By Ángel S. Sanz

Trajectory-based formalisms are an intuitively attractive means of describing quantum techniques simply because they enable using "classical" ideas. starting at an introductory point compatible for college students, this two-volume monograph offers (1) the basics and (2) the purposes of the trajectory description of easy quantum approaches. this primary quantity is focussed at the classical and quantum history essential to comprehend the basics of Bohmian mechanics, which are thought of the most subject of this paintings. Extensions of the formalism to the fields of open quantum platforms and to optics also are proposed and discussed.

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**Additional resources for A Trajectory Description of Quantum Processes. I. Fundamentals: A Bohmian Perspective**

**Example text**

The time Fourier transform of C(t) gives a generalized susceptibility, where the thermal transport coefficients correspond to its zero–frequency limit. TCFs may depend on space and, in general, describe the thermal fluctuations occurring spontaneously in systems at equilibrium as well as the response of a system to a weak, external perturbation (linear response theory). Unlike partition functions, many TCFs can be measured directly [82]. Alternatively, C(t) can also be defined in terms of fluctuations by replacing A and B by δ A(0) = A(0) − A and δ B(t) = B(t) − B .

84). If ρcl is given by two separate Gaussian distributions with width σ , since the superposition principle holds for them, ρcl (x, t) = ρcl,1 e−(x−x¯1 −vt) 2 /2σ 2 + ρcl,2 e−(x−x¯2 +vt) 2 /2σ 2 . 89) Nevertheless, ensembles of trajectories associated with each distribution will evolve independently and, therefore, there is no relevant effect among them (see Fig. 3), contrary to what happens in Bohmian mechanics (see the corresponding applications in Volume 2). 1 Coupled Motion As will be seen in Chap.

Mean square displacements (MSDs) growing faster or slower than linear in time, thus implying a violation of Einstein’s diffusion law. One of the relevant questions when talking about transport properties is that of the decay of correlation functions with time. Also here dynamical instabilities rule the intrinsic relaxation times of correlation functions, allowing one to obtain transport coefficients from them. Time correlation functions are important from an experimental viewpoint, since the spectra measured by means of the different spectroscopic techniques are related to the power spectra of well-defined dynamical variables (see Appendix B).