Related papers: A deformation formula for the heat kernel
We present quantum heat machines using a diatomic molecule modelled by a $q$-deformed potential as a working medium. We analyze the effect of the deformation parameter and other potential parameters on the work output and efficiency of the…
We study heat semigroups generated by self-adjoint Laplace operators on metric graphs characterized by the property that the local scattering matrices associated with each vertex of the graph are independent from the spectral parameter. For…
We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of H\"older continuous functions. As an application we solve the Dirichlet and…
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…
This paper aims to study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic…
A non-relativistic quantum model is considered with a point particle carrying a charge $e$ and moving on the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of…
We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\infty}$ coefficients we obtain Gaussian estimates with best constants, while for…
We provide sharp two-sided estimates of the heat kernel of the Dirichlet fractional Laplacian on the half-line perturbed by the Hardy potential.
Let $(X,g)$ be a product cone with the metric $g=dr^2+r^2h$, where $X=C(Y)=(0,\infty)_r\times Y$ and the cross section $Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the upper boundedness of heat kernel associated…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
In this paper we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function the related thermodynamic functions are derived and studied in…
We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…
We study the heat kernel asymptotics for the Laplace type differential operators on vector bundles over Riemannian manifolds. In particular this includes the case of the Laplacians acting on differential p-forms. We extend our results…
We build a systematic calculational method for the covariant expansion of the two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal differential operators of any order. This is the expansion in powers of dimensional…
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.
While an integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions is available in the literature, a proof of this formula seems to be…
We prove upper and lower bounds of the heat kernel for the operator $\Delta-\nabla (\frac{1}{|x|^{\alpha}})\cdot \nabla $ in $\mathbb{R}^{n}\setminus\{0} $ where $\alpha >0$. We obtain these bounds from an isoperimetric inequality for a…
In this article an intertwining operator is constructed which transforms the harmonic oscillator to the Dirac operator (the first order derivative operator). We give also the explicit solutions to the heat and wave equation associated to…
In this paper we develop the parametrix approach for constructing the heat kernel on a graph $G$. In particular, we highlight two specific cases. First, we consider the case when $G$ is embedded in a Eulidean domain or manifold $\Omega$,…
The heat kernel on the symmetric space of positive definite Hermitian matrices is used to endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of probability measures depending on a choice of the background…