Related papers: Heat content with singular initial temperature and…
The evaluation of the specific heat of an open, damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath…
In this paper we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold $M$ with fibered boundary and a $\Phi$-metric $g_\Phi$. This setting generalizes the asymptotically conical (scattering) spaces and includes…
In this paper we study the asymptotic behavior, as $t\downarrow 0$, of the spectral heat content $Q^{(\alpha)}_{D}(t)$ for isotropic $\alpha$-stable processes, $\alpha\in [1,2)$, in bounded $C^{1,1}$ open sets $D\subset \R^{d}$, $d\geq 2$.…
The aim of this article is to study the noncontrollability of the heat equation with double singular potential at an interior point and on the boundary of the domain.
Quantum Monte Carlo results for the specific heat c of the two dimensional Hubbard model are presented. At half-filling it was observed that $c \sim T^2$ at very low temperatures. Two distinct features were also identified: a low…
We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity…
We use probabilistic tools based on Brownian motion and Feynman-Kac formulae to investigate the heat profile for the ground state Dirichlet and second Neumann eigenfunctions. Among other topics, we comment on supremum norm bounds for ground…
In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The Seeley-DeWitt coefficients of this decomposition…
We consider a compact Riemannian manifold $M$ (possibly with boundary) and $\Sigma \subset M\setminus \partial M$ an interior hypersurface (possibly with boundary). We study observation and control from $\Sigma$ for both the wave and heat…
The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior…
We discuss the exotic properties of the heat-trace asymptotics for a regular-singular operator with general boundary conditions at the singular end, as observed by Falomir, Muschietti, Pisani and Seeley as well as by Kirsten, Loya and Park.…
We consider the heat flow of Yang-Mills-Higgs functional where the base manifold is a Riemannian surface and the fiber is a compact symplectic manifold. We show that the corresponding Cauchy problem admits a global weak solution for any…
Motivated by recent discussion about the possibility of non-Clausius (from cold to hot) heat flow, we revisit the familiar model of an impurity atom of mass $M$ embedded in an otherwise uniform one-dimensional harmonic lattice of host atoms…
We study a free boundary optimization problem in heat conduction, ruled by the infinity-Laplace operator, with lower temperature bound and a volume constraint. We obtain existence and regularity results and derive geometric properties for…
We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…
In this paper, we obtain the existence of Dirichlet problem for VT harmonic map from compact Riemannian manifold with or without boundary into compact manifold via the heat flow method. We also obtain the existence of V T geodesics uncer…
Let $G$ be a connected, real, semisimple Lie group with finite center, and $K$ a maximal compact subgroup of $G$. In this paper, we derive $K$-equivariant asymptotics for heat traces with remainder estimates on compact Riemannian manifolds…
A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the…
We propose a model with a quantized degree of freedom to study the heat transport in quasi-one dimensional system. Our simulations reveal three distinct temperature regimes. In particular, the intermediate regime is characterized by heat…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…