Nonexponential decay of an unstable quantum system: Small-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>-value<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>-wave decay

Jittoh, Toshifumi; Matsumoto, Shigeki; Sato, Joe; Satō, Yoshio; Takeda, Kenta

doi:10.1103/physreva.71.012109

Cited by 51 publications

(63 citation statements)

References 27 publications

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“…In this case, there are no meaningful detection peaks (even ones involving interference): the decay is going to be non-exponential. Note that in this regime, k 0 is near the potential's threshold, and in this sense it is analogous to a regime of non-exponential decay identified in [17]-see also [18]. In general, there is going to be non-exponential decay in any potential characterized by a regime of energies, in which the transmission probability varies rapidly.…”

Section: Non-exponential Decaysmentioning

confidence: 99%

Time-of-arrival probabilities and quantum measurements. III. Decay of unstable states

Anastopoulos

2008

Journal of Mathematical Physics

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We study the decay of unstable states by formulating quantum tunneling as a time-of-arrival problem: we determine the detection probability for particles at a detector located a distance L from the tunneling region. For this purpose, we use a Positive-Operator-Valued-Measure (POVM) for the time-of-arrival determined in [1]. This only depends on the initial state, the Hamiltonian and the location of the detector. The POVM above provides a well-defined probability density and an unambiguous interpretation of all quantities involved. We demonstrate that the exponential decay only arises if three specific mathematical conditions are met. Their physical content is the following: (i) the decay time is much larger than any microscopic timescale, so that the fine details of the initial state can be ignored, (ii) there is no quantum coherence between the different 'attempts' of the particle to traverse the barrier, and (iii) the transmission probability varies little within the momentum spread of the initial state. We also determine the long time limits of the decay probability and we identify regimes, in which the decays have no exponential phase.

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Section: Non-exponential Decaysmentioning

confidence: 99%

Time-of-arrival probabilities and quantum measurements. III. Decay of unstable states

Anastopoulos

2008

Journal of Mathematical Physics

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“…Nevertheless, for the exactly soluble systems, i.e., particle scattering, etc., that have theoretically been studied it is found that broad transitions (relative to the released energy) result in early relative turnover times: [1][2][3][4]11] turnover log E ÿ :…”

Section: Prl 96 163601 (2006) P H Y S I C a L R E V I E W L E T T E mentioning

confidence: 99%

Violation of the Exponential-Decay Law at Long Times

2006

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. First-principles quantum mechanical calculations show that the exponential-decay law for any metastable state is only an approximation and predict an asymptotically algebraic contribution to the decay for sufficiently long times. In this Letter, we measure the luminescence decays of many dissolved organic materials after pulsed laser excitation over more than 20 lifetimes and obtain the first experimental proof of the turnover into the nonexponential decay regime. As theoretically expected, the strength of the nonexponential contributions scales with the energetic width of the excited state density distribution whereas the slope indicates the broadening mechanism.

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“…Continuum threshold influence on non-exponential decay: a brief review While the short time deviations from exponential decay in quantum mechanics can be viewed as resulting simply from the form of the evolution operator (as demonstrated above), it is the existence of a lower or upper bound (threshold) on the energy continuum in open systems that results in non-exponential decay on long time scales [22,23]. Hence it is rather natural that a discrete eigenvalue appearing in the vicinity of the threshold would result in an enhancement of the non-exponential dynamics, including cases in which the exponential decay vanishes completely [6,[28][29][30][31]88]. In particular, it is argued in Ref.…”

Section: Model I: Survival Probability Near the Ep2amentioning

confidence: 99%

“…However, while the short time and long time deviations are always present, there do exist special circumstances in which the exponential decay effect is modified [27] or even vanishes entirely [28][29][30][31][32]. In the former case, the usual exponential decay is modified in the vicinity of a so-called exceptional point [33,34], also referred to as a non-Hermitian degeneracy [35].…”

Section: Introductionmentioning

confidence: 99%

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Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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It has been reported in the literature that the survival probability P (t) near an exceptional point where two eigenstates coalesce should generally exhibit an evolution P (t) ∼ t 2 e −Γt , in which Γ is the decay rate of the coalesced eigenstate; this has been verified in a microwave billiard experiment [B. Dietz, et al., Phys. Rev. E 75, 027201 (2007)]. However, the heuristic effective Hamiltonian that is usually employed to obtain this result ignores the possible influence of the continuum threshold on the dynamics. By contrast, in this work we employ an analytical approach starting from the microscopic Hamiltonian representing two simple models in order to show that the continuum threshold has a strong influence on the dynamics near exceptional points in a variety of circumstances. To report our results, we divide the exceptional points in Hermitian open quantum systems into two cases: at an EP2A two virtual bound states coalesce before forming a resonance, anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two resonances coalesce before forming two different resonances. For the EP2B, which is the case studied in the microwave billiard experiment, we verify the survival probability exhibits the previously reported modified exponential decay on intermediate timescales, but this is replaced with an inverse power law on very long timescales. Meanwhile, for the EP2A the influence from the continuum threshold is so strong that the evolution is non-exponential on all timescales and the heuristic approach fails completely. When the EP2A appears very near the threshold we obtain the novel evolution P (t) ∼ 1 − C1 √ t on intermediate timescales, while further away the parabolic decay (Zeno dynamics) on short timescales is enhanced.

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Nonexponential decay of an unstable quantum system: Small-Q-values-wave decay

Cited by 51 publications

References 27 publications

Time-of-arrival probabilities and quantum measurements. III. Decay of unstable states

Time-of-arrival probabilities and quantum measurements. III. Decay of unstable states

Violation of the Exponential-Decay Law at Long Times

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

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