Critical length for self-trapping and suppression of critical temperature for superconductivity in quasi-one-dimensional quantum nanowires of restricted size

The research presented in this thesis is highly mathematical in nature. The majority of my research is based on a novel approach used by Rashba [1] to solving equations which can be reduced to a particular form and solved in terms of elliptic integrals. In 1994 Rashba showed that a critical length for self-trapping of a one-dimensional ring system occurs which depends on the electron–phonon coupling constant g. I have extended this work to consider an open-ended system, in which the boundary conditions are different to that in the periodic system, and discovered that indeed a critical length for self-trapping also occurs in this case. [Continues.]