arXiv subjects

Ivan G Avramidi

Publications and source records attributed to Ivan G Avramidi.

3 recordsLinked to original sources

arXiv2016

Quantum heat traces

We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the usual classical heat trace and compute the asymptotics of these invariants. The coefficients of these asymptotic expansion are determined by the usual heat trace coefficients (which are locally computable) as well as by some new global invariants.

math-ph↗

arXiv2014

Heat Trace and Functional Determinant in One Dimension

We study the spectral properties of the Laplace type operator on the circle. We discuss various approximations for the heat trace, the zeta function and the zeta-regularized determinant. We obtain a differential equation for the heat kernel diagonal and a recursive system for the diagonal heat kernel coefficients, which enables us to find closed approximate formulas for the heat trace and the functional determinant which become exact in the limit of infinite radius. The relation to the generalized KdV hierarchy is discussed as well.

math-ph↗

arXiv2006

Heat Kernel Asymptotics on Symmetric Spaces

We develop a new method for the calculation of the heat trace asymptotics of the Laplacian on symmetric spaces that is based on a representation of the heat semigroup in form of an average over the Lie group of isometries and obtain a generating function for the whole sequence of all heat invariants.

math.DG↗