Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ=12(γ1+γ2)/Δp, where γi are the radiative decay rates of the excited levels i = 1, 2, and Δp=Δ(2)+(1-p(2))γ1γ2 depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1〉 and |e2〉 and their in-phase coherent superposition |ϕ+〉=1r1+r2(r1|e1〉+r2|e2〉), which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned.
Decoherence and quantum Darwinism explain why pointer states and environment records dominate the quantum-to-classical transition, yet the operational criterion for "classical determinism" has rarely been tested as a falsifiable, pre-registered hypothesis (here the pre-registered objects are the P−1/P−3 criteria and the Phy-F1–F5 failure conditions; the Hill sigmoid reported below was added after data review and is not pre-registered). We consolidate one testable interface built on the standard pure-dephasing Lindblad model: does the emergence of a classicality index K coincide with a sharp threshold R_c in environment record redundancy R_δ = 1/f_δ (P−1), and does R_δ scale with dimensionless decoherence γ_A T as a platform-comparable power law R_δ ∼ (γ_A T)^κ (P−3)? Using N_f environment fragments, fixed seeds, and 2000-bootstrap 95% confidence intervals, we find: (i) the segmented sharp-threshold model is not supported by the model comparison (ΔAIC = +19.9 vs. a linear fit), and a smooth Hill sigmoid (n = 2.7, a gentle S-curve rather than a switch; post hoc) describes the data best, with Spearman ρ(K, R_δ) = 0.999 [0.997, 1.000]; (ii) in the weak-decoherence regime κ = 0.96 [0.94, 0.97], R² = 0.998, and, within the fitting window declared here (γ_A T ≤ 10²), κ is equivalent across superconducting, trapped-ion and optomechanical platforms (TOST, band ±0.2; all pairwise |Δκ| ≤ 0.019); (iii) that cross-platform equivalence is window-dependent: extending the optomechanical fit four decades into the saturated plateau (γ_A T up to 10⁶, where R_δ is pinned at N_f = 100) returns an effective exponent of 0.25 ± 0.07 with R² = 0.61, which we report but do not read as a platform difference. Record redundancy inherits from Zurek quantum Darwinism; we propose no new physical law. Failure conditions Phy-F1–F5 are stated explicitly.
Simple but rigorous derivations are presented for the inequalities2−η≤dγ′/(2β+γ′)≤dγ′/(2−α′),2−η≤d(δ−1)/(δ+1),γ≤(2−η)ν.(Proofs of the first two inequalities have been given by Buckingham and Gunton.1) Here d is the dimensionality and α′, β, γ, γ′ and δ are the exponents characterizing a ferromagnet near its critical point,2 while η and ν describe the decay of the corresponding spin-spin correlation functions2 Γ2(r)=〈S0zSrz〉, according to ∑ |r|<RΓ2(r)∼R2−η(T=Tc,H=0,R→∞),κ1∼(T−Tc)ν,(T→Tc,H=0),where the inverse range of correlation κ1 may be defined by κ1−2=[Σrr2Γ2(r)]/[ΣrΓ2(r)]. The corresponding exponent ηE for the energy-energy correlation function (essentially Γ4(r, a)−[Γ(a)]2, where Γ4(r, a)=〈S0zSazSrzSr+az〉) is proved to satisfy 2−ηE≤dα′,2−ηE≤dαc/(1+ζ+αc),where the specific heat CM at T=Tc diverges with the magnetization as M−αc while the energy derivative | ∂U/∂M |Tc varies as Mζ. (Mean Field or classical values are αc=0, ζ=1.) The proofs are based on the ``intuitively obvious'' properties: (a) positivity, namely, Γ1=〈S0z〉≥0,Γ(r)−Γ12≥0,Γ4(r, a)−[Γ2(a)]2≥0, and (b) monotonic increase of Γ1, Γ2 and Γ4 under increase of magnetic field and decrease of temperature. These properties are known3 to be rigorously valid for Ising models of arbitrary spin, lattice structure and ferromagnetic coupling (Jij≥0). Their validity for real magnets together with the experimental observation δ≤4.7 leads to the significant conclusion η≥0.05.