Analytic expression for the mean time to absorption for a random walker on the Sierpinski gasket. II. The eigenvalue spectrum.
We continue the study of a particle (atom, molecule) undergoing an unbiased random walk on the Sierpinski gasket, and obtain for the gasket and tower the eigenvalue spectrum of the associated stochastic master equation. Analytic expressions for recurrence relations among the eigenvalues are derived. The recurrence relations obtained are compared with those determined for two Euclidean lattices, the closed chain with an absorbing site and a finite chain with an absorbing site at one end. We check and confirm the internal consistency between the smallest eigenvalue and the mean walklength in each of the cases studied. Attention is drawn to the relevance of the results obtained to a problem of electron transfer in proteins.
Bentz
Jonathan L
JL
Cray Inc, 380 Jackson Street, Suite 210, Saint Paul, Minnesota 55101, USA. jnbntz@cray.com
Turner
John W
JW
Kozak
John J
JJ