Quantized Approach to Damped Transversal Mechanical Waves

Abstract

In information transfer, the dissipation of a signal is of crucial importance. The feasibility of reconstructing the distorted signal depends on the related permanent loss. Therefore, understanding the quantized dissipative transversal mechanical waves might result in deep insights. In particular, it may be valid on the nanoscale in the case of signal distortion, loss, or even restoration. Based on the description of the damped quantum oscillator, we generalize the canonical quantization procedure for the case of the transversal waves. Then, we deduce the related damped wave equation and the state function. We point out the two possible solutions of the propagating-damping wave equation. One involves the well-known Gaussian spreading solution superposed with the damping oscillation, in which the loss of information is complete. The other is the Airy function solution, which is non-spreading–propagating, so the information loss is only due to oscillation damping. However, the structure of the wave shape remains unchanged for the latter. Consequently, this fact may allow signal reconstruction, resulting in the capability of restoring the lost information.