# How an incorrect transition from finite to infinite 2D conductor may result in a false negative relaxation

## TL;DR

This paper investigates how incorrect assumptions in transitioning from finite to infinite 2D conductors can lead to false conclusions about relaxation rates, emphasizing the importance of proper limiting procedures in electromagnetic analysis.

## Contribution

It highlights the potential errors in relaxation rate predictions caused by improper finite-to-infinite conductor transitions, challenging previous interpretations of plasmon dispersion.

## Key findings

- Negative relaxation rate in infinite plane with high conductivity
- Finite radius analysis shows relaxation rate approaches zero from above
- Incorrect transition may explain unusual plasmon-dispersion curves

## Abstract

We consider the relaxation of a uniform current in a planar 2D conductor with account taken of electromagnetic retardation effects. If the 2D conductivity is larger than the speed of light, the straightforward solution for an infinite plane gives a negative relaxation rate. However if one starts from a conducting cylinder of finite radius and then increases it to infinity, the relaxation rate just tends to zero while remaining positive. We suggest that recent unusual plasmon-dispersion curves obtained by V. A. Volkov and A. A. Zabolotnykh [arXiv:1605.00430] result from the incorrect finite-to-infinite transition.