Related papers: Discrete time heat kernel and UV modified propagat…
A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…
An approach for solving scattering problems, based on two quantum field theory methods, the heat kernel method and the scattering spectral method, is constructed. This approach converts a method of calculating heat kernels into a method of…
We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation…
We study reflected jump diffusions on Ahlfors regular domains in general metric measure spaces. Under the condition that the Dirichlet form on the ambient space satisfies a capacity upper bound estimate, we construct an extension operator…
We construct a long-time asymptotic profile to the initial value problem of the n-dimensional heat equation. Specifically, we present a modified heat kernel as a long-time asymptotic profile which changes the mass, the center of mass and…
In this paper we propose a generalization of the Gilkey-de Witt heat kernel expansion, designed to provide us with a precise estimation of the heat trace of non-negative Schroedinger type differential operators with non-trivial kernel over…
We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of Jones (Acta Math. 1981) states that uniform domains in…
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…
Within the emerging field of quantum thermodynamics the issues of heat transfer and heat rectification are basic ingredients for the understanding and design of heat engines or refrigerators at nanoscales. Here, a consistent and versatile…
The first heat kernel coefficients are calculated for a dispersive ball whose permittivity at high frequency differs from unity by inverse powers of the frequency. The corresponding divergent part of the vacuum energy of the electromagnetic…
The complex temporal behavior of an ultrashort pulse of light propagating through a multiply scattering medium can be characterized experimentally through a time-gated transmission matrix. Using a spatial light modulator, we demonstrate…
Recently, interest has been growing in studies on discrete or "pixelated" space-time that, through modifications in the dispersion relation, can treat the vacuum as a dispersive medium. Discrete spacetime considers that spacetime has a…
The Herman--Kluk propagator is a popular semi-classical approximation of the unitary evolution operator in quantum molecular dynamics. In this paper we formulate the Herman--Kluk propagator as a phase space integral and discretise it by…
We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection…
We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic…
We use the heat kernel in order to compute the one-loop effective action on a classicalon background. We find that the UV divergences are suppressed relative to the predictions of standard perturbation theory in the interior of the…
The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that the relevant partial differential operator appears in the…
Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…
Perturbation theory is an important tool to describe the properties of QCD at very high temperatures. Recently a new technique has been proposed to compute the one-loop effective action of QCD at finite temperature by making a gauge…
Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…