Nonexponential decay of a stochastic one-channel system

Dittes, Frank-Michael; Harney, H. L.; Müller, Axel

doi:10.1103/physreva.45.701

Cited by 48 publications

(63 citation statements)

References 21 publications

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“…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 Casesupporting

confidence: 52%

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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Section: A More General Casesupporting

confidence: 52%

Long time properties of the evolution of an unstable state

Urbanowski

2009

Open Physics

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“…(5) occurs because P q is an average over exponentially decaying resonances whose decay amplitudes have a Gaussian distribution. (See the introduction of [7]). The quantum system decays almost exponentially if M is large because Eq.…”

Section: Decay Of the Corresponding Quantum Systemmentioning

confidence: 99%

Decay of classical chaotic systems: The case of the Bunimovich stadium

et al. 1996

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The escape of an ensemble of particles from the Bunimovich stadium via a small hole has been studied numerically. The decay probability starts out exponentially but has an algebraic tail. The weight of the algebraic decay tends to zero for vanishing hole size. This behaviour is explained by the slow transport of the particles close to the marginally stable bouncing ball orbits. It is contrasted with the decay function of the corresponding quantum system.

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“…It can not be related to a two-body random ensemble [9]. Further, the states of the GOE do not decay according to an exponential law in the fewchannel case [10]. That means, they cannot be considered to correspond to isolated states although they are well separated from one another in energy.…”

Section: Introductionmentioning

confidence: 99%

Dynamical phase transitions in quantum mechanics

Rotter

2012

EPJ Web of Conferences

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Abstract. The nucleus is described as an open many-body quantum system with a nonHermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points), the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.

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Nonexponential decay of a stochastic one-channel system

Cited by 48 publications

References 21 publications

Long time properties of the evolution of an unstable state

Long time properties of the evolution of an unstable state

Decay of classical chaotic systems: The case of the Bunimovich stadium

Dynamical phase transitions in quantum mechanics

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