Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2511.04185 · Acta Physica Polonica A

Two-exponential decay of Acridine Orange

Francesco Giacosa, Anna Kolbus, Krzysztof Kyziol, Magdalena Plodowska, Milena Piotrowska, Karol Szary, Arthur Vereijken

quant-phhep-phSubmitted Nov 6, 2025• Announced Nov 7, 2025• 1 citation
arXivHTMLPDF

Abstract

In this work, we experimentally study the fluorescence decay of Acridine Orange at late times, in order to test whether a late-time power-law behaviour emerges, a feature expected to be very small but consistent with quantum mechanical and quantum field theoretical predictions. Using two distinct photon detectors, we find that the data are well described by a sum of two exponential functions with lifetimes $τ_1 = 1.7331 \pm 0.001$ ns and $τ_2 = 5.948 \pm 0.012$ ns, in agreement with values reported in the literature. While no deviation from the exponential decay law is observed, this study serves as a reliable test for the experimental setup and enables a precise determination of the sample lifetimes.

Journal reference
ACTA PHYSICA POLONICA A No 6 Vol.148 (2025)
DOI
10.12693/APhysPolA.148.S110
Comments
Proceedings of the 2nd Symposium on new trends in nuclear and medical physics, September 24-26, 2025, Jagiellonian University, Krakow, Poland. 6 pages, 1 figure, 1 table

Related papers

Quantum late-time decay and channel dependence

Francesco Giacosa, A. Kolbus, Krzysztof Kyzioł +4 more

Quantum mechanics predicts deviations from exponential decay at short and long times, yet experimental evidence is limited. We report a power-law tail after $\sim$10 lifetimes in two fluorescent compounds (erythrosine~B and eosine Y), confirmed by two detectors probing distinct bands but yielding different power coefficients. The data match a divergent but normalizable spectral density, and theory predicts oscillations as a future test. A novel and general result is that in multichannel QM (and QFT) decay, the lifetime is universal, but the late-time deviations are channel- (or band-) dependent, a feature consistent with our data.

arXiv:2509.17163•Physical Review A•Jun 12, 2026•0 citations

Late-Time Power Laws in Fluorescence Decays: Quantum Decay or Alternative Mechanisms?

Francesco Giacosa, Anna Kolbus, Krzysztof Kyziol +4 more

In quantum mechanics, the properties of an unstable system are closely related to its corresponding energy distribution. One of the predictions of the theory is the emergence of a late-time power law in the survival probability $P(t)$ of the unstable state. However, in complex systems, similar effects may emerge due to other phenomena. This is the case for nonextensive statistical models, for some continuous lifetime distribution models, and also for certain energy-migration models applied to fluorescence. In this work, these alternative interpretations are confronted with data from time-resolved fluorescence spectroscopy experiments with erythrosine B and eosine Y as fluorophores. It turns out that some of the features expected within the quantum-mechanical description, such as the sharp transition from the exponential to the power-law regime, cannot be reproduced by the specific statistical and energy-migration parametrizations fitted in the analysis.

quant-pharXiv:2610.00603•Oct 2, 2026

Nonexponential decay at late times and a different Zeno paradox

Jay Lawrence

The decay profile of a metastable quantum state decaying in isolation is predicted to depart from exponential behaviour after many lifetimes, and in typical cases to adopt algebraic behaviour as the late-time limit. The effect of environmental interactions, including measurement, is quite different from that of the familiar Zeno (and anti-Zeno) effects that have been observed at very early times. Instead of arresting the decay (or hastening it), the late-time interactions tend to enforce the exponential decay law, without substantially changing the decay constant intrinsic to the isolated system. The experimental challenge is to prevent these interactions and observe the crossover to the nonexponential regime.

Journal of Optics B Quantum and Semiclassical Optics•Aug 1, 2002•11 citations

Quantum decay law: critical times and the equivalence of approaches

David Fernández Jiménez, N. G. Kelkar

Abstract Methods based on the use of Green’s functions or Jost functions and the Fock–Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock–Krylov amplitude in terms of the coefficients introduced in the Green’s functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective of understanding the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, , from the exponential to the inverse power law behaviour at large times. Evaluating for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally.

arXiv:1809.10673•Journal of Physics A Mathematical and Theoretical•Dec 19, 2018•12 citations

True quantum face of the “exponential” decay law

K. Urbanowski

Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, “exponential” (or “canonical”) described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the “exponential” regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.

arXiv:1606.07301•The European Physical Journal D•May 1, 2017•9 citations

The true quantum face of the “exponential” decay: Unstable systems in rest and in motion

