Abstract
The Selberg zeta function {zeta}{sub S}(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, {zeta}{sub S}(s) can be exactly rewritten as the Fredholm-Grothendieck determinant det(1-T{sub s}), where T{sub s} is a generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is given, yielding a method to find not only the spectrum but also the eigenfunctions of the Laplace-Beltrami operator in terms of eigenfunctions of T{sub s}. Various properties of the transfer operator are investigated both analytically and numerically for several systems. (author) 30 refs.; 16 figs.; 2 tabs.
Citation Formats
Bogomolny, E B, and Carioli, M.
Quantum maps from transfer operators.
France: N. p.,
1992.
Web.
Bogomolny, E B, & Carioli, M.
Quantum maps from transfer operators.
France.
Bogomolny, E B, and Carioli, M.
1992.
"Quantum maps from transfer operators."
France.
@misc{etde_10109776,
title = {Quantum maps from transfer operators}
author = {Bogomolny, E B, and Carioli, M}
abstractNote = {The Selberg zeta function {zeta}{sub S}(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, {zeta}{sub S}(s) can be exactly rewritten as the Fredholm-Grothendieck determinant det(1-T{sub s}), where T{sub s} is a generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is given, yielding a method to find not only the spectrum but also the eigenfunctions of the Laplace-Beltrami operator in terms of eigenfunctions of T{sub s}. Various properties of the transfer operator are investigated both analytically and numerically for several systems. (author) 30 refs.; 16 figs.; 2 tabs.}
place = {France}
year = {1992}
month = {Sep}
}
title = {Quantum maps from transfer operators}
author = {Bogomolny, E B, and Carioli, M}
abstractNote = {The Selberg zeta function {zeta}{sub S}(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, {zeta}{sub S}(s) can be exactly rewritten as the Fredholm-Grothendieck determinant det(1-T{sub s}), where T{sub s} is a generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is given, yielding a method to find not only the spectrum but also the eigenfunctions of the Laplace-Beltrami operator in terms of eigenfunctions of T{sub s}. Various properties of the transfer operator are investigated both analytically and numerically for several systems. (author) 30 refs.; 16 figs.; 2 tabs.}
place = {France}
year = {1992}
month = {Sep}
}