Minimal irreversible quantum mechanics. The decay of unstable states

Arbó, D. G.; Castagnino, Mario; Gaioli, Fabian H.; Iguri, Sergio

doi:10.1016/s0378-4371(99)00480-x

Cited by 14 publications

(20 citation statements)

References 36 publications

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“…This effect is in agreement with the general result (24). Effects of this type are sometimes called the "Khalfin effect" (see [23]). The problem of how to detect possible deviations from the exponential form of φ ( ) at the long time region has attracted the attention of physicists since the first theoretical predictions of such an effect [22,[24][25][26].…”

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confidence: 87%

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Long time properties of the evolution of an unstable state

Urbanowski

2009

Open Physics

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Abstract:An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. In 1957 Khalfin proved that this amplitude tends to zero as → ∞ more slowly than any exponential function of . This can be described in terms of the time-dependent decay rate γ( ) which, when considered with the Khalfin result, means that this γ( ) is not a constant for large but that it tends to zero as → ∞. We find that a similar conclusion can be drawn for a large class of models of unstable states for a quantity, which can be interpreted as the "instantaneous energy" of the unstable state. This energy should be much smaller for suitably larger values of than when is of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long ( → ∞) and relatively short (lifetime of the state) time regions, are different. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.

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supporting

confidence: 87%

“…The simplest case occurs for = 0. Note that the asymptotic expansion for φ ( ) of this or a similar form is obtained for a wide class of densities of energy distribution ω( ) [14,16,17,20,21,23], [27] - [35], [39]. From the relation (51) one concludes that…”

Section: A More General Casementioning

confidence: 52%

Long time properties of the evolution of an unstable state

Urbanowski

2009

Open Physics

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“…The pair-correlation function used in the simulation of a non-Poisson system was representative for some physical systems in the atmospheric sciences (see, e.g., Larsen (2006)). Other similar pair-correlation functions (often taking a powerlaw form) are used in several of the treatments to describe the quantum Zeno effect in atomic and nuclear systems (see, e.g., Arbo et al (2000) and Garcia-Calderon et al (2001)).…”

Section: Discussionmentioning

confidence: 99%

Simple dead-time corrections for discrete time series of non-Poisson data

Larsen¹,

Kostinski²

2009

Meas. Sci. Technol.

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The problem of dead time (instrumental insensitivity to detectable events due to electronic or mechanical reset time) is considered. Most existing algorithms to correct for event count errors due to dead time implicitly rely on Poisson counting statistics of the underlying phenomena. However, when the events to be measured are clustered in time, the Poisson statistics assumption results in underestimating both the true event count and any statistics associated with count variability; the 'busiest' part of the signal is partially missed. Using the formalism associated with the pair-correlation function, we develop first-order correction expressions for the general case of arbitrary counting statistics. The results are verified through simulation of a realistic clustering scenario.

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“…. , n. The main difference between asymptotic expansions (10) and (12) is that the amplitude a(t) in ( 10) is obtained as the Fourier transform (9) of such ω(ε) that ω(ε) = 0 for ε < E min and ω(E min ) > 0 whereas the expansion (12) is the asymptotic expansion of the Fourier transform (9) for another type ω(ε): namely for ω(ε) such that ω(E min ) = 0 (see (11)).…”

Section: General Long Time Properties Of the Nondecay Amplitudementioning

confidence: 99%

General properties of the evolution of unstable states at long times

Urbanowski

2009

Eur. Phys. J. D

155

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An effect generated by the nonexponential behavior of the survival amplitude of an unstable state at the long time region is considered. It is known that this amplitude tends to zero as t goes to the infinity more slowly than any exponential function of t. Using methods of asymptotic analysis we find the asymptotic form of this amplitude in the long time region in a general model independent case. We find that the long time behavior of this amplitude affects the form of the instantaneous energy of unstable states: This energy should be much smaller for suitably long times t than the energy of this state for t of the order of the lifetime of the considered unstable state.

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Minimal irreversible quantum mechanics. The decay of unstable states

Cited by 14 publications

References 36 publications

Long time properties of the evolution of an unstable state

Long time properties of the evolution of an unstable state

Simple dead-time corrections for discrete time series of non-Poisson data

General properties of the evolution of unstable states at long times

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