Quantized damped transversal single particle mechanical waves

TL;DR

This paper develops a quantum description of damped transversal mechanical waves, revealing solutions that enable signal reconstruction despite dissipation, with potential applications in nanoscale information transfer.

Contribution

It generalizes canonical quantization for dissipative waves and identifies non-spreading solutions that preserve wavefront structure, aiding in signal restoration.

Findings

Identifies two solutions: spreading and non-spreading Airy function.

Non-spreading solution maintains wavefront structure despite damping.

Enables potential signal reconstruction in dissipative environments.

Abstract

In information transfer, the dissipation of a signal may have crucial importance. The feasibility of reconstructing the distorted signal also depends on this. That is why the study of quantized dissipative transversal single particle mechanical waves may have an important role. It may be true, particularly on the nanoscale in the case of signal distortion, loss, or restoration. Based on the damped oscillator quantum description, we generalize the canonical quantization procedure for the transversal waves. Furthermore, we deduce the related damped wave equation and the state function. We point out the two kinds of solutions of the wave equation. One involves the well-known spreading solution superposed with the oscillation, in which the loss of information is complete. The other is the Airy function solution, which is non-spreading, so there is information loss only due to oscillation damping. However, the structure of the wavefront remains unchanged. Thus, this result allows signal reconstruction, which is important in restoring the lost information.