Related papers: Integral Equations for Heat Kernel in Compound Med…

Let $d\ge1$ and $0<\alpha<2$. Consider the integro-differential operator \[ \mathcal{L}f(x) =\int_{\mathbb{R}^{d}\backslash\{0\}}\left[f(x+h)-f(x)-\chi_{\alpha}(h)\nabla f(x)\cdot…

We consider an approximate solution to the heat equation which consists of the derivatives of heat kernel. Some conditions in the initial value, under which the approximation converges to the solution of the heat equation or diverges when…

We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum over loops, developed by Roth and Kostrykin, Potthoff, and…

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain…

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions…

We prove heat kernel bounds for the operator (1 + |x|^{\alpha})\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.

We present an efficient integral equation approach to solve the heat equation, $u_t (\x) - \Delta u(\x) = F(\x,t)$, in a two-dimensional, multiply connected domain, and with Dirichlet boundary conditions. Instead of using integral equations…

Let $G$ be a connected semisimple Lie group, and $G_0$ be its connected split real form. In this paper, we deduce explicit expressions for the heat kernels $\rho^{G_0}_t$ associated with the Laplace--Beltrami operators $\Delta_{G_0}$ and…

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…

This work introduces novel numerical algorithms for computational quantum mechanics, grounded in a representation of the Laplace operator -- frequently used to model kinetic energy in quantum systems -- via the heat semigroup. The key…

We derive all heat kernel coefficients for Laplacians acting on scalars, vectors, and tensors on fully symmetric spaces, in any dimension. Final expressions are easy to evaluate and implement, and confirmed independently using spectral sums…

The green functions for the heat and Laplace equations with dynamical boundary conditions in a ball are studied. First, the green functions of the Laplace equation with a dynamical boundary condition are given, and the properties of related…

The calculation of heat-kernel coefficients with the classical DeWitt algorithm has been discussed. We present the explicit form of the coefficients up to $h_5$ in the general case and up to $h_7^{min}$ for the minimal parts. The results…

In this paper, we generally expressed the virial expansion of ideal quantum gases by the heat kernel coefficients for the corresponding Laplace type operator. As examples, we give the virial coefficients for quantum gases in $d$-dimensional…

Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n\ge 2$. Consider the conformal perturbation $\tilde{g}=h g$ where $h$ is a smooth bounded positive function on $M$. Denote by $\tilde{p}_t(x,y)$ the heat kernel of manifolds…

We investigate the heat equation corresponding to the Bessel operators on a symmetric cone $\Omega=G/K$. These operators form a one-parameter family of elliptic self-adjoint second order differential operators and occur in the Lie algebra…

Motivated by practical applications in heat conduction and contaminant transport, we consider heat and mass diffusion across a perturbed interface separating two finite regions of distinct diffusivity. Under the assumption of continuity of…

Heat kernel expansion coefficients are calculated for vacuum fluctuations with distributional background potentials and field strengths. Terms up to and including t^5/2 are presented.

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…

The heat kernel in curved space-time is computed to fourth order in a strict expansion in the number of covariant derivatives. The computation is made for arbitrary non abelian gauge and scalar fields and for the Riemann connection in the…