arXiv subjects

Masatomi Iizawa

Publications and source records attributed to Masatomi Iizawa.

6 recordsLinked to original sources

arXiv2026

Big Crunch on Julia and Anti-Julia Sets in the Integrable Limit

The Julia set is defined by the closure of repelling periodic points in chaotic systems. Why does this structure not appear in integrable systems? In this paper, we address this question by demonstrating the existence of the closure of divergences of the periodic equations, which we designate as the "anti-Julia set." We also call the sets before taking the closures the pre-Julia and pre-anti-Julia sets, respectively. We illustrate the transition mechanism by considering a complex map that interpolates between integrable and non-integrable dynamics, by introducing a real deformation parameter $a$. For $0<a\le 1/2$, we show that the Julia set and the anti-Julia set coincide in the complex plane, although the pre-Julia and pre-anti-Julia sets remain completely disjoint. At the integrable limit $a\to 0$, these two dual structures undergo a critical collision and subsequent annihilation, reminiscent of a cosmological Big Crunch. When $1/2<a<1$, on the other hand, the boundary of the pre-anti-Julia set includes the Julia set. We analytically characterize these phenomena, focusing in particular on the asymptotic behavior of the pre-anti-Julia set as it approaches the integrable limit, and provide numerical visualizations that elucidate the underlying mechanisms of this Big Crunch phenomenon.

math-ph↗

arXiv2025

Scattering Angle Dependence of Fano Resonance Profiles in Cold Atomic Collisions Analyzed with the Complex Valued $w$ Parameter

The scattering angle dependence of Fano resonance profiles in cold atomic collisions has been theoretically studied. A complex-valued parameter $ w $ with an analytical formula describing the asymmetry of the resonance profile is proposed as a new development from previous work on electron resonance scattering from atoms [F. Koike, J. Phys. $\mathbf{B10}$, 2883 (1977)]. It serves as the general formulation which leads to the angle-dependence of Fano's $ q $ parameter. Calculations for the case of cold elastic collisions of hydrogen atoms with krypton atoms have been accomplished. The strong angle dependence of the resonance profile asymmetry in the differential scattering cross section due to the interference with non-resonant partial waves is demonstrated. The scattering angle dependence of the resonance profile and thus the newly proposed asymmetry parameter is highly sensitive to the inter-atomic interaction potentials. This is likely to prove useful for the study of interaction potentials themselves.

physics.atom-ph↗

arXiv2025

Evidence for an Inverse Cascade of Magnetic Helicity in the Inner Heliosphere

To elucidate the cascade direction of the solar wind turbulence, we analyzed magnetic helicity density spectra from the Parker Solar Probe data across more than 500 heliocentric distances. For the first time, we confirmed a persistent inverse cascade extending from the Sun to Mercury's orbital vicinity. This finding challenges the conventional hypothesis that the magnetic helicity density within the inner heliosphere is random. Furthermore, our analysis revealed a radial sign change of the spectral magnetic helicity density at a frequency whose value decreases logarithmically with distance. These results provide new insights into the evolution of solar wind turbulence in the inner heliosphere.

astro-ph.SR↗

arXiv2021

The quantum and classical Fano parameter $q$

The Fano resonance has been a familiar and important feature in atomic and molecular physics for more than half a century. Typically, the combination of a discrete state with one or more continua results in an asymmetric peak in the ionization spectrum. The peak-shape, called the Fano profile, can be expressed by a simple formula derived by Fano in 1935. However, the interpretation of its characteristic parameter $q$, which represents the asymmetry of the peak in the formula, is not necessarily intuitively transparent. The Fano resonance is not necessarily a quantum effect, but it is a manifestation of a certain physical mechanism in various systems, both quantum and classical. Through the derivation of $q$ from the known classical pictures with the classical coupled oscillator, we interpret the $q$ value with a geometrical view. And further, we introduce a complex valued $q$ parameter for the description of the resonance with a damped oscillator.

physics.atom-ph↗

arXiv2020

Dynamic Logic of Quantum Field Theory

Although logic of quantum mechanics has been studied for a long time, logic of QFT has not been studied before. We formulate logic of QFT by introducing the perspective of dynamic logic, because the nature of two fundamental operators in QFT, namely creation and annihilation operators, is dynamic in the sense of logic. After we formulate dynamic logic of QFT, we give a dynamic logical interpretation of fermions, the so-called vacuum state, the zero vector and propagators in QFT. We also emphasize that only a tautology $\top$ and a contradiction $\bot$ are atomic formulas of our logic. Finally, we show how Aharonov-Bohm effect can be explained naturally from our dynamic logic of QFT. This paper should be the beginning of studying logic of QFT from a dynamical point of view.

quant-ph↗

arXiv2018

Superfluorescence, free-induction decay, and four-wave mixing: propagation of free-electron laser pulses through a dense sample of helium ions

We report an experimental and numerical study of the propagation of free-electron laser pulses (wavelength 24.3 nm) through helium gas. Ionisation and excitation populates the He$^{+}$ 4$p$ state. Strong, directional emission was observed at wavelengths of 469 nm, 164 nm, 30.4 nm, and 24.5 nm. We interpret the emissions at 469 nm and 164 nm as 4$p$-3$s$-2$p$ cascade superfluorescence, that at 30.4 nm as yoked superfluorescence on the 2$p$-1$s$ transition, and that at 25.6 nm as free-induction decay of the 3$p$ state.

physics.atom-ph↗