arXiv subjects

Nils Wagner

Publications and source records attributed to Nils Wagner.

5 recordsLinked to original sources

arXiv2026

Zero-damped modes of near-extremal Reissner--Nordstr\"{o}m black holes from exact WKB

The late-time ringdown dynamics of near-extremal black holes (BHs) are expected to be dominated by zero-damped modes (ZDMs), whose decay rates are parametrically suppressed relative to those of ordinary quasinormal modes. In this paper, we demonstrate that exact WKB methods provide an exceptionally powerful framework for analyzing the ZDM spectrum of near-extremal Reissner--Nordstr\"{o}m (RN) BHs. Focusing on massless, neutral scalar modes propagating on an RN background, we present the full Stokes geometry derived from the radial eigenvalue problem and establish the corresponding exact quantization condition (EQC). Our analytic computation of the Voros symbols entering the EQC achieves higher-order accuracy for the ZDM spectrum compared to previous studies and is systematically improvable. Ergo, this work serves as a proof of concept for investigations of ZDM spectra of other systems using exact WKB methods.

hep-th↗

arXiv2025

Instantons meet resonances: Unifying two seemingly distinct approaches to quantum tunneling

In the study of quantum-mechanical tunneling processes, numerous approaches have been developed to determine the decay rate of states initially confined within a metastable potential region. Virtually all analytical treatments, however, fall into one of two superficially unrelated conceptual frameworks: the resonant-state approach and the instanton method. Whereas the concept of resonant states and their associated decay widths is grounded in physical reasoning by capturing the regime of uniform probability decay, the instanton method lacks a comparably clear physical interpretation. We demonstrate the equivalence of the two approaches, revealing that the contour-deformation prescription in the functional integral put forward by Callan and Coleman directly corresponds to the outgoing Gamow--Siegert boundary conditions defining resonant states.

hep-th↗

arXiv2025

Path integral analysis of Schr\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states

Schr\"odinger-type eigenvalue problems are ubiquitous in theoretical physics, with quantum-mechanical applications typically confined to cases for which the eigenfunctions are required to be normalizable on the real axis. However, seeking the spectrum of resonant states for metastable potentials or comprehending $\mathcal{PT}$-symmetric scenarios requires the broader study of eigenvalue problems for which the boundary conditions are provided in specific angular sectors of the complex plane. We generalize the conventional path integral treatment to such nonstandard boundary value problems, allowing the extraction of spectral information using functional methods. We find that the arising functional integrals are naturally defined on a complexified integration contour, encapsulating the demanded sectorial boundary conditions of the associated eigenvalue problem. The attained results are applied to the analysis of resonant ground-state energies, through which we identify the previously elusive one-to-one correspondence between decay rates derived from real-time quantum tunneling dynamics and those obtained via the Euclidean instanton method.

hep-th↗

arXiv2024

False vacuum decay of excited states in finite-time instanton calculus

Extracting information about a system's metastable ground state energy employing functional methods usually hinges on utilizing the late-time behavior of the Euclidean propagator, practically impeding the possibility of determining decay widths of excited states. We demonstrate that such obstacles can be surmounted by working with bounded time intervals, adapting the standard instanton formalism to compute a finite-time amplitude corresponding to excited state decay. This is achieved by projecting out the desired resonant energies utilizing carefully chosen approximations to the excited state wave functions in the false vacuum region. To carry out the calculation, we employ unconventional path integral techniques by considering the emerging amplitude as a single composite functional integral that includes fluctuations at the endpoints of the trajectories. This way, we explicitly compute the sought-after decay widths, including their leading quantum corrections, for arbitrary potentials, demonstrating accordance with traditional WKB results. While the initial starting point of weighting Euclidean propagator contributions according to their endpoints using false vacuum states has been proposed earlier, we find several flaws in the published evaluation of the relevant amplitudes. Although we show that the previous proposition of employing a sequential calculation scheme -- where the functional integral is evaluated around extremal trajectories with fixed endpoints, weighted only at a subsequent stage -- can lead to the desired goal, the novel composite approach is found to be more concise and transparent.

hep-th↗

arXiv2021

Theoretical and Experimental Investigation into the flight of an X-Zylo

Flying Gyroscopes are fascinating flight objects, which, due to gyroscopic stabilization, can achieve surprisingly long flight distances when thrown with rapid spin. The most common example hereby is a traditional Frisbee disc. This paper focuses on a similar object called X-Zylo, that shows a remarkable straight flight despite its simple geometry. The main aim of the present study is to investigate the flight behavior of the X-Zylo and to build a reliable groundwork for further quantitative parameter studies on ring wing configurations. To achieve this goal, a six degree of freedom model to predict the flight trajectory was developed. The trajectory computation uses interpolated high-fidelity CFD simulation data to calculate the acting moments and forces on the object during flight. A launch contraption was built to be able to validate the theory systematically and reproducible in experiments without human factors involved in the launch. Despite the complexity of the flight, the theoretical simulations match the real world data qualitatively, however quantitative differences still prevail. The investigation shows that the deviation between theory and experiment mostly stems from uncertainties in the CFD data as well as the optical recording of the experimental data. Despite the methods outperforming those of prior studies, advancements still have to be made in those areas in order to obtain better quantitative accordance between theory and experiment.

physics.class-ph↗