数学物理

In this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their…

We prove upper and lower bounds for the number of eigenvalues of semi-bounded Schr\"odinger operators in all spatial dimensions. As a corollary, we obtain two-sided estimates for the sum of the negative eigenvalues of atomic Hamiltonians…

We describe supertraces on ``queerifications'' (see arxiv:2203.06917) of the algebras of matrices of ``complex size'', algebras of observables of Calogero-Moser model, Vasiliev higher spin algebras, and (super)algebras of…

Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…

The hyperbolic Lie algebras with symmetrizable Cartan matrix are classified, there are 142 of them some of which can be ``superized'' to an almost affine Lie superalgebra. We list all 97 pairs (a hyperbolic Lie algebra $H$, its superized…

In this article we show that the conformal nets corresponding to WZW models are rational, resolving a long-standing open problem. Specifically, we show that the Jones-Wassermann subfactors associated with these models have finite index.…

The paper suggests a Hamiltonian formulation for delay ordinary differential equations (DODEs). Such equations are related to DODEs with a Lagrangian formulation via a delay analog of the Legendre transformation. The Hamiltonian delay…

We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the system such as existence of first integrals,…

We study a Schr\"odinger-like equation for the anharmonic potential $x^{2 \alpha}+\ell(\ell+1) x^{-2}-E$ when the anharmonicity $\alpha$ goes to $+\infty$. When $E$ and $\ell$ vary in bounded domains, we show that the spectral determinant…

We consider the relative dynamics -- the dynamics modulo rotational symmetry in this particular context -- of $N$ vortices in confined Bose--Einstein Condensates (BEC) using a finite-dimensional vortex approximation to the two-dimensional…

We propose a very simple toy model of a $\mathbb{Z}_2^2$-supersymmetric quantum system and show, via Klein's construction, how to understand the system as being an $N=2$ supersymmetric system with an extra $\mathbb{Z}_2^2$-grading. That is,…

A new framework for the reflection positivity, based on order-preserving operator inequalities, is proposed. This framework is utilized to investigate one-dimensional fermion-phonon systems, with a particular focus on the detailed…

We investigate the relationship between the semiclassical wave packets of Hagedorn and the Hermite functions by establishing a relationship between their ladder operators. This Hagedorn--Hermite correspondence provides a unified view as…

A derived algebraic geometric study of classical $\mathrm{GL}_n$-Yang-Mills theory on the $2$-dimensional square lattice $\mathbb{Z}^2$ is presented. The derived critical locus of the Wilson action is described and its local data supported…

It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…

We show the existence of infinite volume limits of resolvents and spectral measures for a class of Schroedinger operators with linearly bounded potentials. We then apply this result to Schroedinger operators with a Poisson distributed…

In some models, periodic configurations can be shown to be stable under, both, global $\ell^2$ or local perturbations. This is not the case for aperiodic media. The specific class of aperiodic media we are interested, in arise from taking…

We construct a generalised notion of Kac-Moody algebras using smooth maps from the non-compact manifolds ${\cal M}=$SL$(2,\mathbb R)$ and ${\cal M}=$ SL$(2,\mathbb R)/U(1)$ to a finite-dimensional simple Lie group $G$. This construction is…

This paper represents the completion of our work on the ODE/IM correspondence for the generalised quantum Drinfeld-Sokolov models. We present a unified and general mathematical theory, encompassing all particular cases that we had already…

Split-step quantum walk operators can be expressed as a generalised version of CMV operators with complex transmission coefficients, which we call rotated CMV operators. Following the idea of Cantero, Moral and Velazquez's original…