Glassy relaxation in hierarchically frustrated Josephson arrays

Abstract

Josephson arrays with hierarchical patterns of frustration may provide a physical prototype for glasses. Flux/disorder patterns {f_I} with f_I=±f, ∑_If_I=0 that have a self-similar character on coarse-graining, can be con structed iteratively, composed of quasi-neutral clusters. A nonequilibrium population of topological excitations {m_I=±1}, ∑_Im_I=0, trapped on such a hierarchical background, should annihilate sequentially ~t^−T/T_a due to the hierarchy of time scales. (Here T/T_a is a scaled temperature.) Arrays with a hierarchical pattern of flux penetration areas/intergrain couplings could show glassy behaviour, on rapid cooling or rapid reduction of magnetic fields H. This might be relevant for understanding magnetic moment relaxation M(t)~-H³Tln t seen in high-T_c glassy superconductors.