Progress of Theoretical Physics Supplement · 1973 · 720 citations · 0 references
Natural SciencesPhysicsCondensed Matter PhysicsQuantum MechanicsTransport PhenomenaDisordered SystemsDissipative SystemsGreen's FunctionsHeat ConductionStatistical MechanicsTransport PropertiesConductivityElectrical Transport PropertiesExponential GrowthLocalization PhenomenaLocalized StatesOne-dimensional Heat ConductionTransport In Low-dimensional SystemsTransport In Solids
The study unifies theories of localization, transmission, heat conduction in harmonic chains, and quantum diffusion by leveraging exponential growth properties of solutions. Exact results, a general proof of exponential growth, singular Green function and spectrum properties, and vanishing d.c.
Some exact results obtained by now are reviewed. A most general proof is given for the exponential growth of particular solutions. Based on this property a unification is brought about into the theories on localization of eigenstates, transmission problem, heat conduction through harmonic chains, and quantum diffusion problem. Singular properties are proved for the Green function and the spectrum of the disordered system. Vanishing of the d.c. conductivity is discussed and numerically calculated eigenstates are collected.