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When Is A Soliton?

  • David W. Brown
  • Katja Lindenberg
  • Xidi Wang
Part of the NATO ASI Series book series (NSSB, volume 243)

Abstract

The title of this article is a paraphrase of another by the high-energy physicist Sidney Drell [2]. The latter article asks the question “When is a particle?” and deals with the changing standards of proof which lead us today to accept as “real” some fundamental particles (quarks) which we may never observe. Our situation is somewhat similar in that “hard evidence” of the existence of Davydov solitons remains elusive despite many years of effort expended in their study. As has been revealed during the discussions at this meeting, a part of this elusiveness does not arise from genuine problems of physics but from problems of communication between workers in the field. Among the latter is a considerable variance in the accepted meanings of the central terms “soliton” and “Davydov soliton” themselves. While most of us have a working knowledge of what the latter term means, the lack of a precise definition has been a root cause of some of the softness in the concept of the Davydov soliton. The physics of the underlying physical problem is, of course, completely indifferent to such linguistic difficulties which are purely of human origin; it is well, therefore, not to imbue them with undue importance. However, as the technical portion of this paper addresses a rather broad spectrum of behaviors open to an exciton in a deformable solid, we shall find it necessary to impose some precision on the terms to be used. In our general discussion, we will try use more general terms; when we encounter more distinct and special structures, we will try to preserve the distinctions in our language. It is inevitable that our terminology will conflict with that accepted by some segments of our audience; however, we hope that that will not prevent our message from being understood.

Keywords

Soliton Solution Small Polaron Adiabatic Limit Quantum Monte Carlo Nonlinear SchrOdinger Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • David W. Brown
    • 1
  • Katja Lindenberg
    • 1
    • 2
  • Xidi Wang
    • 3
  1. 1.Institute for Nonlinear Science, R-002University of California at San DiegoLa JollaUSA
  2. 2.Department of Chemistry, B-040University of California at San DiegoLa JollaUSA
  3. 3.Department of Physics, B-019University of California at San DiegoLa JollaUSA

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