Comment on "Non-Markovian harmonic oscillator across a magnetic field and time dependent force fields"

TL;DR

This paper comments on recent work deriving the Fokker-Planck equation for a non-Markovian harmonic oscillator in magnetic fields, clarifying that two different methods yield the same results upon reexamination.

Contribution

It clarifies that the previous differing results from two methods are actually consistent when reexamined, resolving a discrepancy in the derivation of the Fokker-Planck equation.

Findings

Both methods produce the same Fokker-Planck equation after reexamination.

The initial discrepancy was due to calculation errors, not fundamental differences.

The study confirms the validity of the original derivation by Das et al.

Abstract

In a recent paper Das {\it et al.} [J. Chem. Phys. {\bf 147}, 164102 (2017)] proposed the Fokker-Planck equation (FPE) for the Brownian harmonic oscillator in the presence of magnetic field and the non-Markovian thermal bath, respectively. This system has been studied very recently by J. C. Hidalgo-Gonzalez and J. I. Jim\'enez-Aquino [Phys. Rev. E {\bf{100}}, 062102 (2019)] and the Fokker-Planck equation was derived using the characteristic function. It includes a few extra terms in the FPE and the authors conclude that their method is accurate compared to the calculation by Das {\it et al.}. Then we reexamine our calculation and which is present in this comment. The revised calculation shows that both the methods give the same result.