Path Integral Formulation of Quantum Propagation in a Dislocated Lattice

  • K. Kitahara
  • K. Nakazato
  • H. Araki
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 46)


One simple example of topological disorder is disorder caused by dislocations. A remarkable feature of a dislocation is the following; the numbering of atomic positions is not uniquely determined but rather it is dependent on the path of numbering. In order to make this statement clear, let us consider a straight screw dislocation line in a simple cubic lattice as shown in Fig. l. If we number atomic positions along the path A→C→B, the relative position of B with respect to A is +1 in the x direction, +1 in the y direction and 0 in the z direction. On the other hand, if we number atomic positions along another path A→D→E→B, the relative position of B is +1, +1 and +1 in the three directions respectively. Thus the relative position of B with respect to A is counted differently along different paths.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • K. Kitahara
    • 1
  • K. Nakazato
    • 2
  • H. Araki
    • 3
  1. 1.Department of Liberal ArtsShizuoka UniversityShizuoka 422Japan
  2. 2.Central Research LaboratoryHitachi Co.Kokubunji 185Japan
  3. 3.Technical Research CenterNippon Mining Co.Toda 335Japan

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