Transmission distribution, P(T), of 1D disordered chain: low-T tail

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We demonstrate that the tail of transmission distribution through 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 the dramatic change in the shape of the tail of P(T) from universal Gaussian in T to a simple exponential (in T) with 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).