Negative flow of energy in a mechanical wave
Keywords: wave, dispersion, energy, backﬂow, 1D lattice, oscillator
AbstractA classical system, which is analogous to the quantum one with a backﬂow of probability, is proposed. The system consists of a chain of masses interconnected by springs and attached by other springs to ﬁxed supports. Thanks to the last springs the cutoﬀ frequency and dispersion appears in the spectrum of waves propagating along the chain. It is shown that this dispersion contributes to the appearance of a backﬂow of energy. In the case of the interference of two waves, the magnitude of this backﬂow is an order of magnitude higher than the value of probability backﬂow in the mentioned quantum problem. The equation of Green’s function is considered and it is shown that the backﬂow of energy is also possible when the system is excited by two consecutive short pulses. This classical backﬂow phenomenon is explained by the branching of energy ﬂow to local modes that is conﬁrmed by the results for the forced damped oscillator. It is shown that even in such a simple system the backﬂow of energy takes place (both instantaneous and average).
Mathematical and Computational Physics