arXiv subjects

Filip Ficek

Publications and source records attributed to Filip Ficek.

At least 19 recordsLinked to original sources

arXiv2026

Testing Exotic Electron-Electron Interactions with the Helium Ionization-Energy Anomaly

Precision atomic spectroscopy provides a sensitive probe of physics beyond the Standard Model. A recently reported $9\sigma$ theory-experiment discrepancy in the ionization energy of metastable helium has motivated the hypothesis of a new boson mediating exotic electron-electron interactions. Using a model-independent sign-consistency analysis of the induced energy shifts, we show that the sign requirement alone excludes vector-vector and pseudoscalar-pseudoscalar interactions as possible explanations of the anomaly. Incorporating existing constraints together with improved limits obtained here further excludes axial-vector scenarios. Within the single-boson framework considered in this work, only a narrowly constrained scalar-mediated interaction remains viable. The remaining parameter space could be probed, for example, by modest improvements in the determination of the electron gyromagnetic ratio.

physics.atom-ph↗

arXiv2025

Time-periodic solutions to the cubic wave equation: an elementary constructive approach

We present an elementary proof of existence of infinite family of time-periodic solutions to the one-dimensional nonlinear cubic wave equation with Dirichlet boundary conditions. It relies on the first order perturbative expansion and uses the Banach contraction principle to show existence of nearby solutions. In contrast to the previous results, this approach provides us explicit information about the frequencies and structures of the obtained solutions.

math.AP↗

arXiv2025

Instability mechanisms on asymptotically AdS black hole backgrounds

We investigate dynamics of the conformal scalar equation with defocusing cubic nonlinearity and Robin boundary conditions on the Reissner-Nordstr\"{o}m-anti-de Sitter background. At certain parts of the parameters phase space the zero solution ceases to be stable. We present two mechanisms responsible for this phenomenon.

gr-qc↗

arXiv2025

Nonlinear oscillations of strings and beams

We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and propose a systematic framework for their analysis. A Floquet stability study reveals that this class contains solutions that are linearly stable, suggesting that they may play a significant role in the nonlinear dynamics of the systems.

math-ph↗

arXiv2025

New class of time-periodic solutions to the 1D cubic wave equation

In recent papers (arXiv:2407.16507, arXiv:2408.05158) we presented results suggesting the existence of a new class of time-periodic solutions to the defocusing cubic wave equation on a one-dimensional interval with Dirichlet boundary conditions. Here we confirm these findings by rigorously constructing solutions from this class. The proof uses rational arithmetic computations to verify essential operator bounds.

math.AP↗

arXiv2025

Complex structure of time-periodic solutions decoded in Poincar\'{e}-Lindstedt series: the cubic conformal wave equation on $\mathbb{S}^{3}$

This work explores the rich structure of spherically symmetric time-periodic solutions of the cubic conformal wave equation on $\mathbb{S}^{3}$. We discover that the families of solutions bifurcating from the eigenmodes of the linearised equation form patterns similar to the ones observed for the cubic wave equation. Alongside the Galerkin approaches, we study them using the new method based on the Pad\'{e} approximants. To do so, we provide a rigorous perturbative construction of solutions. Due to the conformal symmetry, the solutions presented in this work serve as examples of large time-periodic solutions of the conformally coupled scalar field on the anti-de Sitter background.

math.AP↗

arXiv2025

Searching for Exotic Interactions between Antimatter

We show that atomic antimatter spectroscopy can be used to search for new bosons that carry spin-dependent exotic forces between antifermions. A comparison of a recent precise measurement of the hyperfine splitting of the $1$S and $2$S electronic levels of antihydrogen and bound-state quantum electrodynamics theory yields the first tests of positron-antiproton exotic interactions, constraining the dimensionless coupling strengths $g_pg_p$, $g_Vg_V$ and $g_Ag_A$, corresponding to the exchange of a pseudoscalar (axionlike), vector, or axial-vector boson, respectively. We also discuss new tests of CPT invariance with exotic spin-dependent and spin-independent interactions involving antimatter.

