Related papers: Gilkey-de Witt heat kernel expansion and zero mode…

We obtain sharp estimates for the Jacobi heat kernel in a range of parameters where the result has not been established before. This extends and completes an earlier result due to the authors. The proof is based on a generalization of the…

We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking…

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…

The proper time method plays an important role in modern mathematics and physics. It includes many approaches, each of which has its pros and cons. This work is devoted to the description of one model case, which reflects the subtleties of…

We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.

We consider a complete non-compact Riemannian manifold satisfying the volume doubling property and a Gaussian upper bound for its heat kernel (on functions). Let -- $\rightarrow$ $\Delta$ k be the Hodge-de Rham Laplacian on differential…

In this article, we prove a general and rather flexible upper bound for the heat kernel of a weighted heat operator on a closed manifold evolving by an intrinsic geometric flow. The proof is based on logarithmic Sobolev inequalities and…

We prove that for a general diffusion process, certain assumptions on its behavior \emph{only within a fixed open subset} of the state space imply the existence and sub-Gaussian type off-diagonal upper bounds of the \emph{global} heat…

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 develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an…

If the zero-field transition in high temperature superconductors such as YBa_2Cu_3O_7-\delta is a critical point in the universality class of the 3-dimensional XY model, then the general theory of critical phenomena predicts the existence…

We introduce a new method that exploits the combination of the Heat Kernel (HK) and Background Field Method to compute gauge-invariant and gauge parameter-independent quantities such as the effective potential, anomalous dimensions, and…

We develop an extension of the Gutzwiller approximation to finite temperatures based on the Dirac-Frenkel variational principle. Our method does not rely on any entropy inequality, and is substantially more accurate than the approaches…

We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the…

This paper is devoted to the study of the one dimensional non homogeneous heat equation coupled to Dirichlet Boundary Conditions. We obtain the explicit expression of the solution of the linear equation by means of a direct integral in an…

Using our recently proposed covariant algebraic approach the heat kernel for a Laplace-like differential operator in low-energy approximation is studied. Neglecting all the covariant derivatives of the gauge field strength (Yang-Mills…

We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU($n$) Heisenberg model with arbitrary $n$. The new method is a novel extension of the well-established…

We consider the Schr{\"o}dinger operator H = --$\Delta$ + V (|x|) with radial potential V which may have singularity at 0 and a quadratic decay at infinity. First, we study the structure of positive harmonic functions of H and give their…

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…

A special class of non-minimal operators which are relevant for quantum field theory is introduced. The general form of the heat kernel coefficients of these operators on manifolds without boundary is described. New results are presented…