Theoretical and Numerical Study of Self-Organizing Processes In a Closed System “Classical Oscillator + Random Environment”

Ashot S. Gevorkyan, Aleksander V. Bogdanov, Vladimir V. Mareev, Koryun A. Movsesyan

wrongmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

From the paper’s complex PDE ∂t Q = (L̂ + u1 + i u2)Q (their eq. (35)), the real–imaginary split yields the coupled system (63), which the model reproduces exactly. However, when the paper passes to the reflection (u1,u2)→(u1,−u2) and then claims two independent PDEs with deviated argument (66), it flips the signs in front of the deviated terms: the paper writes a minus for Q(i) and a plus for Q(r). Direct substitution of the stated symmetry Q(i)(u1,−u2,t)=Q(r)(u1,u2,t) and Q(r)(u1,−u2,t)=Q(i)(u1,u2,t) back into (63) shows the correct equations are the opposite: ∂t Q(i)=(L̂+u1)Q(i)+u2 Q(i)(u1,−u2,t) and ∂t Q(r)=(L̂+u1)Q(r)−u2 Q(r)(u1,−u2,t). The paper’s parity reduction (67) then inherits the same sign error. The operator L̂ commutes with the reflection used (k1 even, k2 odd; see (14),(18)), so no additional sign flips arise there. Therefore the model’s derivation is correct; the paper’s (66)–(67) have sign mistakes that propagate to later formulas (e.g., (68)). Citations: complex PDE and split (35),(63) ; reflection step and claimed independent PDEs (65)–(66) ; parity reduction (67) and subsequent system (68) ; drift/coefficients ensuring L̂ symmetry (14),(18) .

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript’s symmetry-based reduction is appealing and could aid analysis and numerics. However, the transition from the coupled real system (obtained correctly from the complex PDE) to the stated ‘independent’ deviated-argument equations contains a sign error for both real and imaginary parts. This mistake then propagates to the parity-induced decouplings and the later two-equation formulation. These are central to the paper’s claims and must be corrected; the numerical results and interpretations may need reevaluation. The core idea seems sound if the symmetry is justified, but correctness requires substantial revision. Key equations and their derivations should be rewritten with an explicit reflection operator to avoid ambiguity. Evidence: eqs. (35),(63) are correct; the claimed ‘independent’ forms (66) and parity reduction (67) carry the incorrect signs relative to direct substitution from (63) under the stated symmetry (see the discussion around (65) as well).