Related papers: Integral Equations for Heat Kernel in Compound Med…
We consider off-diagonal asymptotic series for integral kernels of functions of Laplace-type operators on curved backgrounds. These expansions are obtained by applying integral transforms to the DeWitt series for the heat kernel of the…
In this article we consider resummed expressions for the heat-kernel's trace of a Laplace operator, the latter including a potential and imposing Dirichlet semitransparent boundary conditions on a surface of codimension one in flat space.…
Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\aa)}$ be the…
Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions…
We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate several first coefficients of the heat kernel expansion. These coefficients are responsible for divergences and conformal…
We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called…
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel admits an approximation involving a number of terms that is…
A distribution on the real line has a continuous primitive integral if it is the distributional derivative of a function that is continuous on the extended real line. The space of distributions integrable in this sense is a Banach space…
An overview about recent progress in the calculation of the heat kernel and the one-loop effective action in quantum gravity and gauge theories is given. We analyse the general structure of the standard Schwinger-De Witt asymptotic…
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…
Networks constitute fundamental organizational structures across biological systems, although conventional graph-theoretic analyses capture exclusively pairwise interactions, thereby omitting the intricate higher-order relationships that…
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…
We establish a reduction principle to derive Li-Yau inequalities for non-local diffusion problems in a very general framework, which covers both the discrete and continuous setting. Our approach is not based on curvature-dimension…
Let $G$ be a noncompact semisimple Lie group equipped with a certain invariant Riemannian metric. Then, we can consider a heat kernel function on $G$ associated to the Riemannian metric. We give an explicit formula for the heat kernel when…
We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…
The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…
We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity is of order two…
Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the…
In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario…
In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \geq -Kg$. We accomplish this extension via…