数学物理
In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical…
Treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh-Schrodinger power series. This power series is proved to be…
This paper is devoted to the study of conformal and projective structures, and especially their connections, in the language of 2-frames, or $G$-structures of 2nd-order. While their normal Cartan connections are well-known, we use the…
With the aim of understanding the localization topology correspondence for non periodic gapped quantum systems, we investigate the relation between the existence of an algebraically well-localized generalized Wannier basis and the…
We study the Schr\"odinger operators ${H}_{\lambda\mu}(K)$ with $K\in\mathbb{T}^2$ being the fixed quasimomentum of a pair of particles, associated with a system of two arbitrary particles on a two-dimensional lattice $\mathbb{Z}^2$ with…
We consider a translation-invariant system of $N$ bosons in $\mathbb{T}^{3}$ that interact through a repulsive two-body potential with scattering length of order $N^{-1}$ in the limit $N\to \infty$. We derive second order expressions for…
We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator $H_0$ does not commute with the spin operator in view of Rashba interactions, as in the typical…
We study the family $H_{\gamma \lambda \mu}(K)$, $K\in \mathbb{T}^2,$ of discrete Schr\"odinger operators, associated to the Hamiltonian of a system of two identical bosons on the two-dimen\-sional lattice $\mathbb{Z}^2,$ interacting…
A new algebra, hitherto not encountered in the usual Lie algebraic varieties or supervarieties, is introduced. The paper explores the rich and novel structure of the algebra, and it compares it on the one hand with the Jordan-Lie…
We consider the Bogoliubov energy functional proposed by Napi\'orkowski, Reuvers and Solovej and analize it in the high density regime. We derive a two term asymptotic expansion of the ground state energy.
The theory of Poisson-Lie groups and Lie bialgebras plays a major role in the study of one dimensional integrable systems; many families of integrable systems can be recovered from a Lax pair which is constructed from a Lie bialgebra…
This study investigates the atomistic spin system in $\rm CrCl_{3}$, which exhibits topologically nontrivial meron structures within its layered hexagonal lattice framework. We analyze the complete model of discrete spin dynamics on a…
The homogeneous causal action principle on a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed. The Euler-Lagrange equations are derived…
We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…
This paper studies the universal first-order Massey product of a prefactorization algebra, which encodes higher algebraic operations on the cohomology. Explicit computations of these structures are carried out in the locally constant case,…
We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack $T^\ast[X/G]$ of a quotient stack, where $X$ is a smooth affine scheme with an action of a (reductive) smooth affine group scheme $G$.…
We review some known results on the superintegrability of monopole systems in the three-dimensional (3D) Euclidean space and in the 3D generalized Taub-NUT spaces. We show that these results can be extended to certain curved backgrounds…
We develop an approach analogous to classical Frobenius theory for the analysis of singularities of ODEs in the case of discrete dynamical systems. Our methodology is based on the Roman-Rota theory of finite operators and relies crucially…
It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities…
This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a large dimension of the group, for various…