Related papers: Distribution of resonances for hyperbolic surfaces

The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…

In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue…

We study the product of Selberg Zeta function and hyperbolic Eisenstein series on a family of degenerating hyperbolic surfaces.

Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…

The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in…

We study the role of finite widths of resonances in a nonlocal version of the Wick-Cutkosky model. The spectrum of bound states is known analytically in this model and forms linear Regge tragectories. We compute the widths of resonances,…

We address the problem of calculating momentum distributions of particles emerging from the three-body decay of a many-body resonance. We show that these distributions are determined by the asymptotics of the coordinate-space complex-energy…

In this succinct note, it is showed that a partition function of equivalent classes of hyperbolic surfaces can be connected to an Ising model located on the boundary of the Poincare disc, as hinted by Poincare's Uniformization theorem and…

The third part of the paper is devoted to ray tracing in optical resonators. The employed method for dealing with the issue uses the elliptical or hyperbolic rotations that Wigner distributions associated with optical fields undergo during…

The thermal partition functions of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local zeta-function approach. The relation with the surface terms previously…

We obtain an estimate from below for the remainder in Weyl's law on negatively curved surfaces. In the constant curvature case, such a bound was proved independently by Hejhal and Randol in 1976 using the Selberg zeta function techniques.…

We use the asymptotic expansion of the heat trace to express all residues of spectral zeta functions as regularized sums over the spectrum. The method extends to those spectral zeta functions that are localized by a bounded operator.

We study Selberg zeta functions $Z(s,\sigma)$ associated to locally homogeneous vector bundles over the unit-sphere bundle of a complete odd-dimensional hyperbolic manifold of finite volume. We assume a certain condition on the fundamental…

Given a compact real hyperbolic space we study the connection between certain phase space distributions, so called Patterson-Sullivan distributions, and dynamical zeta functions. These zeta functions generalize logarithmic derivatives of…

We consider a semi-infinite dielectric with multiple spatially dispersive resonances in the susceptibility. The effect of the boundary is described by an arbitrary reflection coefficient for polarization waves in the material at the…

We define Pollicott-Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows. These resonances are the poles of…

We present a possible way of computing resonance poles and modes in scattering theory. Numerical examples are given for the scattering of electromagnetic waves by finite-size photonic crystals.

This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric…

We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding…

We study resonances of surfaces of revolution obtained by removing a disk from a cone and attaching a hyperbolic cusp in its place. These surfaces include ones with nontrapping geodesic flow (every maximally extended non-reflected geodesic…