physics.atom-ph↗

arXiv2024

Instability of nonlinear scalar field on strongly charged asymptotically AdS black hole background

The conformally invariant scalar equation permits the Robin boundary condition at infinity of asymptotically-AdS spacetimes. We show how the dynamics of conformal cubic scalar field on the Reissner-Nordstr\"{o}m-anti-de Sitter background depend on the black hole size, charge, and choice of the boundary condition. We study the whole range of admissible charges, including the extremal case. In particular, we observe the transition in stability of the field for large black holes at the specific critical value of the charge. Similarities between Reissner-Nordstr\"{o}m and Kerr black hole let us suspect that a similar effect may also occur in rotating black holes.

gr-qc↗

arXiv2024

Spin-dependent exotic interactions

Novel interactions beyond the four known fundamental forces in nature (electromagnetic, gravitational, strong and weak interactions), may arise due to "new physics" beyond the standard model, manifesting as a "fifth force". This review is focused on spin-dependent fifth forces mediated by exotic bosons such as spin-0 axions and axionlike particles and spin-1 Z' bosons, dark photons, or paraphotons. Many of these exotic bosons are candidates to explain the nature of dark matter and dark energy, and their interactions may violate fundamental symmetries. Spin-dependent interactions between fermions mediated by the exchange of exotic bosons have been investigated in a variety of experiments, particularly at the low-energy frontier. Experimental methods and tools used to search for exotic spin-dependent interactions, such as atomic comagnetometers, torsion balances, nitrogen-vacancy spin sensors, and precision atomic and molecular spectroscopy, are described. A complete set of interaction potentials, derived based on quantum field theory with minimal assumptions and characterized in terms of reduced coupling constants, are presented. A comprehensive summary of existing experimental and observational constraints on exotic spin-dependent interactions is given, illustrating the current research landscape and promising directions of further research.

hep-ph↗

arXiv2024

Improved constraints on exotic interactions between electron and proton in hydrogen

Atomic spectroscopy can be used to search for new bosons that carry exotic forces between elementary fermions. A comparison of a recent precise measurement [Bullis \textit{et al.}, Phys. Rev. Lett. \textbf{130}, 203001 (2023)] of the hyperfine splitting of the 2S$_{1/2}$ electronic levels of hydrogen and up-to-date bound-state quantum electrodynamics theory yields improved constraints on electron-proton exotic interactions of the dimensionless coupling strengths $g_Ag_A$, $g_pg_p$, and $g_Vg_V$ corresponding to the exchange of a axial-vector, pseudoscalar (axionlike) or vector boson, respectively.

physics.atom-ph↗

arXiv2024

Trees, trunks, and branches -- bifurcation structure of time-periodic solutions to $u_{tt}-u_{xx}\pm u^{3}=0$

We propose a systematic approach to analysing the complex structure of time-periodic solutions to the cubic wave equation on an interval with Dirichlet boundary conditions first reported in arXiv:2407.16507. The analysis we present is based on a detailed study of sparse mode interactions suggested by the previous numerical work. Our results complement prior rigorous existence proofs and suggest that solutions exist for any frequency, however, they may be arbitrarily large.

math.AP↗

arXiv2024

Periodic Solutions for the 1d Cubic Wave Equation with Dirichlet Boundary Conditions

We study time-periodic solutions for the cubic wave equation on an interval with Dirichlet boundary conditions. We begin by following the perturbative construction of Vernov and Khrustalev and provide a rigorous derivation of the fourth-order expansion in small amplitude, which we use to verify the Galerkin scheme. In the main part, we focus on exploring large solutions numerically. We find an intricate bifurcation structure of time-periodic solutions forming a fractal-like pattern and explore it for the first time. Our results suggest that time-periodic solutions exist for arbitrary frequencies, with appearance of fine bifurcation structure likely related to the Cantor set families of solutions described in previous rigorous works.

