相关论文: Heat Expansion and Zeta
It is well-known that the asymptotic expansion of the trace of the heat kernel for Laplace operators on smooth compact Riemmanian manifolds can be obtained through termwise integration of the asymptotic expansion of the on-diagonal heat…
We study the asymptotics of the heat trace $\Tr\{fPe^{-tP^2}\}$ where $P$ is an operator of Dirac type, where $f$ is an auxiliary smooth smearing function which is used to localize the problem, and where we impose spectral boundary…
We consider the basic heat operator on functions on a Riemannian foliation of a compact, Riemannian manifold, and we show that the trace of this operator has a particular short time asymptotic expansion. The coefficients in this expansion…
We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the…
For an elliptic differential operator $D$ of order $h$ in $n$ dimensions, the spectral $\zeta$-function $\zeta_D(s)$ for $\Re s > \frac{n}{h}$ can be evaluated as an integral over the heat kernel $e^{-t D}$. Here, alternative expressions…
The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic differential second order operator is generalized to manifolds with boundary. The first boundary coefficients of the asymptotic expansion which are…
Heat-kernel expansion and zeta function regularisation are discussed for Laplace type operators with discrete spectrum in non compact domains. Since a general theory is lacking, the heat-kernel expansion is investigated by means of several…
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 explicitly construct parametrices for magnetic Schr\"odinger operators on R^d and prove that they provide a complete small-t expansion for the corresponding heat kernel, both on and off the diagonal.
We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and…
The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of…
The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the…
We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel…
We consider Schroedinger operators on compact and non-compact (finite) metric graphs. For such operators we analyse their spectra, prove that their resolvents can be represented as integral operators and introduce trace-class…
For a given bounded domain $\Omega$ with smooth boundary in a smooth Riemannian manifold $(\mathcal{M},g)$, we establish a procedure to get all the coefficients of the asymptotic expansion of the trace of the heat kernel associated with the…
In this note we answer some questions inspired by the introduction, by Alain Connes, of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of…
I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In continuum theory its asymptotic expansion for t -> +0 provides geometric quantities, and therefore may be used to extract effective geometric quantities for fuzzy…
Asymptotic expansions of heat kernels and heat traces of Schr\"odinger operators on non-compact spaces are rarely explored, and even for cases as simple as $\mathbb{C}^n$ with (quasi-homogeneous) polynomials potentials, it's already very…
We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…