Role of Broken Gauge Symmetry in Transport Phenomena Involving Neutral and Charged Particles in Finite Lattices

As opposed to the conventional, approximate theory of electrical conduction in solids, which is based on energy band, “quasi-particle” states in infinite lattices, a rigorous theory exists that can be used to explain transport phenomena, in finite lattices, at reduced temperature, through the effects of a broken gauge symmetry: The loss of translational invariance with respect to Galilean transformations that maintain particle-particle separation. Implications of this result in areas related to the transport of hydrogen (H) and its isotopes in nano-crystalline structures of palladium (Pd) and of neutral, coherent atomic waves in finite, optical lattices are presented. These include: 1. The prediction of a novel variant of a known, phenomenon, Zener/Electronic Breakdown in insulators, in which ions in nano-scale palladium-deuteride (PdD) crystals (as opposed to electrons in insulating crystals) that initially, effectively, are confined to particular regions of space, begin to move, spread-out, and conduct charge after they are subjected to an applied, external (constant) electric field for a sufficiently long period of time; and 2. A rigorous treatment of scattering at low temperatures that can be used to identify critical time- and length- scales for problems related to the transport of neutral atomic matter waves in finite, optical lattices, in the presence of gravitational fields.