math.AP↗

arXiv2023

Dynamics of nonlinear scalar field with Robin boundary condition on the Schwarzschild--Anti-de Sitter background

This work concerns the dynamics of conformal cubic scalar field on a Schwarzschild--anti-de Sitter background. The main focus is on understanding how it depends on the size of the black hole and the Robin boundary condition. We identify a critical curve in the parameter space that separates regions with distinct asymptotic behaviours. For defocusing nonlinearity, the global attractor undergoes a pitchfork bifurcation, whereas for the focusing case, we identify a region of the phase space where all solutions blow up in finite time. In the course of this study we observe an interplay between black hole geometry, boundary conditions, and the nonlinear dynamics of scalar fields in asymptotically anti-de Sitter spacetime.

gr-qc↗

arXiv2023

Quasinormal modes of Reissner-Nordstr\"{o}m-AdS: the approach to extremality

We consider the quasinormal spectrum of scalar and axial perturbations of the Reissner-Nordstr\"om-AdS black hole as the horizon approaches extremality. By considering a foliation of the black hole by spacelike surfaces which intersect the future horizon we implement numerical methods which are well behaved up to and including the extremal limit and which admit initial data which is nontrivial at the horizon. As extremality is approached we observe a transition whereby the least damped mode ceases to be oscillatory in time, and the late time signal changes qualitatively as a consequence.

gr-qc↗

arXiv2022

Stationary solutions of semilinear Schr\"odinger equations with trapping potentials in supercritical dimensions

Nonlinear Schr\"odinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schr\"odinger-Newton and Gross-Pitaevskii equations with harmonic potentials.

math-ph↗

arXiv2022

Nonlinear Schr\"odinger equations with trapping potentials in higher dimensions

From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric solutions. Then, one can use classical methods coming from the fields of ordinary differential equations and dynamical systems. The results presented here include existence and uniqueness of the stationary solutions, their frequency, and stability. The dynamical properties of the resonant approximation are also explored. The main focus is given to the Schr\"odinger-Newton-Hooke equations that is shown to be a nonrelativistic limit of perturbations of the anti-de Sitter spacetime.

math-ph↗

arXiv2022

Constraints on Spin-Spin-Velocity-Dependent Interaction

The existence of exotic spin-dependent forces may shine light on new physics beyond the Standard Model. We utilize two iron shielded SmCo$_5$ electron-spin sources and two optically pumped magnetometers to search for exotic long-range spin-spin-velocity-dependent force. The orientations of spin sources and magnetometers are optimized such that the exotic force is enhanced and common-mode noise is effectively subtracted. We set direct limit on proton-electron interaction in the force range from 1\,cm to 1\,km. Our experiment represents more than ten orders of magnitude improvement than previous works.

physics.atom-ph↗

arXiv2021

Schr\"odinger-Newton-Hooke system in higher dimensions. Part I: Stationary states

The Schr\"odinger equation with a harmonic potential coupled to the Poisson equation, called the Schr\"odinger-Newton-Hooke (SNH) system, has been considered in a variety of physical contexts, ranging from quantum mechanics to general relativity. Our work is directly motivated by the fact that the SNH system describes the nonrelativistic limit of the Einstein-massive-scalar system with negative cosmological constant. With this paper we begin the investigations aiming at understanding solutions of the SNH system in the energy supercritical spatial dimensions $d\geq 7$, where we expect to observe interesting short wavelength behaviours due to the confinement of waves by the trapping potential. Here we study stationary solutions and prove existence of one-parameter families of nonlinear ground and excited states. The frequency of the ground state as the function of the central density is shown to exhibit different qualitative behaviours in dimensions $7\leq d\leq 15$ and $d\geq 16$, which is expected to affect the stability properties of the ground states in these dimensions. Our results bear many similarities to the analogous problem that has been studied for the Gross-Pitaevskii equation.

math-ph↗