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For a two-dimensional canonical system $y'(t)=zJH(t)y(t)$ on an interval $(0,L)$ with $0<L\le\infty$ whose Hamiltonian $H$ is a.e.\ positive semidefinite, denote by $q_H$ its Weyl coefficient. De~Branges' inverse spectral theorem states…

Spectral Theory · Mathematics 2025-08-14 Matthias Langer , Raphael Pruckner , Harald Woracek

We compute all planar two-loop six-point Feynman integrals entering scattering observables in massless gauge theories such as QCD. A central result of this paper is the formulation of the differential-equations method under the algebraic…

High Energy Physics - Phenomenology · Physics 2024-12-31 Samuel Abreu , Pier Francesco Monni , Ben Page , Johann Usovitsch

We introduce and study a new family of commuting Baxter operators in the Ruijsenaars hyperbolic system, different from that considered by us earlier. Using a degeneration of Rains integral identity we verify the commutativity between the…

Mathematical Physics · Physics 2024-03-25 N. Belousov , S. Derkachov , S. Kharchev , S. Khoroshkin

We propose a numerical technique for modeling the quantum multimode light scattering by a perfectly conducting body. Using the novel quantization technique, we give the quantum adaptation of the characteristic mode approach widely used in…

Quantum Physics · Physics 2021-12-20 Gregory Ya. Slepyan , Dmitri Mogilevtsev , Ilay Levie , Amir Boag

We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal…

Quantum Physics · Physics 2018-05-30 Kevin A. Fischer , Rahul Trivedi , Vinay Ramasesh , Irfan Siddiqi , Jelena Vučković

We present a method for efficiently finding solutions of L\"uscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such…

High Energy Physics - Lattice · Physics 2020-07-01 Antoni J. Woss , David J. Wilson , Jozef J. Dudek

A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…

Symplectic Geometry · Mathematics 2007-05-23 Yarema A. Prykarpatsky , Anatoliy M. Samoilenko

This article studies the rational solutions of the Half-Wave Maps equation (HWM) in the non-singular spectrum case. We first provide characterizations to what we call \emph{scattering behavior}, and show that they imply scattering in…

Analysis of PDEs · Mathematics 2025-03-03 Gaspard Ohlmann

Converting solar energy into chemical energy by splitting water is a promising means to generate a sustainable and renewable solution without detrimental environmental impact. The two-dimensional semiconductors serve as potential catalysts…

Mesoscale and Nanoscale Physics · Physics 2019-09-18 Srilatha Arra , Rohit Babar , Mukul Kabir

Based on the Hamiltonian formalism approach, a generalized L\"uscher's formula for two particle scattering in both the elastic and coupled-channel cases in moving frames is derived from a relativistic Lippmann-Schwinger equation. Some…

High Energy Physics - Lattice · Physics 2013-08-09 Peng Guo , Jozef Dudek , Robert Edwards , Adam P. Szczepaniak

In this paper we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly related to the $S^{(0,0)}$ and $S^{(1,0)}$ variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of $S^{(0,0)}$ and $S^{(1,0)}$…

Exactly Solvable and Integrable Systems · Physics 2021-10-19 Aye Aye Cho , Maebel Mesfun , Da-Jun Zhang

Let $\mathbf{G}$ be a reductive group and $\mathbf{X}$ a spherical $\mathbf{G}$-variety over a local non-archimedean field $\mathbb{F}$. We denote by $S(\mathbf{X}(\mathbb{F}))$ the Schwartz-functions on $\mathbf{X}(\mathbb{F})$. In this…

Representation Theory · Mathematics 2025-07-15 Johannes Droschl

We theoretically analyze a discrete Schr\"odinger chain with hopping to the first and second neighbors, as can be realized with zigzag arrangements of optical waveguides or lattice sites for cold atoms. Already at moderate values, the…

Quantum Gases · Physics 2015-08-11 J. Stockhofe , P. Schmelcher

Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…

Mathematical Physics · Physics 2014-03-13 Yuri B. Suris

We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition…

Mathematical Physics · Physics 2026-05-18 Mattia Scomparin

In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $\mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous…

High Energy Physics - Theory · Physics 2017-02-01 Fabiano M. Andrade , Cleverson Filgueiras , Edilberto O. Silva

For a finite abelian group action on a linear category, we study the dual action given by the character group acting on the category of equivariant objects. We prove that the groups of equivariant autoequivalences on these two categories…

Representation Theory · Mathematics 2021-09-27 Jianmin Chen , Xiao-Wu Chen , Shiquan Ruan

Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of $SU(n,n)$, to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses $BC_n$ symmetry and is shown to be…

Mathematical Physics · Physics 2013-12-24 Ian Marshall

Subwavelength atomic arrays are a leading platform for engineering light-matter interactions, enabling near-perfect single-photon mirrors and robust quantum memories based on long-lived dark spin waves. However, a comprehensive theory of…

Quantum Physics · Physics 2025-09-23 Yidan Wang , Oriol Rubies-Bigorda , Valentin Walther , Susanne F. Yelin

We consider scattering theory for a pair of operators $H_0$ and $H=H_0+V$ on $L^2(M,m)$, where $M$ is a Riemannian manifold, $H_0$ is a multiplication operator on $M$ and $V$ is a pseudodifferential operator of order $-\mu$, $\mu>1$. We…

Analysis of PDEs · Mathematics 2014-08-01 Shu Nakamura