Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 1, Pages 169-177

Quantum fluctuations of elementary excitations in discrete media

Hermann Haken

Institute for Theoretical Physics, Center of Synergetics, University of Stuttgart, Pfaffenwaldring 57/4, Stuttgart D-70550, Germany

Received 3 February 2004

Copyright © 2004 Hermann Haken. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Elementary excitations (electrons, holes, polaritons, excitons, plasmons, spin waves, etc.) on discrete substrates (e.g., polymer chains, surfaces, and lattices) may move coherently as quantum waves (e.g., Bloch waves), but also incoherently (“hopping”) and may lose their phases due to their interaction with their substrate, for example, lattice vibrations. In the frame of Heisenberg equations for projection operators, these latter effects are often phenomenologically taken into account, which violates quantum mechanical consistency, however. To restore it, quantum mechanical fluctuating forces (noise sources) must be introduced, whose properties can be determined by a general theorem. With increasing miniaturization, in the nanotechnology of logical devices (including quantum computers) that use interacting elementary excitations, such fluctuations become important. This requires the determination of quantum noise sources in composite quantum systems. This is the main objective of my paper, dedicated to the memory of Ilya Prigogine.