相关论文: Large time behavior of the heat kernel of two-dime…
We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum over loops, developed by Roth and Kostrykin, Potthoff, and…
We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^\mu\N_\mu$. Our…
In this paper, we study the Schr\"odinger operator $\Delta-V$, where $V$ is a supercritical non-negative potential belonging to a large class of functions containing functions of the form $b|x|^{-(2+2\beta)}$, $b, \beta>0$. We obtain…
We consider non-local Schr\"odinger operators $H=-L-V$ in $L^2(\mathbf{R}^d)$, $d \geq 1$, where the kinetic terms $L$ are pseudo-differential operators which are perturbations of the fractional Laplacian by bounded non-local operators and…
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres.…
The time-dependent behavior of the Heisenberg model in contact with a phonon heat bath and in an external time-dependent magnetic field is studied by means of a path integral approach. The action of the phonon heat bath is taken into…
We study the heat semigroup maximal operator associated with a well-known orthonormal system in the d-dimensional ball. The corresponding heat kernel is shown to satisfy Gaussian bounds. As a consequence, we can prove weighted $L^p$…
We study the law of a hypoelliptic Brownian motion on an infinite-dimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous…
We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel…
The thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets (HFM) in an external magnetic field is investigated within a second-order two-time Green function formalism in the wide temperature and field range. A crucial point of…
Let $\alpha(x)$ be a measurable function taking values in $ [\alpha_1,\alpha_2]$ for $0<\A_1\le \A_2<2$, and $\kappa(x,z)$ be a positive measurable function that is symmetric in $z$ and bounded between two positive constants. Under a…
Heating under periodic driving is a generic nonequilibrium phenomenon, and it is a challenging problem in nonequilibrium statistical physics to derive a quantitatively accurate heating rate. In this work, we provide a simple formula on the…
We relate Gruet formula for the heat kernel on real hyperbolic spaces to the commonly used one derived from Millson induction. The bridge between both formulas is settled by Yor result on the joint distribution of a Brownian motion and of…
In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…
Recently, Nagel and Stein studied the $\square_b$-heat equation, where $\square_b$ is the Kohn Laplacian on the boundary of a weakly-pseudoconvex domain of finite type in $\C^2$. They showed that the Schwartz kernel of $e^{-t\square_b}$…
In this work, we study the heat equation with Grushin's operator. We present an expression for its heat kernel, prove its decay in $L^p$ spaces, and that it is an approximation of the identity. As a consequence, the heat semigroup…
In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of…
We show that, under a natural scaling, the small-time behavior of the logarithmic derivatives of the subelliptic heat kernel on $SU(2)$ converges to their analogues on the Heisenberg group at time 1. Realizing $SU(2)$ as $\mathbb{S}^3$, we…
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…
In this article we give explicit solutions for the wave equations associated to the modified Schr\"odinger operators with magnetic field on the disc and the upper half plane models of the hyperbolic plane. We show that the modified…