A Trajectory Description of Quantum Processes. I. by Ángel S. Sanz

February 23, 2017 | Quantum Theory | By admin | 0 Comments

By Ángel S. Sanz

Trajectory-based formalisms are an intuitively beautiful means of describing quantum strategies simply because they enable using "classical" strategies. starting at an introductory point compatible for college kids, this two-volume monograph provides (1) the basics and (2) the functions of the trajectory description of easy quantum methods. this primary quantity is focussed at the classical and quantum heritage essential to comprehend the basics of Bohmian mechanics, which might be thought of the most subject of this paintings. Extensions of the formalism to the fields of open quantum structures and to optics also are proposed and discussed.

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In this case, An interesting case is that√of the weak coupling limit, κ12 ω± ≈ ω0 (1 ± ), where ω0 = (κ + κ12 )/m is the natural frequency of either oscil1 is a small perturbation introlator when the other is held fixed and = κ12 /2κ duced by the coupling (the presence of the other oscillator). 105a) x10 (sin ω+ t + sin ω− t) ≈ x10 sin ω0 t sin ω0 t. 105b) As it can be seen in Fig. 4, this means that, as time goes on, the amplitude of x1 starts to decrease slowly with frequency ω0 due to an energy transfer to the second oscillator.

Simple, non-Brownian random-walk models accounted well for the first observations of anomalous diffusion. These models also provide an intuitive physical picture of such processes: superdiffusion is originated by anomalously long 22 1 From Trajectories to Ensembles in Classical Mechanics jumps of a random walker, namely a Lévy walk, while subdiffusion is associated with unusually long waiting times between successive walks. Subdiffusive processes are usually modelled by a continuous-time random walk (CTRW) with a fractal distribution of waiting times and, therefore, are also called “fractal time” processes.

T = 1) on the Poincaré map, the monodromy matrix becomes M1 = eα1 0 0 e−α1 . 46) The stability of the orbit can be inferred directly from the trace of this matrix as follows. If the eigenvalues are complex, Tr(M1 ) = 2 cos σ1 (α1 = iσ1 ); if they are real, Tr(M1 ) = 2 cosh α1 . Therefore, the orbit will be: • Stable: if |Tr(M1 )| ≤ 2, • Unstable: if |Tr(M1 )| > 2. This criterion is also valid if the periodic orbit is a fixed point of period n on the Poincaré map, although replacing M1 by Mn .

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