Full-time nonexponential decay in double-barrier quantum structures

García–Calderón, Gastón; Villavicencio, Jorge

doi:10.1103/physreva.73.062115

Cited by 33 publications

(41 citation statements)

References 26 publications

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“…This result describes the system dynamics near the EP on the longest time scales, for which the t 3 effect is quite typical in open quantum systems [6,11,30,31,[89][90][91]. Hence we see that while the EP dramatically modifies the dynamics on intermediate time scales, the long time dynamics are qualitatively the same as the ordinary case away from the EP; although the time scale T EP at which the long time effect sets in may be modified according to the proximity of the EP2A to the band edge.…”

Section: Inverse Power Law Evolution On Long Timescales Near the Ep2amentioning

confidence: 99%

“…The latter result for the far zone dynamics is fairly well known in the literature; for example, see Refs. [6,11,30,31,[89][90][91].…”

Section: Model I: Survival Probability Near the Ep2amentioning

confidence: 99%

“…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%

“…In particular, the influence of the continuum threshold is not considered in this approach. However, it has been demonstrated in a variety of studies that the influence of the continuum threshold on both exponential [12,[67][68][69][70] and non-exponential processes [28][29][30][31] can be quite significant in open quantum systems 3 .…”

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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Section: Inverse Power Law Evolution On Long Timescales Near the Ep2amentioning

confidence: 99%

“…The latter result for the far zone dynamics is fairly well known in the literature; for example, see Refs. [6,11,30,31,[89][90][91].…”

Section: Model I: Survival Probability Near the Ep2amentioning

confidence: 99%

Section: Model I: Survival Probability Near the Ep2amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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Amplification of non‐Markovian decay due to bound state absorption into continuum

Garmon

Petrosky

Simine

et al. 2012

Fortschritte der Physik

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Key words non-Markovian decay, power law decay, bound stateIt is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time 'near zone' and long time 'far zone.' In the near zone the survival probability falls off according to a t −1 power law, and in the far zone it falls off as t −3 . We show that the timescale TQ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale TQ diverges and the survival probability follows the t −1 power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t −1 power law dominates precisely at the point of ejection.

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