数学物理
We propose analogs of the generalized MICZ-Kepler system on the three-dimensional sphere and (two-sheet) hyperboloid. We then construct their energy spectra and normalized wave functions, concluding that the suggested systems are minimally…
This paper describes the reduced phase space of $N=1$, $D=4$ supergravity in the fully off-shell Palatini--Cartan formalism. This is achieved through the KT construction, allowing an explicit description of first-class constraints on the…
We present a novel matrix product representation of the Laughlin and related fractional quantum Hall wavefunctions based on a rigorous version of the correlators of a chiral quantum field theory. This representation enables the quantitative…
We study quantum transport for the discrete one-dimensional random Jacobi operator of divergence-gradient type. For strictly positive and bounded random variables, we analyze the q-moments of the position operator and establish both upper…
We consider the Landau Hamiltonian $\widehat H_B+V$ on $L^2({\mathbb R}^2)$ with a periodic electric potential $V$. For every $m\in {\mathbb N}$ we prove that there exist nonconstant periodic electric potentials $V\in C^{\infty }({\mathbb…
In this paper, we study the momentum distribution of an electron gas in a $3$-dimensional torus. The goal is to compute the occupation number of Fourier modes for some trial state obtained through random phase approximation. We obtain the…
In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an…
The bulk boundary correspondence, one of the most significant features of topological matter, theoretically connects the existence of edge modes at the boundary with topological invariants of the bulk spectral bands. However, it remains…
In the previous study (Ishida, 2025), the author proved the uniqueness of short-range potential functions using the Enss-Weder time-dependent method (Enss and Weder, 1995) for a two-body quantum system described by time-decaying harmonic…
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero-Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero-Sutherland and rational Ruijsenaars…
We develop the method for constructing solutions to the nonlocal nonlinear Schr\"{o}dinger equation (NLSE) with an anti-Hermitian term that are semiclassically localized on a one-dimensional manifold (a curve). The evolution of the curve is…
Bound states in the continuum (BICs) are localized states embedded within a continuum of propagating waves. Perturbations that disrupt BICs typically induce ultra-strong resonances, a phenomenon enabling diverse applications in photonics.…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
Global minimality, boundedness, and uniqueness are established for a general, physically motivated class of inverse source problems in non-homogeneous electromagnetic media with generalized constitutive parameters. The existence of a…
Extending a previous paper, we present a generalization in dimension 3 of the traditional Szebehely-type inverse problem. In that traditional setting, the data are curves determined as the intersection of two families of surfaces, and the…
This book is devoted to the spectral analysis of the magnetic Laplacian in various geometric situations. In particular the influence of the geometry on the discrete spectrum is analysed in many asymptotic regimes.
We construct degeneration limits of vertex operators for the Virasoro algebra. Our method relies on the rearranged expansion of compositions of vertex operators together with their integral representations. Using this framework, we obtain a…
In this paper, we explore the evolution of plane curves and surfaces governed by the hyperbolic mean curvature flow. We propose a mesh-free approach based on the physics-informed neural networks (PINNs), which eliminates the need for…
We present exact analytical solutions for the radial Dunkl-Schr\"odinger equation (DSE) confined by the Deng-Fan molecular potential. By employing the Pekeris approximation to resolve the centrifugal singularity and applying the parametric…
We deform block triangular Jacobi matrices appearing in geometry, look at multi-scale Barycentric limits of geometries and droplet boundary manifolds in Potts networks.