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arXiv:quant-ph/0302047 · Lecture notes in physics

Concepts and Methods in the Theory of Open Quantum Systems

Heinz‐Peter Breuer, Francesco Petruccione

Published Jan 1, 2003• 745 citations
arXivHTMLPDF
DOI
10.1007/3-540-44874-8_4

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We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions.
We propose the consistent statistical approach for the quantitative description of simple psychological phenomena using the methods of quantum theory of open systems (QTOS). Taking as the starting point the K. Lewin's psychological field theory we show that basic concepts of this theory can be naturally represented in the language of QTOS. In particular provided that all stimuli acting on psychological system (that is individual or group of interest) are known one can associate with these stimuli corresponding operators and after that to write down the equation for evolution of density matrix of the relevant open system which allows one to find probabilities of all possible behavior alternatives. Using the method proposed we consider in detail simple model describing such interesting psychological phenomena as cognitive dissonance and the impact of competition among group members on its unity.