Related papers: Quantum-classical correspondence on associated vec…

We establish a direct classical-quantum correspondence on convex cocompact hyperbolic manifolds between the spectrums of the geodesic flow and the Laplacian acting on natural tensor bundles. This extends previous work detailing the…

We study the resonances of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type. The symmetric space is assumed to have rank-one but the…

For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves…

With each resonance of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type, One can associate a residue representation. The purpose of this paper…

We describe the complex poles of the power spectrum of correlations for the geodesic flow on compact hyperbolic manifolds in terms of eigenvalues of the Laplacian acting on certain natural tensor bundles. These poles are a special case of…

We show that the autocorrelation of quantum spectra of an open chaotic system is well described by the classical Ruelle-Pollicott resonances of the associated chaotic strange repeller. This correspondence is demonstrated utilizing microwave…

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

If X is a contact Anosov vector field on a smooth compact manifold M and V is a smooth function on M, it is known that the differential operator A=-X+V has some discrete spectrum called Ruelle-Pollicott resonances in specific Sobolev…

We prove that the twisted De Rham cohomology of a flat vector bundleover some smooth manifold is isomorphic to the cohomology of invariant Pollicott--Ruelleresonant states associated with Anosov and Morse--Smale flows. As a consequence,…

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle,…

We study the asymptotic behaviour of eigenvalues and eigenmodes of the Witten Laplacian on a smooth compact Riemannian manifold without boundary. We show that they converge to the Pollicott-Ruelle spectrum of the corresponding gradient flow…

First an `irregular Riemann-Hilbert correspondence' is established for meromorphic connections on principal G-bundles over a disc, where G is any connected complex reductive group. Secondly, in the case of poles of order two, isomonodromic…

We consider the isomonodromy problems for flat $G$-bundles over punctured elliptic curves $\Sigma_\tau$ with regular singularities of connections at marked points. The bundles are classified by their characteristic classes. These classes…

In this article we consider the continuity of the eigenvalues of the connection Laplacian of $G$-connections on vector bundles over Riemannian manifolds. To show it, we introduce the notion of the asymptotically $G$-equivariant measured…

Let $\varphi_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying…

Let $(M,g)$ be a smooth Anosov Riemannian manifold and $\mathcal{C}^\sharp$ the set of its primitive closed geodesics. Given a Hermitian vector bundle $\mathcal{E}$ equipped with a unitary connection $\nabla^{\mathcal{E}}$, we define…

We establish an equidistribution result for Ruelle resonant states on compact locally symmetric spaces of rank one. More precisely, we prove that among the first band Ruelle resonances there is a density one subsequence such that the…

We investigate the correspondence between the decay of correlation in classical system, governed by Ruelle--Pollicott resonances, and the properties of the corresponding quantum system. For this purpose we construct classical systems with…

A three-dimensional quasi-Fuchsian Lorentzian manifold $M$ is a globally hyperbolic spacetime diffeomorphic to $\Sigma\times (-1,1)$ for a closed orientable surface $\Sigma$ of genus $\geq 2$. It is the quotient $M=\Gamma\backslash…

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…