Related papers: Connecting quasinormal modes and heat kernels in 1…
The heat kernel transform H_t for the Heisenberg group is studied in detail. The main result shows that the image of H_t is a direct sum of two weighted Bergman spaces whose associated weighted functions are of oscillatory nature, i.e.…
We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Horava gravity (and in Lifshitz field theories in general). This method maintains covariance at all stages of the calculation,…
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres.…
Two different methods of the covariant relativistic separable kernel construction in the Bethe-Salpeter approach are considered. One of them leads in the center-of-mass system of two particles to the quasipotential equation. The constructed…
Using an orbifold description of the Euclidean BTZ black hole, we show that there is a special relation between the spectrum and the truncated heat kernel of this black hole with the Patterson-Selberg zeta function.
We construct the fundamental solution (the heat kernel) $p^{\kappa}$ to the equation $\partial_t=\mathcal{L}^{\kappa}$, where under certain assumptions the operator $\mathcal{L}^{\kappa}$ takes one of the following forms, \begin{align*}…
We propose a new type of approximation to quantum determinants, ``quantum Fredholm determinant", and conjecture that, compared to the quantum Selberg zeta functions derived from Gutzwiller semiclassical trace formulas, such determinants…
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…
Let $\theta$ and $\mu$ denote the location and the size of the mode of a probability density. We study the joint convergence rates of semirecursive kernel estimators of $\theta$ and $\mu$. We show how the estimation of the size of the mode…
We review the status of covariant methods in quantum field theory and quantum gravity, in particular, some recent progress in the calculation of the effective action via the heat kernel method. We study the heat kernel associated with an…
Heat kernel coefficients encode the short distance behavior of propagators in the presence of background fields, and are thus useful in quantum field theory. We present a Mathematica program for computing these coefficients and their…
The scattering problems of a scalar point particle from a finite assembly of n>1 non-overlapping and disconnected hard disks, fixed in the two-dimensional plane, belong to the simplest realizations of classically hyperbolic scattering…
Integrals involving the kernel function $sech (\pi x)$ over a semi-infinite range are of general interest in the study of Riemann's function $\zeta(s)$ and Hurwitz' function $\zeta(s,a)$. Such integrals that include the $arctan$ and $log$…
In this paper, we investigate the quasinormal modes of two covariant effective black holes characterized by the quantum parameter $\zeta$, charge $Q$, and cosmological constant $\Lambda$, under the scalar perturbation. By employing the…
The heat-kernel expansion and $\zeta$-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with…
In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the…
This is the second in a series of two articles where we study various aspects of the spectral theory associated to families of hyperbolic Riemann surfaces obtained through elliptic degeneration. In the first article, we investigate the…
This paper systematically investigates the quasinormal modes (QNMs) and tidal Love numbers of covariant quantum-modified black holes (BHs) within two cosmological constant-dependent metric frameworks. By deriving axial/polar perturbation…
Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and…
We give an asymptotic expansion of the relative entropy between the heat kernel $q_Z(t,z,w)$ of a compact Riemannian manifold $Z$ and the normalized Riemannian volume for small values of $t$ and for a fixed element $z\in Z$. We prove that…