# Small-time behaviour of quantum nondecay probability and Zeno's paradox in quantum mechanics

@article{Ghirardi1979SmalltimeBO, title={Small-time behaviour of quantum nondecay probability and Zeno's paradox in quantum mechanics}, author={Giancarlo Ghirardi and C. Omero and Tullio Weber and Alberto Rimini}, journal={Il Nuovo Cimento A (1965-1970)}, year={1979}, volume={52}, pages={421-442} }

SummaryA detailed investigation of the small-time deviations of the quantum nondecay probability from a pure exponential is made to study their physical consequences. Specific consideration is given to the problem of the dependence of the lifetime on the characteristics of the measuring apparata whose possible occurrence has recently been pointed out. In particular we investigate the problem of the indefinite increase of the lifetime when the frequency of the measurement processes tends to…

## Figures from this paper

## 43 Citations

Quantum Zeno Effect

- Physics
- 1997

A quantum system always evolves through coherent superposition of states—an initial state develops into a superposition of states, with the relative weight factors changing with time in a continuous…

Measurement-assisted Landau-Zener transitions

- Physics
- 2015

Nonselective quantum measurements, i.e., measurements without reading the results, are often considered as a resource for manipulating quantum systems. In this work, we investigate optimal…

Real successive measurements on unstable quantum systems take nonvanishing time intervals and do not prevent them from decaying

- Physics
- 1983

SummaryAn alarming result has been derived in the theory of unstable systems by considering a sequence of instantaneous observations. According to it, continued observation prevents decay. We show…

The Role of phase space geometry in Heisenberg's uncertainty relation

- Physics
- 2003

Abstract Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty…

Chapter 3 Quantum Zeno and inverse quantum Zeno effects

- Physics
- 2001

This chapter discusses the quantum Zeno and inverse quantum Zeno effects. The quantum Zeno effect is a consequence of the new dynamical features introduced by a series of measurement processes. In…

CONTINUOUS TIME-DEPENDENT MEASUREMENTS: QUANTUM ANTI-ZENO PARADOX WITH APPLICATIONS

- Physics
- 2002

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series…

Time Symmetry and Quantum Dephasing

- Physics
- 1998

We first stress that the time symmetry in quantum mechanics manifests itself in the analytical properties of the Fourier transform of the evolution operator in the complex E-plane (Ebeing the…

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

- Physics
- 2012

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…

The Minimal Modal Interpretation of Quantum Theory

- Mathematics, Physics
- 2014

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the…

Quantum evolution disturbed by successive collapses

- Physics
- 1990

Abstract The process in which the evolution of a quantum system is interrupted in equal time intervals by the collapse is studied. The analysis is performed without any assumption about the source of…

## References

SHOWING 1-10 OF 12 REFERENCES

Zeno's paradox in quantum theory

- Physics, Mathematics
- 1976

A quantum-theoretic expression is sought for the probability that an unstable particle prepared initially in a well-defined state will be found to decay sometime during a given interval. It is argued…

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

- Physics
- 1976

The time evolution of quantum states for unstable particles can be conveniently divided into three domains: the very short time where Zeno's paradox is relevant, the intermediate interval where the…

Decay theory of unstable quantum systems

- Physics
- 1978

The present review article is aimed at a clear formulation of the basic problematics of the decay and at a description of the various recent attempts to solve this delicate problem, illustrating both…

On a reinterpretation of decay experiments

- Physics
- 1971

Abstract Discussion of the basic formula conventionally used to interpret decay measurements shows that it is incompatible with the accepted physical interpretation of quantum mechanics. Two…

On the quantum foundations of the exponential decay law

- Physics
- 1973

SummaryBy assuming that in every actual decay process the unstable system is subject to repeated processes of measurement which ascertain whether the system is decayed or not, we prove that the decay…

Does the lifetime of an unstable system depend on the measuring apparatus?

- Physics
- 1974

SummaryWithin the description of the experimental determination of the decay law recently proposed we investigate the possibility that the experimentally determined lifetime τ be different from the…

Scattering theory of waves and particles

- Mathematics
- 1966

Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to…

The time of arrival in quantum mechanics I

- Physics, Computer Science
- 1969

Electrical elements on the support includes a circuit connected so that a putter stroking the ball from operative position toward operated position and also striking a contactor will cause the associated signaling light to be activated.

Small-time behaviour and dependence of the lifetime of a particle on the measuring apparatus

- Physics
- 1979

SummaryWithin the decay theory proposed recently which takes into account the unavoidable repeated interactions between the unstable particle and the measuring apparatus, we evaluate the dependence…

A unitarity bound on the evolution of nonstationary states

- Physics
- 1973

SummaryA version of an equation derived by Ersak is studied to obtain rigorous bounds on the rate of change of the integrity of a normalized state.RiassuntoSi studia una versione di un'equazione…