arXiv subjects

Thomas Stucker

Publications and source records attributed to Thomas Stucker.

5 recordsLinked to original sources

arXiv2026

Derivation and application of sheath boundary conditions for drift-kinetic simulations in a linear plasma device based on a gyromoment approach

Boundary conditions for a drift-kinetic model at the collisional presheath entrance with perpendicular incidence of the magnetic field to the wall are derived and numerically implemented. The drift-kinetic model for the plasma is based on the expansion of the ion distribution function on a Hermite-Laguerre basis, and the evolution of the resulting gyromoments. A linear-plasma-device geometry is considered. Comparison with simpler simulations with previously used ad hoc boundary conditions is presented. For the new set of boundary conditions, a significant increase of the plasma outflow to the wall is observed, leading to a significantly smaller plasma density in the whole volume of the device.

physics.plasm-ph↗

arXiv2026

Semiclassical estimates near threshold energies and resonance counting on Schwarzschild black holes

We prove a Weyl law for the number of quasinormal modes (QNM) of a Schwarzschild black hole contained in a sector below the real axis. This requires introducing a new pseudodifferential operator calculus tailored to the study of semiclassical spectral problems near threshold energies. Elliptic theory in this calculus can be combined with the method of complex scaling to give uniform resolvent estimates near zero energy for operators that behave at infinity like a semiclassical Schr\"odinger operator with a repulsive inverse-square potential. Applied to the Regge-Wheeler potential, our methods imply the absence of high angular momentum QNM from a disc whose radius grows linearly with the angular momentum. Together with the asymptotic description of Schwarzschild QNM recently obtained by Hitrik and Zworski, this shows that the number of QNM contained in a small sector below the real axis and with modulus bounded by $\lambda$ grows as $C\lambda^3$. We also study the effect of cutting off the Schwarzschild resolvent away from the event horizon and show that such a cutoff does not lead to any pole cancellations.

math.AP↗

arXiv2025

On the local constancy of regularized superdeterminants along special families of differential operators

We consider the flat-regularized determinant of families of operators of the form $D_\tau=[\delta_\tau,d_\nabla]$, where $\tau\to\delta_\tau$ are families of degree $-1$ maps in the twisted de Rham complex $\left(\Omega^\bullet(M,E),d_\nabla\right)$ generalizing the (twisted) Hodge codifferential. We show that under suitable assumptions, both geometrical and analytical in nature, the flat-regularized determinant of $D_\tau$, restricted to the subspace $\mathrm{im}(\delta_\tau)$, is constant in $\tau$. The general result we present implies both local constancy of the Ray--Singer torsion and of the value at zero of the Ruelle zeta function for a contact Anosov flow, upon choosing $\delta_\tau = \delta_{g_\tau}$, the Hodge codifferential for a family of metrics, and $\delta_\tau=\iota_{X_\tau}$, the contraction along a family of (regular, contact) Anosov vector fields, respectively.

math.DG↗

arXiv2024

Quasinormal modes for the Kerr black hole

We provide a rigorous definition of quasinormal modes for the Kerr black hole. They are obtained as the discrete set of poles of the meromorphically continued cutoff resolvent. The construction combines the method of complex scaling near asymptotically flat infinity with microlocal methods near the black hole horizon. We study the distribution of quasinormal modes in both the high and low energy regimes. We establish the existence of a high energy spectral gap and exclude the accumulation of quasinormal modes at zero energy.

math.AP↗

arXiv2023

Perturbative BF theory in axial, Anosov, gauge

The twisted Ruelle zeta function of a contact, Anosov vector field is shown to be equal, as a meromorphic function of the complex parameter $\hbar\in\mathbb{C}$ and up to a phase, to the partition function of an $\hbar$-linear quadratic perturbation of $BF$ theory, using an "axial" gauge fixing condition given by the Anosov vector field. Equivalently, it is also obtained as the expectation value of the same quadratic, $\hbar$-linear, perturbation, within a perturbative quantisation scheme for $BF$ theory, suitably generalised to work when propagators have distributional kernels.

math-ph↗