Related papers: Hermite Polynomials and Quasi-classical Asymptotic…

A non-Hermitian generalisation of the Marsden--Weinstein reduction method is introduced to construct families of quantum $\mathcal{PT}$-symmetric superintegrable models over an $n$-dimensional sphere $S^n$. The mechanism is illustrated with…

In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a…

Using the Riesz-Feller fractional derivative, we apply the factorization algorithm to the fractional quantum harmonic oscillator along the lines previously proposed by Olivar-Romero and Rosas-Ortiz, extending their results. We solve the…

We consider the asymptotics of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$. We show that for the correlation function of any even order the asymptotic coincides with this…

Other than the commonly used Wilson's regularization of quantum field theories (QFTs), there is a growing interest in regularizations that explore lattice models with a strictly finite local Hilbert space, in anticipation of the upcoming…

We pose and discuss several Hermitian analogues of Hilbert's $17$-th problem. We survey what is known, offer many explicit examples and some proofs, and give applications to CR geometry. We prove one new algebraic theorem: a non-negative…

Non-Hermitian Hamiltonians enrich quantum physics by extending conventional phase diagrams, enabling novel topological phenomena, and realizing exceptional points with potential applications in quantum sensing. Here, we present an…

We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be independent and identically distributed up to…

We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.

By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric…

We obtain the asymptotic variance, as the degree goes to infinity, of the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size. Our main tools are the Kac-Rice formula for the second factorial…

Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz…

We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact…

We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on…

We adapt the direct approach to the semiclassical Bergman kernel asymptotics, developed recently by A. Deleporte, J. Sj\"ostrand, and the first-named author for real analytic exponential weights, to the smooth case. Similar to that work,…

In this paper, the structures to a family of biorthogonal polynomials that approximate to the Hermite and Generalized Laguerre polynomials are discussed respectively. Therefore, the asymptotic relation between several orthogonal polynomials…

A semiclassical theory of a quantum spin$-S$ model with competing ring and Heisenberg exchange terms on the triangular lattice is obtained. A mechanism for the generation of $Z_2$ vortices is exhibited. The vortices are shown to carry a…

Motivated by the connection between the eigenvalues of the complex Ginibre matrix model and the magnetic Laplacian in the complex plane, we derive analogues of the complex Hermite polynomials for the elliptic Ginibre model. To this end, we…

We give a result on the asymptotic behavior of the Hurwitz-Lerch multiple zeta functions near non-positive integer points by using the Apostol-Bernoulli polynomials. From this result, we can evaluate limit values at non-positive integer…

We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes \mathrm{H}_3,$ which arises in the context of quantum gravity. We relate quantum observables…