相关论文: Resonance chains in open systems, generalized zeta…

Resonance chains have been observed in many different physical and mathematical scattering problems. Recently numerical studies linked the phenomenon of resonances chains to an approximate clustering of the length spectrum on integer…

In ballistic open quantum systems one often observes that the resonances in the complex-energy plane form a clear chain structure. Taking the open 3-disk system as a paradigmatic model system, we investigate how this chain structure is…

We quantitatively relate the resonance sets of topologically finite infinite-area hyperbolic surfaces with no cusps to the resonance sets of certain metric graphs via the spine graph construction. In particular, we prove the existence of…

We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard…

We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree…

For the paradigmatic three-disk scattering system, we confirm a recent conjecture for open chaotic systems, which claims that resonance states are composed of two factors. In particular, we demonstrate that one factor is given by universal…

This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…

A resonant chain may be formed in a multi-planetary system when ratios of the orbital periods can be expressed as ratios of small integers $T_1:T_2: \cdots :T_N=k_1: k_2: \cdots: k_N$. We investigate the dynamics and possible formation of…

This paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and…

The multifractal structure underlying a self-similar measure stems directly from the weighted self-similar system (or weighted iterated function system) which is used to construct the measure. This follows much in the way that the dimension…

In the framework of quantum open systems, that is, simple quantum systems coupled to quantum baths, our aim is to characterize those actions of the quantum environment which give rise to dynamics dictated by classical noises. First, we…

Aspects of the properties, enumeration and construction of points on diagonal and Hermitian surfaces have been considered extensively in the literature and are further considered here. The zeta function of diagonal surfaces is given as a…

We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…

We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…

For the random interval partition of $[0,1]$ generated by the uniform stick-breaking scheme known as GEM$(1)$, let $u_k$ be the probability that the first $k$ intervals created by the stick-breaking scheme are also the first $k$ intervals…

We discuss stochastic resonance-like effects in the context of coupled quantum spin systems. We focus here on an information-theoretic approach and analyze the steady state quantum correlations (entanglement) as well as the global…

Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations in turn reduce the labor and improve the…

We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of…

The purpose of this note is to give a brief overview on zeta functions of curve singularities and to provide some evidences on how these and global zeta functions associated to singular algebraic curves over perfect fields relate to each…

The distortion of the regular motion in a quantum system by its coupling to the continuum of decay channels is investigated. The regular motion is described by means of a Poissonian ensemble. We focus on the case of only few channels K<10.…