…”

“…Here, we will consider a squared amplitude dependence of the defect masses on the position that effectively results in nonlinear motion equations for the masses coupled by the nonreciprocal spring, characterized by the nonlinearity parameter χ. In particular, we will show that, in opposite to the linear case [52], this model system depicts a frequency dependent rectification factor and multistability, which can lead to a more efficient diode-like action. We also explore the asymmetric scattering of the reflected waves, which displays a significant rectifying effect which is absent in the linear regime.…”

“…Recently, a study of the transport properties of an harmonic wave propagating through a spring-mass chain with intrinsic spring defects that do not obey Newton's third law was put forward [52]. This system can be thought as a classical analogous of a non-Hermitian tight-binding lattice [53,54].…”