By Ángel S. Sanz
Trajectory-based formalisms are an intuitively beautiful approach of describing quantum techniques simply because they permit using "classical" thoughts. starting as an introductory point appropriate for college students, this two-volume monograph offers (1) the basics and (2) the purposes of the trajectory description of uncomplicated quantum tactics. This moment quantity is focussed on easy and simple functions of quantum tactics corresponding to interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering difficulties. The corresponding research is conducted in the Bohmian framework. by means of stressing its interpretational features, the publication leads the reader to another and complementary strategy to larger comprehend the underlying quantum dynamics.
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Additional resources for A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective
1). Moreover, since there is no coupling between the motion along each direction—within this simple model, V (x, z) = 0 everywhere—the spreading along x is independent of the translational motion along z. 2). A series of snapshots of the probability density, ρ(x, z), describing the diffraction process are displayed in Fig. 3 in order to illustrate its time-evolution. 34) t. As it can be noticed, while ρ spreads along the x-direction, developing a series of maxima (for the sake of clarity, the maximum value in all plots has been set up at a 10 % of the probability density maximum), its width along the z-direction remains essentially throughout the whole time-evolution.
Regarding the phase δt , it should be mentioned that at short times it depends linearly with time (ϕt ∼ −t/4τ ), increasing or decreasing depending on which mechanism (translation or spreading) is stronger. However, at longer times it approaches asymptotically (also like t −1 ) the value ϕ∞ = −π/4 regardless of which mechanism is the dominant one. Once we have introduced the previous elements, let us now focus on the standard QZE scenario, where a series of projective or von Neumann measurements are performed on the system at regular intervals of time Δt.
8 Quantum Zeno and Anti-Zeno Effects 35 2. For τ ≤ Δt ≤ τZ , according to the literature one should observe QZE. However, this is not exactly the case. 071, changing from convex to concave. Thus, for Δt between τinflx and τZ , pure AZE is still found due to the convexity of the time correlation function. 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.
A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective by Ángel S. Sanz