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Dynamics of Open Classical Systems

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A Trajectory Description of Quantum Processes. I. Fundamentals

Part of the book series: Lecture Notes in Physics ((LNP,volume 850))

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Abstract

The theoretical framework for dissipative and stochastic dynamics of open classical systems is presented and discussed. Only linear friction is explicitly considered. In spite of the different approaches one may find in the literature, there are essentially three main ways to introduce stochasticity. First, phenomenologically, describing Brownian-like motions by means of the standard Langevin equation, where the system-environment interaction is governed by two parameters: temperature and friction. Second, by starting from the Liouville equation, which is satisfied by any dynamical variable. And third, the system-plus-bath approach, where the equations of motion can be expressed in terms of a generalized Langevin equation. System trajectories issued from solving such equations describe erratic or random motion and, therefore, they are usually called (classical) stochastic trajectories. In those cases where noise becomes negligible or zero, the stochastic dynamics becomes dissipative (trajectories then become smoother).

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  1. Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain

    Ángel S. Sanz & Salvador Miret-Artés

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  1. Ángel S. Sanz
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  2. Salvador Miret-Artés
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Sanz, Á.S., Miret-Artés, S. (2012). Dynamics of Open Classical Systems. In: A Trajectory Description of Quantum Processes. I. Fundamentals. Lecture Notes in Physics, vol 850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18092-7_2

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  • DOI: https://doi.org/10.1007/978-3-642-18092-7_2

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