Exact electronic spectra and inverse localization lengths in one-dimensional random systems

摘要: Analytic continuations into the complex energy plane of Dyson-Schmidt type equations for calculation density states are constructed a random alloy model, liquid metal and alloy. In all these models characteristic function follows from solution this equation. Its imaginary part yields accumulated its real is measure inverse localization length eigenfunctions. The have been solved exactly some distributions variables. case strengths delta-potentials an exponential distribution. They may also finite, exponentially distributed values with probability 0 ⪕ p 1 be infinite q = −p. particles assumed to behave like hard rods. This implies distribution distances between particles. common electronic potential arbitrary, but vanish outside one-dimensional there is, apart positional randomness particles, delta-potentials. For Cauchy argument Lloyd extended obtain one in model equal strengths. point three parameter class shown yield form known functions equation mentioned above. several cases numerical calculations eigenfunctions presented discussed. New results found: decay near special energies metal; divergence at certain non-classical exponent 13 if average vanishes; small broadening bound-state levels low concentrations particles; peak energies, which becomes narrow concentrations; different large delta potentials square-well potentials. Further expression grand given, involving sum over points zero-point found