Temporal behavior of quantum mechanical systems

Hiromichi Nakazato, Mikio Namiki, Saverjo Pascazio

    Research output: Contribution to journalArticle

    184 Citations (Scopus)

    Abstract

    The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called "survival" probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum. The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences. After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann's projection postulate in quantum measurement theory are critically overviewed from a dynamical point of view. We also discuss the so-called quantum Zeno effect from this standpoint. The behavior of the survival amplitude is then scrutinized by investigating the analytic properties of its Fourier and Laplace transforms. The analytic property that there is no singularity except a branch cut running along the real energy axis in the first Riemannian sheet is an important reflection of the time-reversal invariance of the dynamics governing the whole process. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system, since the exponential behavior is regarded as a manifestation of a complete loss of coherence of the quantum subsystem under consideration. In this respect, a few attempts at extracting the exponential decay form on the basis of quantum theory, aiming at the master equation, are briefly reviewed, including van Hove's pioneering work and his well-known "X2T" limit.

    Original languageEnglish
    Pages (from-to)247-295
    Number of pages49
    JournalInternational Journal of Modern Physics B
    Volume10
    Issue number3
    Publication statusPublished - 1996 Jan 30

    Fingerprint

    Quantum theory
    Mechanical Systems
    Quantum Systems
    Measurement theory
    Hamiltonians
    Laplace transforms
    Invariance
    Poles
    Fourier transforms
    History
    Quantum Theory
    Exponential Decay
    Branch Point
    Survival Probability
    Master Equation
    quantum theory
    decay
    Measurement Theory
    Quantum Measurement
    radioactive decay

    ASJC Scopus subject areas

    • Electronic, Optical and Magnetic Materials
    • Mathematical Physics
    • Physics and Astronomy (miscellaneous)
    • Condensed Matter Physics
    • Statistical and Nonlinear Physics

    Cite this

    Temporal behavior of quantum mechanical systems. / Nakazato, Hiromichi; Namiki, Mikio; Pascazio, Saverjo.

    In: International Journal of Modern Physics B, Vol. 10, No. 3, 30.01.1996, p. 247-295.

    Research output: Contribution to journalArticle

    Nakazato, H, Namiki, M & Pascazio, S 1996, 'Temporal behavior of quantum mechanical systems', International Journal of Modern Physics B, vol. 10, no. 3, pp. 247-295.
    Nakazato, Hiromichi ; Namiki, Mikio ; Pascazio, Saverjo. / Temporal behavior of quantum mechanical systems. In: International Journal of Modern Physics B. 1996 ; Vol. 10, No. 3. pp. 247-295.
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