Hermitian symplectic geometry and the factorization of the scattering matrix on graphs

Harmer, M.

doi:10.1088/0305-4470/33/49/302

Cited by 44 publications

(77 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For more on this classical theory, see for example [32,33,41,55,66,67] and for its use to analyze second order regular singular operators, see [10, 11, 38-40, 49, 54, 56], and see Gil and Mendoza [24] and Lesch [44] for the analysis of more general Fuchs type or cone operators in the sense of Schulze [59,60]; finally, see [16] for applications of self-adjoint extensions to quantum physics.…”

Section: Hermitian Symplectic Formalism Of Self-adjoint Extensionsmentioning

confidence: 99%

Exotic Expansions and Pathological Properties of ζ-Functions on Conic Manifolds

2008

View full text Add to dashboard Cite

We give a complete classification and present new exotic phenomena of the meromorphic structure of ζ -functions associated to general self-adjoint extensions of Laplace-type operators over conic manifolds. We show that the meromorphic extensions of these ζ -functions have, in general, countably many logarithmic branch cuts on the nonpositive real axis and unusual locations of poles with arbitrarily large multiplicity. The corresponding heat kernel and resolvent trace expansions also exhibit exotic behaviors with logarithmic terms of arbitrary positive and negative multiplicity. We also give a precise algebraic-combinatorial formula to compute the coefficients of the leading order terms of the singularities.

show abstract

Section: Hermitian Symplectic Formalism Of Self-adjoint Extensionsmentioning

confidence: 99%

Exotic Expansions and Pathological Properties of ζ-Functions on Conic Manifolds

2008

View full text Add to dashboard Cite

show abstract

“…This correspondence is a direct consequence of von Neumann's classical theory of self-adjoint extensions; a partial list of relevant references is [33,34,35,65,81,86,80,69,70,72,77,78,79,80,90,93,104,105]. …”

Section: The Hermitian Symplectic Theory Of Self-adjoint Extensionsmentioning

confidence: 99%

Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

2007

View full text Add to dashboard Cite

Abstract. In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with [13], a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.

show abstract

“…However eigenvalues ±1 which coincide with the eigenvalues ±1 of S do not depend on k. All other eigenvalues tend to 1 as k → ∞. The high energy limit of S V (k) exists [4,5,8] and is given by…”

Section: Vertex Scattering Matricesmentioning

confidence: 97%