By Ángel S. Sanz
Trajectory-based formalisms are an intuitively beautiful method of describing quantum procedures simply because they enable using "classical" options. 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 simple quantum strategies. This moment quantity is focussed on uncomplicated and easy functions of quantum tactics reminiscent of 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 facets, the booklet leads the reader to another and complementary technique to higher comprehend the underlying quantum dynamics.
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Extra info for A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective
Accordingly, the noise fluctuations acting on each degree of freedom are given by δFi (t) = Fi (t) − Fi , where i = x, y. At high (surγ or, equivalently, γ −1 tc ∼ β, where the face) temperatures, we have β −1 coherence time, tc , is commonly known as thermal time and gives us an idea of the time scales at which thermal effects start playing a role. Under these conditions, the noise can be assumed to be classical and, hence, its autocorrelation function at two different times is well described by a Dirac δ-function.
Thus, as Δt becomes smaller, we approach an exponential decay law and Δ(t) goes to zero for any time (see blue curve in the figure), this being the signature of Markovianity. On the contrary, if the time evolution is not Markovian, as time increases and the system keeps memory for longer times, the value of Δ(t) displays important deviations from zero (see black and red curves in the figure). These deviations mainly concentrate on the short and medium term dynamics, where values are relatively large to 38 1 Wave-Packet Dynamics: The Free-Particle Physics be remarkable.
A set of representative Bohmian trajectories illustrating the dynamics associated with these patterns is displayed in Fig. 5 for the diffraction through the slit with width w = 23 µm. , without displaying very convoluted or intricate motions—as the stream of a non-turbulent fluid. Though simple, this example allows us to notice how Bohmian trajectories provide a clear and intuitive physical picture of the quantum probability density current or quantum 14 1 Wave-Packet Dynamics: The Free-Particle Physics Fig.