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

By Ángel S. Sanz

Trajectory-based formalisms are an intuitively attractive method of describing quantum procedures simply because they permit using "classical" innovations. starting at an introductory point appropriate for college kids, this two-volume monograph offers (1) the basics and (2) the functions of the trajectory description of easy quantum techniques. this primary quantity is focussed at the classical and quantum historical past 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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**Additional resources for A Trajectory Description of Quantum Processes. I. Fundamentals: A Bohmian Perspective**

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Linked to the (electromagnetic) energy flow. 5 Classical Mechanics of Continuum Media Fig. 5 From a to d, snapshots illustrating the time-evolution of a classical wave or perturbation consisting of two counter-propagating Gaussian pulses according to the standard vision. 3 The Hydrodynamic Approach When dealing with the dynamics of many microscopic particles, both length and time scales need to be simultaneously considered [70]. Typically, wavelengths are compared with the mean free path, lm , and times with the mean collision time, τc .

3) via fractional derivatives, generalized thermostatistics or combined approaches. As it was stated above, chaotic dynamics can mimic the behavior displayed by stochastic systems with no need to introduce any external noise source. It has been widely shown that an unbound deterministic dynamical system fulfilling the ergodic property can be described by a diffusion equation, thus exhibiting a normal diffusive behavior. , with coexistence of regular and chaotic regions) are more interesting: inside a chaotic region the ergodic property is expected to be approximately valid, although the existence of stability islands may subtly change the statistical properties of the system.

The total Hamiltonian describing this effect is expressed as a sum of two terms, H = H0 + H1 , where the zeroth–order Hamiltonian, H0 , describes the system equilibrium state and the interaction Hamiltonian, H1 , introduces a time-dependence. The phase–space density can then be expressed as a power series expansion of the perturbation, f = f0 + f1 + · · · . 71b) whenever the zeroth–order equation can be solved or f 0 is known (typically f 0 is the canonical distribution function). 72) t0 where it is usually assumed f 1 (t0 ) = 0.