By Ángel S. Sanz
Trajectory-based formalisms are an intuitively beautiful approach of describing quantum procedures simply because they enable using "classical" recommendations. starting as an introductory point appropriate for college kids, this two-volume monograph offers (1) the basics and (2) the purposes of the trajectory description of uncomplicated quantum approaches. This moment quantity is focussed on uncomplicated and easy purposes of quantum strategies comparable to interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering difficulties. The corresponding research is performed in the Bohmian framework. by means of stressing its interpretational elements, the ebook leads the reader to an alternate and complementary technique to greater comprehend the underlying quantum dynamics.
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Additional info for A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective
These trajectories are displayed in Fig. 10 for three different values of the friction. Moreover, to compare with, the frictionless case has also been included in each panel. 1 after some time. 46 it is reached at t = 5. We thus notice how the viscid medium causes a braking of the system dispersion as friction increases, which eventually leads the system to display a uniform motion without spreading. 7 Stochastic Wave-Packet Dynamics One of the simplest integrable dissipative quantum systems that we may devise is the diffusion of a wave packet.
In Fig. 12 we show a comparative analysis between the correlation functions √|C(t)| displayed in Fig. 11 and their respective envelopes, given by CΔt (t) ≡ PΔt (t); the former are denoted with dotted line and the latter with solid line of the same color (again, the gray dotted line represents the unperturbed correlation function). 25 (blue). As it can be seen, the agreement between the correlation function and its envelope CΔt (t) becomes better as Δt decreases (see Figs. 8 Quantum Zeno and Anti-Zeno Effects 37 by Pn (t), whereas both will converge as Δt becomes smaller.
Now, if τ ≤ Δt ≤ τinflx , the initial falloff of (0) the perturbed correlation function is slower, CΔt becomes concave and the overall decay gets slower than that associated with the unperturbed correlation function (red dashed line in Fig. 11(a)). This lasts out for some time, after which the perturbed correlation function falls below the unperturbed one (red dashed line in Fig. 11(b)). It is worth stressing here how the decay is indeed faster than in the case of pure AZE, with the quantum shuffling making the perturbed correlation function to acquire a seemingly exponential-like shape.