Quantum Hamlet Effect- a New Example

Details Quantum Hamlet Effect- a New Example Quantum Hamlet Effect- a New Example

2009-08-10

arxiv.org/abs/0908.1301v2

Physics

Quantum Physics

4 pages no figures

Scientific paper

In this work we consider a new example of the recently introduced quantum Hamlet effect. We consider an especial, abstract, "unstable" quantum system whose dynamical evolution during a small time interval is interrupted by frequent measurements. Here three different final situations exist. First one corresponds to quantum Zeno effect, second one - to quantum anti-Zeno effect and third one - to so-called quantum Hamlet effect. By quantum Zeno effect final "non-decay" probability is function of number of the decay measurements variable and "dynamical degree" parameter equivalent to two. When measurements number tends toward infinity "non-decay" probability has the one limit, or, it tends analytically toward one and system stands "non-decayed". By quantum anti-Zeno effect final "non-decay" probability is function of number of the decay measurements variable and "dynamical degree" parameter equivalent to one. When measurements number tends toward infinity "non-decay" probability has the zero limit, or, it tends analytically toward zero and system becomes "decayed". By quantum Hamlet effect, final "non-decay" probability is function of two variable, number of the decay measurements and "dynamical degree". When measurements number tends toward infinity and "dynamical degree" toward one, final "non-decay" probability depends not only of final value of given variables, but, also, on the ways on which given variables tends toward their final values. It means that final "no-decay" probability has not (analytical) limit, or that there is no {\it analytical} prediction on the final "no-decay" probability. To be "decayed" or "no-decayed" that is analytically unsolvable question for given quantum system.

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