Related papers: An Itzykson-Zuber-like Integral and Diffusion for …
We present a direct and simple method for the computation of the total scattering matrix of an arbitrary finite noncompact connected quantum graph given its metric structure and local scattering data at each vertex. The method is inspired…
An easy generalization of Beukers' integrals allows us to conjecture a double integral formula involving the zeta and the gamma functions. A special case of this formula is Sondow's double integral formula for Euler's constant gamma.
Numerical methods for fractional calculus attract increasing interests due to its wide applications in various fields such as physics, mechanics, etc. In this paper, we focus on constructing high-order algorithms for Riesz derivatives,…
In analogy with the classical theory of Eichler integrals for integral weight modular forms, Lawrence and Zagier considered examples of Eichler integrals of certain half-integral weight modular forms. These served as early prototypes of a…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.
In the Euclidean-space formulation of integral equations for the structure of quantum chromodynamics (QCD) bound states, the quark propagators with complex-valued momentum are densely sampled. We therefore propose an accurate and efficient…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details.…
The ZX-calculus is a powerful framework for reasoning in quantum computing. It provides in particular a compact representation of matrices of interests. A peculiar property of the ZX-calculus is the absence of a formal sum allowing the…
In the usual matrix-model approach to random discretized two-dimensional manifolds, one introduces n Ising spins on each cell, i.e. a discrete version of 2D quantum gravity coupled to matter with a central charge n/2. The matrix-model…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
In linear algebra applications, elementary matrices hold a significant role. This paper presents a diagrammatic representation of all $2^m\times 2^n$-sized elementary matrices in algebraic ZX-calculus, showcasing their properties on…
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…
In the paper we prove integral formulae for a Riemannian manifold endowed with $k>2$ orthogonal complementary distributions, which generalize well-known formula for $k=2$ and give applications to splitting and isometric immersions of…
In a previous paper, it was shown that a soluble model can be constructed for the description of a decaying system in analogy to the Lee-Friedrichs model of complex quantum theory. It is shown here that this model also provides a soluble…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…
This article is devoted to the asymptotic expansion of the generalized Harish Chandra-Itzykson-Zuber matrix integral for non-unitary symmetries characterized by a parameter beta(as usual beta =1,2 and 4 correspond to the orthogonal, unitary…