Related papers: Comment on `Index-free Heat Kernel Coefficients'

In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…

We consider long-range interactions between two alkali-metal atoms in their respective ground states. We extend the previous relativistic many-body calculations of C_6 dispersion coefficients [Phys.Rev. Lett. {\bf 82}, 3589 (1999)] to…

Let $p$ be an odd prime, $F$ a field with a primitive $p^2$th root of unity, and $E=F(\sqrt[p]{b_1},\sqrt[p]{b_2})$ an elementary abelian extension of degree $p^2$. This paper studies the cohomological kernel $H^n(E/F,{\mathbb Z}/p{\mathbb…

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…

A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the…

We consider a gauge symmetry in a quantum Hilbert space. The symmetry leads to that of the heat-kernel and of the anomaly formulae which were previously obtained by the authors. This greatly simplifies and clarifies the structure of the…

Let $H=-\Delta+V$ be a Schr\"odinger operator on $\mathbb{R}^n$. We show that gradient estimates for the heat kernel of $H$ with upper Gaussian bounds imply polynomial decay for the kernels of certain smooth dyadic spectral operators. The…

It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The associated diffusion operator is…

We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.

We derive a local Gaussian upper bound for the $f$-heat kernel on complete smooth metric measure space $(M,g,e^{-f}dv)$ with nonnegative Bakry-\'{E}mery Ricci curvature, which generalizes the classic Li-Yau estimate. As applications, we…

The van der Waals coefficients, from C_11 through to C_16 resulting from 2nd, 3rd and 4th order perturbation theory are estimated for the alkali (Li, Na, K and Rb) atoms. The dispersion coefficients are also computed for all possible…

A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and…

We consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…

We calculate the first three Gilkey-DeWitt (heat-kernel) coefficients, a0, a1 and a2, for massive particles having the spins of most physical interest in n dimensions, including the contributions of the ghosts and the fields associated with…

We prove that in presence of $L^2$ Gaussian estimates, so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.

We construct an index of first-order, self-adjoint, elliptic differential operators in the $K$-theory of a Fr\'echet algebra of smooth kernels with faster than exponential off-diagonal decay. We show that this index can be represented by an…

The claim in \cite{Al-Badawi:2025ipr} that *"the errors in the foundational components (3) and (5) of Ref. [1] invalidate all subsequent analyses, numerical results, and physical interpretations that depend on them"* is **entirely…

A short informal overview about recent progress in the calculation of the effective action in quantum gravity is given. I describe briefly the standard heat kernel approach to the calculation of the effective action and discuss the…

We prove pointwise and $L^p$ gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hodge semigroup in that setting and prove estimates for its…

In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation…