Disorder-Induced Exponential Scaling of Subradiant Decay Rates

Guoqing Tian; Xin-You L\"u

arxiv: 2604.03576 · v1 · submitted 2026-04-04 · 🪐 quant-ph

Disorder-Induced Exponential Scaling of Subradiant Decay Rates

Guoqing Tian , Xin-You L\"u This is my paper

Pith reviewed 2026-05-13 17:38 UTC · model grok-4.3

classification 🪐 quant-ph

keywords decayratesscalingsubradiantlocalizationphenomenontransitionanderson

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The pith

Disorder induces a transition from power-law to exponential scaling of subradiant decay rates in waveguide QED, driven by Anderson localization with a critical point at zero disorder.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

In waveguide quantum electrodynamics, groups of atoms can interact with light in ways that slow down the loss of energy, a effect called subradiance. Without disorder, the rate at which this energy is lost typically follows a power-law decrease as the number of atoms grows. The authors find that random variations in the system parameters cause this decay to switch to an exponential form, which drops much faster with size. They call this change the subradiant scaling transition and show it behaves like a critical point where a characteristic scale diverges exactly at zero disorder strength. The underlying reason is Anderson localization, where the collective states become spatially confined, directly tying the decay scale to the localization length. This connects two previously separate ideas in quantum optics and condensed matter physics.

Core claim

disorder drives a sharp transition in the typical subradiant decay rates from power-law to exponential scaling, a phenomenon we term the subradiant scaling transition (SST). Through rigorous finite-size scaling analysis, we establish the SST as a critical phenomenon, characterized by a diverging characteristic scale of the decay rates at the transition point W_c=0. Physically, the SST originates from Anderson localization, manifested by the physical equivalence between the characteristic scale and the localization length of the subradiant states.

Load-bearing premise

The finite-size scaling analysis and numerical results accurately reflect the behavior in the thermodynamic limit without additional unmodeled effects such as non-Markovian dynamics or higher-order interactions beyond the standard waveguide QED Hamiltonian with disorder.

read the original abstract

Subradiance, a hallmark cooperative phenomenon in waveguide QED, is characterized by a universal power-law scaling of decay rates with system size and underpins many applications in quantum information storage. Here, we demonstrate that disorder drives a sharp transition in the typical subradiant decay rates from power-law to exponential scaling, a phenomenon we term the subradiant scaling transition (SST). Through rigorous finite-size scaling analysis, we establish the SST as a critical phenomenon, characterized by a diverging characteristic scale of the decay rates at the transition point $W_c=0$. Physically, the SST originates from Anderson localization, manifested by the physical equivalence between the characteristic scale and the localization length of the subradiant states. Our findings provide deep insights into the interplay between disorder and collective dynamics, unifying the underlying physical mechanisms of exponentially-scaled subradiant decay rates and Anderson localization in waveguide QED.

Editorial analysis

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Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Based on abstract only; the central claim rests on the standard waveguide QED model with added disorder and the validity of finite-size scaling to extract critical behavior.

free parameters (1)

W_c = 0
Transition point stated as exactly zero disorder strength; may be an input or derived quantity.

axioms (2)

domain assumption The system is described by the standard waveguide QED Hamiltonian with on-site or coupling disorder.
Invoked implicitly as the setup for observing subradiance and the SST.
domain assumption Finite-size scaling analysis reliably identifies the critical point and diverging scale in the thermodynamic limit.
Central to establishing SST as a critical phenomenon.

pith-pipeline@v0.9.0 · 5445 in / 1435 out tokens · 33200 ms · 2026-05-13T17:38:29.750838+00:00 · methodology

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IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Through rigorous finite-size scaling analysis, we establish the SST as a critical phenomenon, characterized by a diverging characteristic scale of the decay rates at the transition point W_c=0. Physically, the SST originates from Anderson localization, manifested by the physical equivalence between the characteristic scale and the localization length of the subradiant states.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

the non-Hermitian effective Hamiltonian is Ĥ_eff = −iγ/2 ∑_{m,n} e^{i|x_m−x_n|k_0} σ̂†_m σ̂_n

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