Transmission distribution, 'Equation missing' <!-- No EquationSource Format='TEX', only image -->(ln T), of 1D disordered chain: Low-T tail

We demonstrate that the tail of transmission distribution through a 1D disordered Anderson chain is a strong function of the correlation radius of the random potential, a, even when this radius is much shorter than the de Broglie wavelength, kF−1. The reason is that the correlation radius defines the phase volume of the trapping configurations of the random potential, which are responsible for the low-T tail. To see this, we perform the averaging over the low-T disorder configurations by first introducing a finite lattice spacing ∼a, and then demonstrating that the prefactor in the corresponding functional integral is exponentially small and depends on a even as a → 0. Moreover, we demonstrate that this restriction of the phase volume leads to a dramatic change in the shape of the tail of Open image in new window (ln T) from universal Gaussian in lnT to a simple exponential (in lnT) with the exponent depending on a. Severity of the phase-volume restriction affects the shape of the low-T disorder configurations, transforming them from almost periodic (Bragg mirrors) to periodically-sign-alternating (loose mirrors).