Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
35 (1994), S. 2024-2035
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Operators of the form Tβf(x)=∑Jj=1 cursive-phij(βx)f(σj +ρjx) are considered herein where β is a real parameter; σj and ρj are real numbers, and {cursive-phij} are holomorphic functions which satisfy certain additional conditions. Transfer operators of this form appear in statistical physics: the leading eigenvalue may be interpreted as the free energy of a lattice of interacting particles, as a function of inverse temperature β. A method for obtaining Taylor series expansions in β of the leading and second leading eigenvalues, and the leading eigenfunction are given. The method may be extended to find series expansions for other eigenvalues and eigenfunctions. The radii of convergence of these series have not been found. These results generalize the author's findings in another article [J. Math. Phys. 32, 2718 (1991)].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530535
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