Watching it boil: Continuous observation for the quantum zeno effectSchulman, L.
doi: 10.1007/BF02551441pmid: N/A
The quantum Zeno effect (QZE) is often associated with the ironic maxim, “a watched pot never boils”, although the notion of “watching” suggests a continuous activity at odds with the usual (pulsed measurement) presentation of the QZE. We show how continuous watching can provide the same halting of decay as the usual QZE, and, for incomplete hindrance, we provide a precise connection between the interval between projections and the response time of the continuous observer. Thus, watching closely, but not so closely as to halt the “boiling”, is equivalent to—gives the same degree of partial hindrance as—pulsed measurements with a particular pulsing rate. Our demonstration is accomplished by treating the apparatus for the continuous watching as a fully quantum object. This in turn allows us a second perspective on the QZE, in which it is the modified level structure of the combined system/apparatus Hamiltonian that slows the decay. This and other considerations favor the characterization “dominated time evolution” for the QZE.
Decoherence in continuous measurements: From models to phenomenologyMensky, Michael
doi: 10.1007/BF02551442pmid: N/A
Decoherence is the name for the complex of phenomena leading to appearance of classical features of quantum systems. In the present paper decoherence in continuous measurements is analyzed with the help of restricted path integrals (RPI) and (equivalently in simple cases) complex Hamiltonians. A continuous measurement results in a readout giving information in the classical form on the evolution of the measured quantum system. The quantum features of the system reveal themselves in the variation of possible measurement readouts. For example, the monitoring energy of a multi-level system may visualize a transition between levels as a process evolving in time but with an unavoidable quantum noise. Decoherence of a continuously measured system is completely determined by the measurement readout, i.e., by the information recorded in its environment. It is shown that the ideology of RPI makes the Feynman version of quantum mechanics closed, contrary to the conventional operator form of quantum mechanics which needs quantum theory of measurement as a necessary additional part.
Dynamical origin of the quantum Zeno effectPascazio, Saverio
doi: 10.1007/BF02551443pmid: N/A
The quantum Zeno effect is often studied and understood in term of nonunitary evolutions, involving projections à la von Neumann (measurements). We propose a dynamical explanation of this effect, which involves only unitary operators. The limit of infinitely frequent measurements is critically discussed: it is unphysical, yet interesting and peculiar.
Atomic quantum zeno effect for ensembles and single systemsBeige, Almut; Hegerfeldt, Gerhard; Sondermann, Dirk
doi: 10.1007/BF02551444pmid: N/A
The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account.
Compound objects as particles in quantum mechanicsRimini, Alberto
doi: 10.1007/BF02551445pmid: N/A
The property of fundamental mechanical theories which allows one to treat compound objects as particles under suitable conditions is considered. It is argued that such a property, called composition invariance, is a nonreleasable property of any fundamental mechanical theory. The proof that standard quantum mechanics enjoys composition invariance is reviewed. Finally, it is shown that the requirement of composition invariance allows one to choose between two alternative forms of quantum mechanics with spontaneous localization.
On the theory of metastable statesKirillov, A.
doi: 10.1007/BF02551446pmid: N/A
It is shown that the stationary states of stochastic systems are stable. Therefore one cannot use the stationary probability distributions for describing the stochastic systems in metastable states. It is shown that the nonstationary stochastic processes can have sample paths with stationary parts. It is proposed to consider these stationary parts as the metastable states.
Time development of a wave packet and the time delayNakazato, Hiromichi
doi: 10.1007/BF02551447pmid: N/A
A one-dimensional scattering problem off a δ-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schrödinger equation. The exact and explicit expression of the scattered wave packet supplies us with interesting information about the “time delay” by potential scattering in the asymptotic region. It is demonstrated that a wave packet scattered by a spin-flipping potential can give us quite a different value for the delay times from that obtained without spin-degrees of freedom.
Short-time critical dynamics of statistical systems and field theoryOkano, K.; Schülke, L.; Zheng, B.
doi: 10.1007/BF02551449pmid: N/A
Recent investigation on the short-time dynamic scaling of critical dynamics is reviewed, with the aim of applying it to the field theory. The contents of this paper are as follows: (1) Short-time behavior of the critical relaxation dynamics, (2) Numerical evidence of the short-time scaling—2-dimensional Ising model and Universality, (3) Theoretical background of the generalized scaling form, (4) Application to a field theoretical model—(2+1)-dimensional SU(2) lattice gauge theory at finite temperature, and (5) Concluding remarks.