#### Document Type

Post-Print

#### Publication Date

2004

#### Abstract

For a Dirac particle in one dimension with random mass, the time evolution for the average wavefunction is considered. Using the supersymmetric representation of the average Green’s function, we derive a fourth order linear difference equation for the low-energy asymptotics of the average wavefunction. This equation is of Poincar´e type, though highly critical and therefore not amenable to standard methods. In this paper we show that, nevertheless, asymptotic expansions of its solutions can be obtained.

#### Editor

Bernd Aulbach, Saber Elaydi, Gerasimos Ladas

#### Publisher

CRC Press

#### City

Boca Raton

#### ISBN

9780415316750

#### Repository Citation

Aulbach, B., Elaydi, S., & Ziegler, K. (2004). Asymptotic solutions of a discrete Schrödinger equation arising from a Dirac equation with random mass. In B. Aulbach, S. Elaydi, & G. Ladas (Eds.), *Proceedings of the Sixth International Conference on Difference Equations, Augsburg, Germany 2011: New Progress in Difference Equations* (pp. 349-358). Boca Raton: CRC Press.

#### Publication Information

Proceedings of the Sixth International Conference on Difference Equations, Augsburg, Germany 2011: New Progress in Difference Equations