Geometrical structure of torsional and rotational degrees of freedom in defect systems

The geometrical and physical significance of the translational and rotational degrees of freedom of a dislocation in two-dimensional (2-D) systems is established. It is shown that the phase space accessible to the non-conservative translational motion of dislocations, in the presence of point defects, can also be realized by means of their conservative motion described by a set of torsion angles. This leads to the concept of torsional degrees of freedom providing wandering type slow motion in phase space and glass type behavior. The equation of motion of a N-particle torsional oscillator is derived and qualitatively discussed. Transitions between its rotational states being mediated by dislocation reaction processes, and its point defect generation regime leading to self-sustained non-conservative motion is studied. Physical consequences of the intricate geometry of the phase space for the melting transition are worked out. The three-dimensional (3-D) problem is studied in lesser detail.