数学物理
Assume $X$ is a variety for which the elliptic stable envelope exists. In this note we construct natural $q$-difference equations from the elliptic stable envelope of $X$. In examples, these equations coincide with the quantum difference…
In this study, we explore the precise physical quantities in the thermodynamic limit of the one-dimensional Hubbard model with nonparallel boundary magnetic fields based on the off-diagonal Bethe ansatz solution. A particular emphasis is…
We study conservation laws of a general class of quantum many-body systems subjected to an external time dependent quasi-periodic driving. {When the frequency of the driving is large enough or the strength of the driving is small enough, we…
The quantum Rabi model (QRM), one of the fundamental models used to describe light and matter interaction, has a deep mathematical structure revealed by the study of its spectrum. In this paper, from the explicit formulas for the partition…
We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schr\"odinger equation and the singular waveguide by appropriate jump conditions along the…
We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists…
Recently, it has been observed that the Floquet-Bloch transform with real quasiperiodicities fails to capture the spectral properties of non-reciprocal systems. The aim of this paper is to introduce the notion of a generalised Brillouin…
We investigate the thermodynamic limit and exact surface energy of the isotropic spin-1 Heisenberg chain with integrable generic open boundary conditions by a novel Bethe ansatz method. We obtain the homogeneous Bethe ansatz equations for…
We prove a uniform weighted resolvent estimate for the massless Klein-Gordon operator on a curved spacetime which is sufficiently close to the Minkowski spacetime. This particularly implies the existence and H\"{o}lder continuity of the…
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…
The problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equation from observed data has received attention from researchers in physics, applied mathematics and statistics. This is motivated by the various physical…
We investigate a modified version of the $AB$ random sequential adsorption model. Specifically, this model involves the deposition of two distinct types of particles onto a lattice, with the constraint that different types cannot occupy…
This paper surveys the long-standing connections and impact between Vaughan Jones's theory of subfactors and various topics in mathematical physics, namely statistical mechanics,quantum field theory,quantum information and two-dimensional…
We prove the equivalence between the integral central limit theorem and the local central limit theorem for two-body potentials with long-range interactions on the lattice $\mathbb{Z}^d$ for $d\ge 1$. The spin space can be an arbitrary,…
We present an example of an integrable Hamiltonian system with scalar potential in the three-dimensional Euclidean space whose integrals of motion are quadratic polynomials in the momenta, yet its Hamilton-Jacobi / Schrodinger equation…
In this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant…
We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem,…
The motivation for this thesis is to find a fluctuating hydrodynamic description of quantum coherent effects in mesoscopic quantum systems with diffusive transport properties. Coherent effects are inscribed into the coherences (two-point…
We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schr\"odinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the…
A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary…