By Ángel S. Sanz
Trajectory-based formalisms are an intuitively beautiful method of describing quantum tactics simply because they permit using "classical" recommendations. starting at an introductory point appropriate for college kids, this two-volume monograph provides (1) the basics and (2) the purposes of the trajectory description of easy quantum methods. this primary quantity is focussed at the classical and quantum historical past essential to comprehend the basics of Bohmian mechanics, that 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
Butterworth– Heinemann, London (1975) 12. : Some generalisations of Brachistochrone problem. Acta Phys. Pol. A 93, S55–S64 (1998) 13. : Johann Bernoulli’s Brachistochrone solution using Fermat’s principle of least time. Eur. J. Phys. 20, 299–304 (1999) 14. , Henry, C. ): Œuvres de Fermat, pp. 354–457. Gauthier–Villars, Paris (1894) 15. Hero of Alexandria, Catoptrica (circa 60 AC) 16. Ibn al-Haytham “Alhazen”, Book of Optics (1021) 17. : Accord de différentes lois de la nature qui avoient jusqu’ici paru incompatibles.
In general, they appear in dynamical systems described by nonlinear differential equations. More specifically, according to the Poincaré–Bendixon theorem , a system will display a chaotic dynamics if it is described by at least a set of three autonomous (time-independent) coupled equations or two if the system is nonautonomous (the third equation is supplied by the time-dependence). Hence, in the case of an autonomous Hamiltonian system, it is necessary, at least, two degrees of freedom with a nonseparable potential function.
In a similar vein, canonical ensembles are characterized by the same values of number of particles, volume and temperature. 68) ensures dimensionless quantities and goes over correctly to the corresponding quantum statistical values. To deal with nonequilibrium properties, in the 1950s Green and Kubo developed the time-correlation function (TCF) formalism . 69) where f (q, p) is the equilibrium phase space distribution function (for vectorial variables, a scalar product is used). If A = B, C(t) is the so-called autocorrelation function.
A Trajectory Description of Quantum Processes. I. Fundamentals: A Bohmian Perspective by Ángel S. Sanz