When Is A Soliton?
The title of this article is a paraphrase of another by the high-energy physicist Sidney Drell . 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.
KeywordsSoliton Solution Small Polaron Adiabatic Limit Quantum Monte Carlo Nonlinear SchrOdinger Equation
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- 1.David Böhm, Quantum Theory, (Prentice-Hall, New York, 1951).Google Scholar
- 3.T. D. Lee, Particle Physics and Introduction to Field Theory, Contemporary Concepts in Physics, Vol. 1, edited by H. Feshbach, N. Bloembergen, L. Kadanoff, M. Ruderman, S. B. Treiman and H. Primakoff (Harwood Academic Publishers, New York, 1988).Google Scholar
- S. I. Pekar, Zh. Eksp. Theor. Fiz. 16, 335 (1946)Google Scholar
- L. D. Landau and S. I. Pekar, Zh. Eksp. Teor. Fiz. 18, 419 (1948).Google Scholar
- 7.I. Pekar, Untersuchungen Uber die Electronentheorie der Kristalle, (Akademie Verlag, Berlin, 1954).Google Scholar
- 9.Emmanuel I. Rashba, in Excitons, edited by E. I. Rashba and M. D. Sturge (North-Holland, Amsterdam, 1982).Google Scholar
- 19.J. Frenkel, Wave Mechanics, Advanced General Theory (Clarendon Press, Oxford, 1974).Google Scholar
- 22.I. G. Lang and Yu. A. Firsov Zh. Eksp. Teor. Fiz. 43, 1834 (1962).Google Scholar
- 28.M. Sataric, Z. Ivic, Z. Shemsedini and R. Zakula, J. Molec. Elec. 4, 223 (1988).Google Scholar
- 30.A. S. Davydov, Solitons in Molecular Systems (Reidel Publishing Co., Boston 1985).Google Scholar