相关论文: A heat trace anomaly on polygons

The heat trace of a planar polygon contains corner terms depending only on the opening angles, while the heat trace of a smooth planar domain contains curvature terms along the boundary. We show that, for curvilinear polygons, these two…

Let $(M,g)$ be a two-dimensional Riemannian manifold of finite diameter with a conical singularity. Under the assumption that the metric near the cone point $C$ is rotationally invariant, but not necessarily flat, we give an explicit…

Let $\mathcal O$ be a compact Riemannian orbisurface. We compute formulas for the contribution of cone points of~$\mathcal O$ to the coefficient at $t^2$ of the asymptotic expansion of the heat trace of $\mathcal O$, the contributions at…

In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate…

For a given bounded domain $\Omega$ with smooth boundary in a smooth Riemannian manifold $(\mathcal{M},g)$, we establish a procedure to get all the coefficients of the asymptotic expansion of the trace of the heat kernel associated with the…

We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic…

Let $M$ be a Riemannian manifold and $\Omega$ a smooth domain of $M$. We study the following heat diffusion problem: assume that the initial temperature is equal to $1$, uniformly on $\Omega$, and is $0$ on its complement. Heat will then…

We show that, in odd dimensions, any real valued, bounded potential of compact support has at least one scattering resonance. For dimensions three and higher this was previously known only for sufficiently smooth potentials. The proof is…

We consider the Hodge Laplacian on manifolds with incomplete edge singularities, with infinite dimensional von Neumann spaces and intricate elliptic boundary value theory. We single out a class of its algebraic self-adjoint extensions. Our…

The trace anomaly of gluodynamics on the lattice shows clear fingerprints of a dimension two condensate above the phase transition. The condensate manifests itself through even powers of the inverse temperature while the total perturbative…

The specific heat anomaly (SHA) is broadly observed in statistical mechanics, appearing as a smooth, system-size-independent peak in the specific heat, in contrast to the singular behavior typical of second-order phase transitions (PTs).…

Let $\Omega$ be an open set in a complete, smooth, non-compact, $m$-dimensional Riemannian manifold $M$ without boundary, where $M$ satisfies a two-sided Li-Yau gaussian heat kernel bound. It is shown that if $\Omega$ has infinite measure,…

Heat-invariants are a class of spectral invariants of Laplace-type operators on compact Riemannian manifolds that contain information about the geometry of the manifold, e.g., the metric and connection. Since Brownian motion solves the heat…

We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in…

The low-temperature normal-state specific heat and resistivity curves of various nonmagnetic intermetallic compounds manifest an anomalous thermal evolution. Such an anomaly is exhibited as a break in the slope of the linearized C/T versus…

We consider the heat equation in a smooth bounded convex domain $\Omega \subset \mathbb{R}^2$ with nonlinear Neumann boundary condition $\partial_\nu u = \lambda (u - u^3)$. Stable non-constant stationary solutions do not exist when…

We study the asymptotic behavior of the heat trace coefficients $a_n$ as n tends to infinity for the scalar Laplacian in the context of locally symmetric spaces. We show that if the Plancherel measure of a noncompact type symmetric space is…

D.Freed has formulated and proved an index theorem on odd dimensional spin manifolds with boundary. The proof is based on analysis by Calderon and Seeley. In this note we are going to give a proof of this theorem using the heat kernels…

This is the second in a series of two articles where we study various aspects of the spectral theory associated to families of hyperbolic Riemann surfaces obtained through elliptic degeneration. In the first article, we investigate the…

The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space M is…