Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics.

摘要: We study the statistical properties of wave scattering in a disordered waveguide. The "building block" length deltaL are derived from potential model and used to find evolution with expectation value physical quantities. In units consist thin slices, idealized as delta perpendicular longitudinal direction waveguide; variation transverse may be arbitrary. sets parameters defining given slice taken statistically independent those any other identically distributed. dense-weak-scattering limit, which slices very weak their linear density is large, so that resulting mean free paths fixed, corresponding full waveguide depend only on no property distribution. universality arises demonstrates existence generalized central-limit theorem. Our final result diffusion equation space transfer matrices our system, describes L transport interest. contrast earlier publications, present analysis energy incident particle fully into account. For one propagating mode, N=1 , we have been able solve for number particular observables, solution excellent agreement results microscopic calculations. general, not succeeded finding equation. thus developed numerical simulation, called "random walk matrix space," universal first implemented numerically, then various building blocks combined reported obtained (in use was made "short-wavelength approximation") good arising truly calculations, both bulk surface disorder. Since paper has clear pedagogical aim, included, benefit experts non-experts, appendixes contain more involved