Quantum Post-Exponential Decay

Martorell, J.; Muga, J. G.; Sprung, D. W. L.

doi:10.1007/978-3-642-03174-8_9

Cited by 29 publications

(39 citation statements)

References 128 publications

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“…It is well-established that on long time scales the asymptotic dynamics in typical quantum systems follows an inverse power law decay [20,21] associated with the existence of the continuum threshold (band edge) [22,23]. Starting with the expression for the integral I(λ A , t) reported in Eq.…”

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

confidence: 99%

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%

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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“…It is observed in many quantum systems, in virtually all fields of physics (particle, nuclear, atomic, molecular, and condensed matter), but its microscopic derivation from the Schrödinger equation is not as straighforward as in classical physics, due to initial state reconstruction [1], and deviations are predicted at both short and long times [2,3,4]. The Zeno effect, in particular, is associated with the short time deviation.…”

Section: Introductionmentioning

confidence: 99%

Enhanced observability of quantum postexponential decay using distant detectors

Torrontegui¹,

Muga²,

Martorell³

et al. 2009

Phys. Rev. A

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We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability density at the transition time, and thus its observability, increases with the distance of the detector from the source, up to a critical distance beyond which exponential decay is no longer observed. Solvable models provide explicit expressions for the dependence of the transition on resonance and observational parameters, facilitating the choice of optimal conditions.

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“…So the amplitude a 0 (t), and thus the decay law P 0 (t) of the unstable state |ϕ⟩, are completely determined by the density of the mass (energy) distribution ω(µ) for the system in this state [22] (see also: [5,6,[23][24][25][26][27]. From (10) and from the Riemann-Lebesque lemma it follows that |a(t)| → 0 as t → ∞.…”

Section: Preliminariesmentioning

confidence: 99%

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

Urbanowski

2017

EPJ Web Conf.

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Abstract.Results of theoretical studies and numerical calculations presented in the literature suggest that the survival probability P 0 (t) has the exponential form starting from times much smaller than the lifetime τ up to times t ≫ τ, and that P 0 (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 P 0 (t) from the exponential form begin to dominate). More detailed analysis of the problem shows that in fact the survival probability P 0 (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 ⃗ p 0. 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.

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Quantum Post-Exponential Decay

Cited by 29 publications

References 128 publications

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Enhanced observability of quantum postexponential decay using distant detectors

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

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