K. Urbanowski

Results of theoretical studies and numerical calculations presented in the literature suggest that the survival probability P0(t) has the exponential form starting from times much smaller than the lifetime τ up to times t ⪢τ and that P0(t) exhibits inverse power–law behavior at the late time region for times longer than the so–called crossover time T ⪢ τ (The crossover time T is the time when the late time deviations of P0(t) from the exponential form begin to dominate). More detailed analysis of the problem shows that in fact the survival probability P0(t) can not take the pure exponential form at any time interval including times smaller than the lifetime τ or of the order of τ and it has has an oscillating form. We also study the survival probability of moving relativistic unstable particles with definite momentum . These studies show that late time deviations of the survival probability of these particles from the exponential–like form of the decay law, that is the transition times region between exponential–like and non-exponential form of the survival probability, should occur much earlier than it follows from the classical standard considerations.

EPJ Web of Conferences•Jan 1, 2017•0 citations
In this work, we experimentally study the fluorescence decay of Acridine Orange at late times, in order to test whether a late-time power-law behaviour emerges, a feature expected to be very small but consistent with quantum mechanical and quantum field theoretical predictions. Using two distinct photon detectors, we find that the data are well described by a sum of two exponential functions with lifetimes τ1=1.7331±0.001τ_1 = 1.7331 \pm 0.001τ1​=1.7331±0.001 ns and τ2=5.948±0.012τ_2 = 5.948 \pm 0.012τ2​=5.948±0.012 ns, in agreement with values reported in the literature. While no deviation from the exponential decay law is observed, this study serves as a reliable test for the experimental setup and enables a precise determination of the sample lifetimes.
Quantum mechanics predicts deviations from exponential decay at short and long times, yet experimental evidence is limited. We report a power-law tail after $\sim$10 lifetimes in two fluorescent compounds (erythrosine~B and eosine Y), confirmed by two detectors probing distinct bands but yielding different power coefficients. The data match a divergent but normalizable spectral density, and theory predicts oscillations as a future test. A novel and general result is that in multichannel QM (and QFT) decay, the lifetime is universal, but the late-time deviations are channel- (or band-) dependent, a feature consistent with our data.
In quantum mechanics, the properties of an unstable system are closely related to its corresponding energy distribution. One of the predictions of the theory is the emergence of a late-time power law in the survival probability P(t)P(t)P(t) of the unstable state. However, in complex systems, similar effects may emerge due to other phenomena. This is the case for nonextensive statistical models, for some continuous lifetime distribution models, and also for certain energy-migration models applied to fluorescence. In this work, these alternative interpretations are confronted with data from time-resolved fluorescence spectroscopy experiments with erythrosine B and eosine Y as fluorophores. It turns out that some of the features expected within the quantum-mechanical description, such as the sharp transition from the exponential to the power-law regime, cannot be reproduced by the specific statistical and energy-migration parametrizations fitted in the analysis.
The decay profile of a metastable quantum state decaying in isolation is predicted to depart from exponential behaviour after many lifetimes, and in typical cases to adopt algebraic behaviour as the late-time limit. The effect of environmental interactions, including measurement, is quite different from that of the familiar Zeno (and anti-Zeno) effects that have been observed at very early times. Instead of arresting the decay (or hastening it), the late-time interactions tend to enforce the exponential decay law, without substantially changing the decay constant intrinsic to the isolated system. The experimental challenge is to prevent these interactions and observe the crossover to the nonexponential regime.
Abstract Methods based on the use of Green’s functions or Jost functions and the Fock–Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock–Krylov amplitude in terms of the coefficients introduced in the Green’s functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective of understanding the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, , from the exponential to the inverse power law behaviour at large times. Evaluating for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally.
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, “exponential” (or “canonical”) described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the “exponential” regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.
Results of theoretical studies and numerical calculations presented in the literature suggest that the survival probability P0(t) has the exponential form starting from times much smaller than the lifetime τ up to times t ⪢τ and that P0(t) exhibits inverse power–law behavior at the late time region for times longer than the so–called crossover time T ⪢ τ (The crossover time T is the time when the late time deviations of P0(t) from the exponential form begin to dominate). More detailed analysis of the problem shows that in fact the survival probability P0(t) can not take the pure exponential form at any time interval including times smaller than the lifetime τ or of the order of τ and it has has an oscillating form. We also study the survival probability of moving relativistic unstable particles with definite momentum . These studies show that late time deviations of the survival probability of these particles from the exponential–like form of the decay law, that is the transition times region between exponential–like and non-exponential form of the survival probability, should occur much earlier than it follows from the classical standard considerations.