We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an an...

Consider an irreducible Markov chain which satisfies a ratio limit theorem, and let $\rho$ be the spectral radius of chain. We investigate relation $\rho\,$-Martin boundary with induced by $\rho\,$-harmonic kernel appears in limit. Special emphasis is on random walks non-amenable groups, specifically, free groups hyperbolic groups.

T he optimal allocation of natural gas resources to various uses such as final and intermediate consumption, injection into oil fields, and exports can help policymakers to use this kind of resources efficiently. Empirical evidence support using hyperbolic discount rates instead of fixed discount rates in the economic literature. The purpose of this study is to maximize the social we...

We investigate the scale-shift operator for discrete-time signals via action of hyperbolic Blaschke group. Practical implementation issues are discussed and given any arbitrary scale, in framework very classical linear filtering. Our group theoretical standpoint leads to a purely harmonic analysis definition Mellin transform signals. Explicit analytical expressions atoms Fourier-Mellin decompos...

New estimates are derived concerning the behavior of self-dual hamonic 2-forms on a compact Riemannian 4-manifold with non-trivial Seiberg-Witten invariants. Applications include a vanishing theorem for certain Seiberg-Witten invariants on compact 4-manifolds of constant negative sectional curvature.

On a periodic planar graph whose edge weights satisfy a certain simple geometric condition, the discrete Laplacian and ∂̄ operators have the property that their determinants and inverses only depend on the local geometry of the graph. We obtain explicit expressions for the logarithms of the (normalized) determinants, as well as the inverses of these operators. We relate the logarithm of the dete...

Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein’s equations with the harmonic slicing condition is presented. Significant errors in the mass function are shown to arise from the steep gradient zone behind the black hole horizon, which challenge the Computational Fluid Dyna...

Let (Mn; g) be a compact Riemannian manifold with Ric (n 1). It is well known that the bottom of spectrum 0 of its unverversal covering satis…es 0 (n 1) =4. We prove that equality holds i¤ M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy. 1. Introduction Complete Riemannian manifolds with nonnegative Ricci curvature have been intensively studied by many people and...

‎The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]‎. ‎In [1]‎, ‎Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups ‎and gyrovector spaces for dealing with the Lorentz group and its ‎underlying hyperbolic geometry‎. ‎They defined the Chen addition and then Chen model of hyperbolic geomet...