aqora

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

Ching-Yi Chiu, E. C. G. Sudarshan, Baidyanath Misra

Unknown eBooksJan 1, 19761 citation

A Continuously Observed Two-level System Interacting with a Vacuum Field

Ricardo Kullock, Nami Fux Svaiter

A discussion of the quantum Zeno effect and paradox is given. The quantum Zeno paradox claims that a continuously observed system, prepared in a state which is not an eigenstate of the Hamiltonian operator, never decays. To recover the classical behavior of unstable systems we consider a two-level system interacting with a Bose field, respectively prepared in the excited state and in the Poincare invariant vacuum state. Using time-dependent perturbation theory, we evaluate for a finite time interval the probability of spontaneous decay of the two-level system. Using the standard argument to obtain the quantum Zeno paradox, we consider N measurements where N goes to infinity and we obtain that the non-decay probability law is a pure exponential, therefore recovering the classical behavior.A discussion of the quantum Zeno effect and paradox is given. The quantum Zeno paradox claims that a continuously observed system, prepared in a state which is not an eigenstate of the Hamiltonian operator, never decays. To recover the classical behavior of unstable systems we consider a two-level system interacting with a Bose field, respectively prepared in the excited state and in the Poincare invariant vacuum state. Using time-dependent perturbation theory, we evaluate for a finite time interval the probability of spontaneous decay of the two-level system. Using the standard argument to obtain the quantum Zeno paradox, we consider N measurements where N goes to infinity and we obtain that the non-decay probability law is a pure exponential, therefore recovering the classical behavior.

arXiv:quant-ph/0703167Mar 19, 20071 citation

Contribution to the decay theory of unstable quantum systems

Luciano Fonda, G. C. Ghirardi

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fieldsMay 1, 197017 citations

The Zeno’s paradox in quantum theory

Baidyanath Misra, E. C. G. Sudarshan

We seek a quantum-theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle which is continuously observed to see whether it decays will never be found to decay!. Since recording the track of an unstable particle (which can be distinguished from its decay products) approximately realizes such continuous observations, the above conclusion seems to pose a paradox which we call Zeno’s paradox in quantum theory. The relation of this result to that of some previous works and its implications and possible resolutions are briefly discussed. The mathematical transcription of the above-mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the general formulation and the proof given here are believed to be new. We also note that the known ’’no-go’’ theorem concerning the semigroup law for the reduced evolution of any physical system (including decaying systems) is subsumed under our theorem as a direct corollary.We seek a quantum-theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle which is continuously observed to see whether it decays will never be found to decay!. Since recording the track of an unstable particle (which can be distinguished from its decay products) approximately realizes such continuous observations, the above conclusion seems to pose a paradox which we call Zeno’s paradox in quantum theory. The relation of this result to that of some previous works and its implications and possible resolutions are briefly discussed. The mathematical transcription of the above-mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the general formulation and the proof given here are believed to be new. We also note that the known ’’no-go’’ theorem concerning the semigroup law for the reduced evolution of any physical system (including decaying systems) is subsumed under our theorem as a direct corollary.

Journal of Mathematical PhysicsApr 1, 19772,271 citations

Contribution to the decay theory of unstable quantum systems. — II

Luciano Fonda, G. C. Ghirardi

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fieldsDec 1, 197110 citations

Zeno paradox in quantum theory

Asher Peres

The coupling of an unstable quantum system with a measuring apparatus alters the dynamical properties of the former, in particular, its decay law. The decay is usually slowed down and can even be completely halted by a very tight monitoring.

American Journal of PhysicsNov 1, 1980319 citations

Solution to two paradoxes in the quantum theory of unstable systems

Related papers

Solution to two paradoxes in the quantum theory of unstable systems

Related papers