Mathematical Physics
We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy…
Integrable quantum spin chains display distinctive physical properties making them a laboratory to test and assess different states of matter. The study of the finite temperature properties is possible by use of the thermodynamic Bethe…
Two-band Chern insulators are topologically classified by the Chern number, $c$, which is given by the integral of the Berry curvature of the occupied band over the Brillouin torus. The curvature itself comes from the imaginary part of a…
We present a representation of skew-orthogonal polynomials of symplectic type ($\beta=4$) in terms of a matrix Riemann-Hilbert problem, for weights of the form ${\rm e}^{-V(z)}$ where $V$ is a polynomial of even degree and positive leading…
We consider a class of non-linear supersymmetric hyperbolic sigma models with long-range interactions on boxes in $\mathbb{Z}^d$ and on a hierarchical lattice. We prove that the random field associated to a marginal in horospherical…
The bulk-edge correspondence is a condensed matter theorem that relates the conductance of a Hall insulator in a half-plane to that of its (straight) boundary. In this work, we extend this result to domains with curved boundaries. Under…
Despite the large number of publications on symmetry analysis of the geopotential forecast equation, its group foliations laws have not been considered previously. The present publication aims to address this shortcoming. First, group…
We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical…
The linearized field equations for causal fermion systems in Minkowski space are analyzed systematically using methods of functional analysis and Fourier analysis. Taking into account a direction-dependent local phase freedom, we find a…
We perform a complete spectral analysis of the linear three-dimensional Boltzmann BGK operator resulting in an explicit transcendental equation for the eigenvalues. Using the theory of finite-rank perturbations, we confirm the existence of…
Inspired by Fr\"{o}hlich-Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase transition for ferromagnetic long-range Ising models on…
In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expressions of the resulting reduced differential equations, the…
This paper presents an in-depth mathematical investigation into the intersection of two advanced Lie algebraic structures: the extended Schr\"odinger-Virasoro Lie algebra (ESVLA) and the Symplectic Novikov Lie algebra (SNLA). By rigorously…
We study the Laurent property, the irreducibility and the coprimeness for lattice equations (partial difference equations), mainly focusing on how the choice of initial value problem (the choice of domain) affects these properties. We show…
We discuss elliptic quantum Calogero-Moser-Sutherland models, including their relativistic generalizations due to Ruijsenaars and van Diejen, and the relations of these models to classes of special functions developed and explored in recent…
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…