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A. R. Bishop

Bio: A. R. Bishop is an academic researcher. The author has contributed to research in topics: Quantum field theory & Path integral formulation. The author has an hindex of 1, co-authored 1 publications receiving 50 citations.

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TL;DR: In this paper, structural phase transitions are extended to two-dimensional systems and the model has relevance to transitions in ferroelectrics, to highly anisotropic organic and polymeric materials, and possibly to current discussions of nonlinear quantum field theories.
Abstract: Previous theoretical descriptions of one-dimensional structural phase transitions are extended to two- and three-dimensional systems. The model has relevance to transitions in ferroelectrics, to highly anisotropic organic and polymeric materials, and possibly to current discussions of nonlinear quantum field theories (following from the analogy between functional integral representations of statistical-mechanical partition functions for continuous fields, and Feynman path-integral formulation of quantum mechanics). (auth)

50 citations


Cited by
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TL;DR: In this article, a detailed description of quasiequilibrium systems in which phase transitions are accompanied by heterophase fluctuations is given, which lead to the appearance of the so-called pretransitional, or precursor, phenomena.

158 citations

Journal ArticleDOI
TL;DR: The results of scattering experiments revealing this phenomenon are surveyed in detail, and are used in an assessment of current theories, subdivided into three categories: those which seek to describe the phenomenon within an extended phonon-based theory; those which attempt to trace the effect to the formation of long-lived clusters of precursor order; and those which associate the quasi-elastic scattering with crystal imperfections as mentioned in this paper.
Abstract: The dynamical behaviour of systems exhibiting structural phase transitions is reviewed, with particular emphasis on the problems posed by the simultaneous existence of quasi-elastic and phonon features in the dynamic response of the soft coordinates. The results of scattering experiments revealing this phenomenon are surveyed in detail, and are used in an assessment of current theories, subdivided into three categories: those which seek to describe the phenomenon within an extended phonon-based theory; those which attempt to trace the effect to the formation of long-lived clusters of precursor order; and those which associate the quasi-elastic scattering with crystal imperfections.

141 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the asymptotic behavior of the scattering amplitude when the pomeron has intercept α (0) larger than one and showed that the spectrum of such a system shows a degenerate ground state for α(0) > α c >~ 1 and a continuum with vanishing excitation gap at α ( 0) = α c.

108 citations

Journal ArticleDOI
TL;DR: In this paper, the authors examined and obtained analytic expressions for the basic nonlinear excitations in a monoatomic chain with cubic and quartic interatomic potentials and verified their stability under collision.
Abstract: The authors have examined and obtained analytic expressions for the basic nonlinear excitations in a monoatomic chain with cubic and quartic interatomic potentials and verified their stability under collision. They determined bounds on the potential parameters for which kink, breather, envelope and dark solitons exist. The kink and the envelope of a soliton are determined in the long-wavelength approximation, while the oscillations of the carrier in the envelope soliton are treated exactly. The introduction of second-neighbour interactions (SNI) changes drastically the character of the solutions. Kinks are supersonic if the dispersive term is positive and subsonic if it is negative. In a cubic potential the envelope solitons are asymmetric (there is a net displacement). There is a switch from a kink to a symmetric envelope as the potential parameters are changed; these parameters also determine the regions for which plane waves are unstable. The above excitations can be created by using arbitrary initial conditions which, however, have a net displacement for kinks and the correct Fourier components for an envelope soliton. The asymmetric envelope solitons explain earlier computer simulations using as initial conditions optical gaussian pulses.

88 citations