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We propose a highly efficient numerical method to describe inhomogeneous superconductivity by using the kernel polynomial method in order to calculate the Green's functions of a superconductor. Broken translational invariance of any type…

Let $\Omega$ be a $m$-hyperconvex domain of $\mathbb{C}^n$ and $\beta$ be the standard K\"{a}hler form in $\mathbb{C}^n$. We introduce finite energy classes of $m$-subharmonic functions of Cegrell type, $\mathcal{E}_m^p, p>0$ and…

We determine the two-point invariants of the equivariant quantum cohomology of the Hilbert scheme of points of surface resolutions associated to type A_n singularities. The operators encoding these invariants are expressed in terms of the…

Determining the Hamiltonian of a quantum system is essential for understanding its dynamics and validating its behavior. Hamiltonian learning provides a data-driven approach to reconstruct the generator of the dynamics from measurements on…

Hamiltonians ${\cal H}^{a}_k$ of new integrable systems associated with the integer rays $(1,a)$ (commutative subalgebras) of Ding-Iohara-Miki (DIM) algebra in the $N$-body representation are closely related to commuting twisted Cherednik…

We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_\theta$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the…

We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation.…

A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation.…

We start with a Riemann-Hilbert problem (RHP) related to a BD.I-type symmetric spaces $SO(2r+1)/S(O(2r-2s +1)\otimes O(2s))$, $s\geq 1$. We consider two Riemann-Hilbert problems: the first formulated on the real axis $\mathbb{R}$ in the…

This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…

The rational quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the Lie algebra $sl_2$ is a system of linear difference equations with values in a tensor product of $sl_2$ Verma modules. We solve the equation in terms…

We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide…

In the present paper, we consider the integral operator, which acts in Hilbert space and has sine kernel. This operator generates two operator identities and two corresponding canonical differential systems. We find the asymptotics of the…

Consider in $L^2 (\R^l)$ the operator family $H(\epsilon):=P_0(\hbar,\omega)+\epsilon Q_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $\om$, $Q_0$ a bounded pseudodifferential operator with symbol…

In this paper we provide another application of the Inhomogeneous Hopf-Ole\u{\i}nik Lemma (IHOL) proved in \cite{BM-IHOL-PartI} or \cite{Boyan-2}. As a matter of fact, we also provide a new and simpler proof of a slightly weaker version…

The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and…

We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized…

We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function (see Theorem \ref{t:U.t1}). The…

We construct a solution of Cherednik's quantum Knizhnik Zamolodchikov equation associated with the root system of type $C_n$. This solution is given in terms of a restriction of a $q$-Jordan-Pochhammer integral. As its applicaton, we give…

This paper proposes a unified theoretical framework based on the Kolmogorov-Arnold representation theorem and kernel methods. By analyzing the mathematical relationship among kernels, B-spline basis functions in Kolmogorov-Arnold Networks…