Anomalous Zeno effect for sharply localized atomic states

Sokolovski, D.; Pons, M.; Kamalov, T. F.

doi:10.1103/physreva.86.022110

Cited by 6 publications

(16 citation statements)

References 19 publications

(25 reference statements)

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“…Further study of the characterization of initial states is needed [32]. It is also worth mentioning that a nonquadratic t 3/2 short-time behavior does not prevent the occurrence of the quantum Zeno effect [4,13,15]. Finally, we believe that our results may be relevant for quests regarding the description of the short-time behavior of unstable systems in relativistic quantum field theory where it has been found that the second moment to the Hamiltonian diverges [33].…”

Section: Discussionmentioning

confidence: 72%

Analytical study of quadratic and nonquadratic short-time behavior of quantum decay

Cordero

García–Calderón

2012

Phys. Rev. A

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The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time behavior of the survival probability S(t) has a dependence on the initial state and may behave as either S(t) = 1 − O(t 3/2 ) or 1 − O(t 2 ). These cases are illustrated by solvable models. The experiment reported by Wilkinson et al. [Nature (London) 387, 575 (1997)] does not distinguish between the above short-time behaviors.

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Section: Discussionmentioning

confidence: 72%

Analytical study of quadratic and nonquadratic short-time behavior of quantum decay

Cordero

García–Calderón

2012

Phys. Rev. A

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“…Experimentally, it was first demonstrated in [11] and its existence sets the ground for the quantum Zeno effect [12]. It is a consequence of unitary time-evolution, provided that the first and second moments of the Hamiltonian exist, see [13,14] for exceptional cases. That deviations from exponential decay are as well to be expected at long times was pointed out by Khalfin in 1957, for systems whose energy spectrum is bounded from below [8].…”

Section: Introductionmentioning

confidence: 99%

Exact quantum decay of an interacting many-particle system: the Calogero–Sutherland model

Campo

2016

New J. Phys.

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The exact quantum decay of a one-dimensional Bose gas with inverse-square interactions is presented. The system is equivalent to a gas of particles obeying generalized exclusion statistics. We consider the expansion dynamics of a cloud initially confined in a harmonic trap that is suddenly switched off. The decay is characterized by analyzing the fidelity between the initial and the time-evolving states, also known as the survival probability. It exhibits early on a quadratic dependence on time that turns into a power-law decay, during the course of the evolution. It is shown that the particle number and the strength of interactions determine the power-law exponent in the latter regime, as recently conjectured. The nonexponential character of the decay is linked to the many-particle reconstruction of the initial state from the decaying products. OPEN ACCESS RECEIVED

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“…Yet, we also note that this short-time behavior relies on the existence of the second moment of the Hamiltonian and deviations are expected whenever energy fluctuations diverge, even under unitary dynamics. For example, a fractional exponent 3/2 has been reported in the early decay of the survival probability of sharply localized wavepackets undergoing free evolution [24].…”

Section: B Short-time Nonexponential Decaymentioning

confidence: 99%

Scrambling the spectral form factor: Unitarity constraints and exact results

2017

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Quantum speed limits set an upper bound to the rate at which a quantum system can evolve and as such can be used to analyze the scrambling of information. To this end, we consider the survival probability of a thermofield double state under unitary time-evolution which is related to the analytic continuation of the partition function. We provide an exponential lower bound to the survival probability with a rate governed by the inverse of the energy fluctuations of the initial state. Further, we elucidate universal features of the non-exponential behavior at short and long times of evolution that follow from the analytic properties of the survival probability and its Fourier transform, both for systems with a continuous and for systems with a discrete energy spectrum. We find the spectral form factor in a number of illustrative models, notably we obtain the exact answer in the Gaussian unitary ensemble for any N with excellent agreement with recent numerical studies. We also discuss the relationship of our findings to models of black hole information loss, such as the

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Anomalous Zeno effect for sharply localized atomic states

Cited by 6 publications

References 19 publications

Analytical study of quadratic and nonquadratic short-time behavior of quantum decay

Analytical study of quadratic and nonquadratic short-time behavior of quantum decay

Exact quantum decay of an interacting many-particle system: the Calogero–Sutherland model

Scrambling the spectral form factor: Unitarity constraints and exact results

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