相关论文: Stability theorems for chiral bag boundary conditi…
We study the asymptotic expansion of the smeared L2-trace of fexp(-tP^2) where P is an operator of Dirac type, f is an auxiliary smooth smearing function which is used to localize the problem, and chiral bag boundary conditions are imposed.…
We study the asymptotics of the heat trace $\Tr\{fPe^{-tP^2}\}$ where $P$ is an operator of Dirac type, where $f$ is an auxiliary smooth smearing function which is used to localize the problem, and where we impose spectral boundary…
Let $\ui\di$ be the Dirac operator on a $D=2d$ dimensional ball $\mcB$ with radius $R$. We calculate the spectral asymmetry $\eta(0,\ui\di)$ for D=2 and D=4, when local chiral bag boundary conditions are imposed. With these boundary…
We prove strong ellipticity of chiral bag boundary conditions on even dimensional manifolds. From a knowledge of the heat kernel in an infinite cylinder, some basic properties of the zeta function are analyzed on cylindrical product…
This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the…
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 consider the classical and local thermodynamic stability of non- and near-extremal Dp-branes smeared on a transverse direction. These two types of stability are connected through the correlated stability conjecture for which we give a…
We propose a relation between the $\eta$ invariant on a manifold with boundary, the $\eta$ invariants of edge states, and the $\eta$ invariant in an infinite volume limit. With the example of planar fermions with bag and chiral bag boundary…
In this paper we study the interplay between Lagrangian cobordisms and stability conditions. We show that any stability condition on the derived Fukaya category $D\mathcal{F}uk(M)$ of a symplectic manifold $(M,\omega)$ induces a stability…
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…
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…
Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.
The paper is concerned with the stability property under perturbation $Q\to\widetilde Q$ of different spectral characteristics of a BVP associated in $L^2([0,1];\Bbb C^2)$ with the following $2\times2$ Dirac type equation…
Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.
This is a survey of recent results on zeta- and eta-function poles and values for realizations of Laplace- and Dirac-type operators defined by pseudodifferential projection boundary conditions (including the Atiyah-Patodi-Singer operator…
It is known that in the zeta function regularization and in the Fujikawa method chiral anomaly is defined through a coefficient in the heat kernel expansion for the Dirac operator. In this paper we apply the heat kernel methods to calculate…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
We consider the dynamics of rotationally supported thin galactic disc composed of stars and gas under the influence of external tidal field and derive the coupled differential equations governing the evolution of instabilities. Further…
We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent diffeomorphisms, $L_p$-maximal regularity theory, and the…
For an arbitrary parameter $p\in [1,+\infty]$, we consider the problem of exponential stabilization in the spatial $L^{p}$-norm, and $W^{1,p}$-norm, respectively, for a class of anti-stable linear parabolic PDEs with space-time-varying…