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The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument…

Numerical Analysis · Mathematics 2012-05-08 U. D. Jentschura , E. Lötstedt

Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the…

Combinatorics · Mathematics 2008-02-25 Stavros Garoufalidis

In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…

Numerical Analysis · Mathematics 2022-04-26 Richard M. Slevinsky , Hassan Safouhi

We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 G. A. P. Ribeiro , M. J. Martins

Let $F$ be a finite field, and let $\mathbb{E}$ be either a quadratic field extension $E/F$ or the split algebra $F \oplus F$. We study distinguished representations of $\rm{SL}_{2n}(F)$ by the subgroup $H_{\flat} := \rm{SL}_{2n}(F) \cap…

Representation Theory · Mathematics 2025-11-18 Kwangho Choiy , Shiv Prakash Patel

The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer…

Mathematical Physics · Physics 2019-06-05 Guang-Liang Li , Junpeng Cao , Panpan Xue , Zhi-Rong Xin , Kun Hao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We show the result for the BFKL Pomeron intercept at N=4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion j0=2-2 lambda**(-1/2)- lambda**(-1) + 1/4 lambda**(-3/2) + 2(1+3zeta3) lambda**(-2) + O(lambda**(-5/2)),…

High Energy Physics - Theory · Physics 2015-06-11 A. V. Kotikov , L. N. Lipatov

Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…

Quantum Physics · Physics 2025-11-04 Jing Zhou , D. L. Zhou

We develop an advanced method of solving homogeneous and inhomogeneous Bethe-Salpeter equations by using the expansion over the complete set of 4-dimensional spherical harmonics. We solve Bethe-Salpeter equations for bound and scattering…

Nuclear Theory · Physics 2011-04-26 S. S. Semikh , S. M. Dorkin , M. Beyer , L. P. Kaptari

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform…

Combinatorics · Mathematics 2020-02-27 Richard J. Martin , M. J. Kearney

We survey and discuss the applications of the non-linear integral equation in the framework of the Bethe Ansatz type equations which are conjectured to give the eigenvalues of the dilatation operator in ${\cal {N}}=4$ SYM. Moreover, an…

High Energy Physics - Theory · Physics 2007-11-20 Diego Bombardelli , Davide Fioravanti , Marco Rossi

We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their…

Disordered Systems and Neural Networks · Physics 2021-03-16 A. F. Tzortzakakis , K. G. Makris , A. Szameit , E. N. Economou

We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by $\mathfrak{gl}(m|n)$ superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their…

Mathematical Physics · Physics 2018-03-14 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are…

Spectral Theory · Mathematics 2025-10-20 B. M. Brown , E. B. Davies , P. K. Jimack , M. D. Mihajlovi'c

The treatment of the Random-Phase Approximation Hamiltonians, encountered in different frameworks, like Time-Dependent Density Functional Theory or Bethe-Salpeter equation, is complicated by their non-Hermicity. Compared to their Hermitian…

Materials Science · Physics 2011-02-21 Myrta Grüning , Andrea Marini , Xavier Gonze

A soliton ensemble is a particular kind of approximation of the solution of an initial-value problem for an integrable equation by a reflectionless potential that is well adapted to singular asymptotics like the small-dispersion limit. We…

Analysis of PDEs · Mathematics 2024-07-30 Elliot Blackstone , Louise Gassot , Peter D. Miller

Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…

Functional Analysis · Mathematics 2023-09-20 L. M. Anguas , D. Barrios Rolanía

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak Konig's Lemma within the…

Logic · Mathematics 2010-03-26 Guido Gherardi , Alberto Marcone

The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in…

Probability · Mathematics 2019-06-05 Tom Claeys , Benjamin Fahs , Gaultier Lambert , Christian Webb

The Bethe ansatz can be used to compute anomalous dimensions in N=4 SYM theory. The classical solutions of the sigma-model on AdS(5)xS(5) can also be parameterized by an integral equation of Bethe type. In this note the relationship between…

High Energy Physics - Theory · Physics 2008-11-26 K. Zarembo