Related papers: Heat kernel coefficients for chiral bag boundary c…
Computer algebra methods are applied to investigation of spectral asymptotics of elliptic differential operators on curved manifolds with torsion and in the presence of a gauge field. In this paper we present complete expressions for the…
The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(-tP) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The…
We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…
Being motivated by physical applications (as the phi^4 model) we calculate the heat kernel coefficients for generalised Laplacians on the Moyal plane containing both left and right multiplications. We found both star-local and star-nonlocal…
In this paper, we prove that the L^2 Betti numbers of an amenable covering space can be approximated by the average Betti numbers of a regular exhaustion, under some hypotheses. We also prove that some L^2 spectral invariants can be…
In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss…
We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in $\mathbb{R}^d$. They are…
Let $J$ be the L\'evy density of a symmetric L\'evy process in $\mathbb{R}^d$ with its L\'evy exponent satisfying a weak lower scaling condition at infinity. Consider the non-symmetric and non-local operator $$ {\mathcal L}^{\kappa}f(x):=…
Spectral boundary conditions for Laplace-type operators, of interest in string and brane theory, are partly Dirichlet, partly Neumann-type conditions, partitioned by a pseudodifferential projection. We give sufficient conditions for…
Local boundary conditions for spinor fields are expressed in terms of a 1-parameter family of boundary operators, and find applications ranging from (supersymmetric) quantum cosmology to the bag model in quantum chromodynamics. The present…
We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity is of order two…
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…
We study the $\eta$-invariant of a Dirac operator on a manifold with boundary subject to local boundary conditions with the help of heat kernel methods. In even dimensions, we relate this invariant to $\eta$-invariants of a boundary Dirac…
We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the…
The generator of time-translations on the solution space of the wave equation on stationary spacetimes specialises to the square root of the Laplacian on Riemannian manifolds when the spacetime is ultrastatic. Its spectral analysis…
We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this expansion by a natural intertwining property. In particular we will give a closed formula for…
The $N_f$-flavour Schwinger Model on a finite space $0\leq x^1\leq L$ and subject to bag-type boundary-conditions at $x^1=0$ und $x^1=L$ is solved at finite temperature $T=1/\beta$. The boundary conditions depend on a real parameter…
We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admits an asymptotic expansion at t=0 with coefficients that…
We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…
We study Schroedinger operators with Robin boundary conditions on exterior domains in $\R^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of…