By Ángel S. Sanz
Trajectory-based formalisms are an intuitively attractive manner of describing quantum approaches simply because they permit using "classical" ideas. starting as an introductory point appropriate for college students, this two-volume monograph provides (1) the basics and (2) the functions of the trajectory description of easy quantum approaches. This moment quantity is focussed on easy and simple functions of quantum strategies resembling 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 booklet leads the reader to an alternate and complementary solution to higher comprehend the underlying quantum dynamics.
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Extra resources for A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective
63) with i = x, y. 65) . 66) with Φ(γ t) = 1 − exp(−γ t). For each degree of freedom, one obtains the same spreading because both the initial width and the noise fluctuations are assumed to be the same in both directions (isotropic surface). 7 Stochastic Wave-Packet Dynamics 27 with ∞ F (γ t; T ) = z 1 − cos z dz. 67) as si (t) = 1 2kB T t − Φ(γ t) . 70) while the MSD is linear with time, s(t) ≈ 2kB T t. 72) in both directions. Accordingly, the overall time-dependent spreading can be expressed as w 2 (t) ≈ σ02 + 2 4m2 σ02 γ 2 + 2kB T t.
According to the last expression, we find that the energies associated with both the translational motion and the spreading are suppressed exponentially fast, at a rate of twice γ . 55) is decreased up to a certain fraction at a given time. 5. The corresponding dissipative Bohmian trajectories are displayed in the right-hand side column for the same values of the friction constant. Moreover, the frictionless Bohmian trajectories have also been superimposed. 57) while αt and γt keep the same functional form as in the free damped case (although L˜ t varies for the latter due to the presence of a nonzero potential function), because only second-order derivatives are relevant to these factors.
Notice that the effective decay rate (γeff (τ ) = τ v 2 /σ0 ) is independent of the γ friction. Hence the dynamical system displays a friction-free motion with a quadratic time behavior of the decay rate. 111) also applies for R(t) and claim that in the absence of friction, the QZE always holds. However, after Kofman and Kurizki, for Ohmic friction or linear spectral density, the QZE is not expected to occur. In the indirect measurement scheme used here, the dynamical system and the reservoir are entangled at all times except for such a regime since γ is not playing any role yet.
A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective by Ángel S. Sanz