Scattering theory for mesoscopic quantum systems with non-trivial spatial asymptotics in one dimension

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Abstract
Basic results which are needed for the formulation of a quantitative theory of charge transport in mesoscopic quantum-interference devices are derived. In particular, orthogonality and proper normalization of scattering states for one-dimensional quantum systems with nonzero and periodic potential asymptotics are discussed. Properties of the S-matrix are investigated. Results are obtained within the framework of ordinary linear differential equations by investigation of the spectral resolution of the identity and, alternatively, directly from asymptotic properties of Jost solutions and the theory of generalized functions. Based on the S-matrix and properties of the scattering states, an independent-particle model for the current response of mesoscopic (quasi-) one-dimensional electronic devices may be formulated.