Related papers: HeatK: A Mathematica Program for Computing Heat Ke…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an…
We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the…
A method for calculation of the DWSG coefficients for operators in spaces with metric incompatible with connection is suggested based on a generalization of the pseudodifferential operators technique. By using the proposed method, the…
We present a method for the calculation of the $a_{3/2}$ heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special…
Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In…
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…
One of the principal objectives of quantum thermodynamics is to explore quantum effects and their potential beneficial role in thermodynamic tasks like work extraction or refrigeration. So far, even though several papers have already shown…
In this paper we shall study vacuum fluctuations of a single scalar field with Dirichlet boundary conditions in a finite but very long line. The spectral heat kernel, the heat partition function and the spectral zeta function are calculated…
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…
In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of…
We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature. The algorithm exploits the fact that quantum effects are short-range in these…
We consider smeared zeta functions and heat-kernel coefficients on the bounded, generalized cone in arbitrary dimensions. The specific case of a ball is analysed in detail and used to restrict the form of the heat-kernel coefficients $A_n$…
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…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
We establish heat kernel and gradient estimates for the density of kinetic degenerate Kolmogorov stochastic differentia equations. Our results are established under somehow minimal assumptions that guarantee the SDE is weakly well posed.
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 present a detailed thermodynamic analysis of a three-level quantum heat engine coupled continuously to hot and cold reservoirs. The system is driven by an oscillating external field and is described by the Markovian quantum master…
In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well-established methodology of diffusion wavelets. This novel…
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four…
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…