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Dynamics of Open Quantum 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

Strictly speaking, real physical systems do not exist in complete isolation in nature. The interaction with the environment generally causes the system to become a statistical mixture, leading to correlation or entanglement between them and decoherence. The theory of open quantum systems was formulated precisely to deal with this kind of problems as well as the measurement process. In analogy to open classical systems, there are also three main different approaches to treat quantum dissipative dynamics: (i) effective time-dependent Hamiltonians, (ii) nonlinear Schrödinger equations and (iii) the system-plus-bath models within a conservative scenario. This theoretical scheme is valid for both dissipative and stochastic dynamics. In this context, the terminology of quantum trajectories is used, to be not confused with those found in Bohmian mechanics. As an illustrative example, adsorbate diffusion on flat surfaces will be considered since it is susceptible to analytical work. This system will also provide the grounds for a more detailed study of wave-packet stochastic dynamics presented in Volume 2.

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Notes

  1. 1.

    Throughout this chapter, to simplify the notation, quantum operators will be represented as dynamical variables, i.e., without the hat symbol on top (e.g., O instead of \(\hat{O}\)). Depending on the context, the reader will be able to identify easily whether a given symbol is acting either as a variable or as an operator.

  2. 2.

    The \(\delta\)-function counts only one half when the integration is carried out from zero to infinity.

  3. 3.

    This type of quantum trajectories must not be confused with Bohmian trajectories (see Chap. 6), which are also regarded as quantum or causal trajectories. Here, the concept refers to the time series or realization associated with a given observable, i.e., it is synonymous of stochastic trajectory (see Sect. B.2 of Appendix B).

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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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Sanz, Á.S., Miret-Artés, S. (2012). Dynamics of Open Quantum 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_5

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