This is a review on theoretical and experimental studies on dielectric microcavities, which
play a significant role in fundamental and applied research. The basic concepts and theories …

There are words in the language we speak and concepts in our minds. For present
purposes, we can use a relatively common-sense, unsophisticated notion of a linguistic …

A hyperbolic surface is a surface with geometry modeled on the hyperbolic plane. Spectral
theory in this context refers generally to the Laplacian operator induced by the hyperbolic …

Mathematical study of scattering resonances | Bulletin of Mathematical Sciences Skip to main
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We study quantum scattering on manifolds equivalent to the Euclidean space near infinity, in
the semiclassical regime. We assume that the corresponding classical flow admits a non …

We present a conjecture relating the density of quantum resonances for an open chaotic
system to the fractal dimension of the associated classical repeller. Mathematical arguments …

We review recent studies on the resonance spectrum of quantum scattering systems, in the
semiclassical limit and assuming chaotic classical dynamics. Stationary quantum properties …

We consider bounds on the number of semiclassical resonances in neighbourhoods of the
size of the semiclassical parameter, h, around energy levels at which the flow is hyperbolic …

In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence
of instantaneous decay modes guided by classical escape faster than the Ehrenfest time …

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky
group acting on the hyperbolic space ℍ n+ 1: in strips parallel to the imaginary axis the zeta …