By Ángel S. Sanz
Trajectory-based formalisms are an intuitively attractive means of describing quantum approaches simply because they permit using "classical" strategies. starting as an introductory point compatible for college students, this two-volume monograph offers (1) the basics and (2) the purposes of the trajectory description of uncomplicated quantum methods. This moment quantity is focussed on easy and easy functions of quantum approaches comparable to interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering difficulties. The corresponding research is conducted in the Bohmian framework. via stressing its interpretational points, the booklet leads the reader to an alternate and complementary approach to greater comprehend the underlying quantum dynamics.
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Extra resources for A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective
The same time-dependence is obtained if Gaussian integrations are carried out in the corresponding ratio instead of evaluating it at (x, y) = (0, 0). 116) for high temperatures. Two time regimes can be then considered: γ t 1 (short time) and γ t 1 (long time). 117) which corresponds to the wave packet spreading in the absence of dissipation. 8 Quantum Zeno and Anti-Zeno Effects 41 where the prefactor is the thermal velocity in two dimensions. 119) with v2 = 2 kB T + . 121) which is the standard short-time, t 2 -behavior usually associated with QZE.
The inhibition of the evolution of a quantum system, though, was already noted by von Neumann  and others—an excellent account on the historical perspective of the QZE can be found in . From an experimental viewpoint, this effect was formerly detected by Itano et al.  considering the oscillations of a two-level system, a modification suggested by Cook  of the original theoretical proposal. Nonetheless, the first experimental evidences with unstable systems, as originally considered by Misra and Sudarshan, were observed later on by Raizen’s group [73, 74].
Consider first p0 = 0. 102) which is nearly three times larger than τ . According to the standard scenario, provided that Δt is smaller than τZ , one should observe QZE. However, the characteristic time τ also plays a key role: as shown below, QZE is observable provided that measurements are performed at time intervals much shorter than the time scales ruling the wave-packet linear spreading regime. Otherwise, only AZE will be observed. 103) 1 + 2(p0 /ps )2 which implies that, in order to observe QZE, the time intervals Δt between two consecutive measurements have to be even shorter (apart from the fact that the con√ dition p0 /ps 1/ 2 should also be satisfied).