Time evolution of unstable quantum states and a resolution of Zeno's paradox

Chiu, Charles B.; Sudarshan, E. C. G.; Misra, B.

doi:10.1103/physrevd.16.520

Cited by 318 publications

(213 citation statements)

References 7 publications

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“…After several exponential lifetimes 1/Γ of the pole term A P (t) have been exhausted [24], then the non-exponential t −3/2 term gives the larger contribution to Eq. (102); from this point forward the survival probability decreases in time as P (t) ∼ t −3 cos 2 (2t + π/4), as shown in figures 5(b) and (d).…”

Section: Inverse Power Law Evolution On Long Timescales Near the Ep2bmentioning

confidence: 99%

“…[24] it is argued that in typical circumstances the long-time deviation does not manifest until after several lifetimes of the exponential decay, by which time the survival probability is so depleted that the process is rendered undetectable. Despite the challenge, in recent decades both the short time [25] and long time deviations [26] have been experimentally observed.…”

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 Ep2bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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“…Most studies of the validity of the exponential decay law (see in particular [10,11,12,13]) proceed through the determination of the properties of the survival amplitude φ 0 |e −iĤt |φ 0 , where φ 0 is the initial (unstable) state and H the system's Hamiltonian. The modulus square of the amplitude is the probability that the system lies at the state |φ 0 at time t. The exponential decay then refers to the behavior of this probability.…”

Section: Comparison To Other Approachesmentioning

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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“…This simply means that the more frequently the wave function collapses, the harder it becomes for the algorithm to significantly depart from the initial state. Therefore, in this case the algorithm behaves as an example of the quantum Zeno effect, where the a high frequency of measurements hinders the departure of the system from its initial state [6,7].…”

Section: Repeated Measurements In the Algorithmmentioning

confidence: 99%

Quantum games via search algorithms

Romanelli

2007

Physica A: Statistical Mechanics and its Applications

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We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the two possible states. These games are characterized by a continuous space of strategies and the selection of a particular strategy is determined by the moments when the players measure.

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Time evolution of unstable quantum states and a resolution of Zeno's paradox

Cited by 318 publications

References 7 publications

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

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

Quantum games via search algorithms

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