Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 1, Pages 169-177
doi:10.1155/S1026022604402015
Quantum fluctuations of elementary excitations in discrete media
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.
Abstract
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.