Plasticity, defect dynamics and superfluid phenomena in deformed solid $^4$He*

We present a numerical study of a continuum plasticity field coupled to a Ginzburg-Landau model for superfluidity. The results suggest that a supersolid fraction may appear as a long-lived transient during the time evolution of the plasticity field at higher temperatures where both dislocation climb and glide are allowed. Supersolidity, however, vanishes with annealing. As the temperature is decreased, dislocation climb is arrested and any residual supersolidity due to incomplete annealing remains frozen. We show that superfluid response will be experimentally observable only if certain mechanical and structural conditions are satisfied. Study of the superfluid phenomena in solid $^4$He in the presence of a dynamic defect density gives rise to many interesting observations and may provide a resolution to some of the perplexing issues concerning a variety of experiments on bulk solid $^4$He.