---
res:
bibo_abstract:
- "Abstract\r\n For a compact Riemannian
locally symmetric space $\\mathcal M$ of rank 1 and an associated vector bundle
$\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal M$, we
give a precise description of those classical (Pollicott–Ruelle) resonant states
on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the Anosov-unstable
directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal M$. In particular,
we show that they are isomorphically mapped by natural pushforwards into generalized
common eigenspaces of the algebra of invariant differential operators $D(G,\\sigma
)$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$ over $\\mathcal
M$. As a consequence of this description, we obtain an exact band structure of
the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations
$\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau }$ and $\\mathbf
W_{\\sigma }$, we obtain a very explicit description of the generalized common
eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to
quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of
$\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory
and Lie theory.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Benjamin
foaf_name: Küster, Benjamin
foaf_surname: Küster
- foaf_Person:
foaf_givenName: Tobias
foaf_name: Weich, Tobias
foaf_surname: Weich
bibo_doi: 10.1093/imrn/rnz068
bibo_issue: '11'
bibo_volume: 2021
dct_date: 2021^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1073-7928
- http://id.crossref.org/issn/1687-0247
dct_language: eng
dct_publisher: Oxford University Press (OUP)@
dct_subject:
- General Mathematics
dct_title: Quantum-Classical Correspondence on Associated Vector Bundles Over Locally
Symmetric Spaces@
...