Mathematical Physics
We examine the kinematic foundations of relativity by considering two inertial frames, $S$ and $S'$, in a standard configuration, where $S'$ moves along the common spatial $x$-axis at a constant velocity $v$. By relaxing Einstein's second…
We study the Kohmoto model, a family of discrete Schr\"odinger operators with Sturmian potentials depending on a frequency and a coupling constant. We prove that, for all non-vanishing coupling constants, all spectral bands admit a…
Rapidly scaling autonomous science is limited not only by algorithms, compute or data volume, but by which physical records a platform exposes before action. We formulate physically accessible decision-making (PADM) and a measurement-access…
For a class of polaron-type models, we establish a lower bound on the energy-momentum relation in terms of the vacuum overlap and the spectral gap of the total momentum zero Hamiltonian. We show convergence of the rescaled mean square…
We investigate elastic binary collisions of relativistic spinning particles in special relativity. The spin of each particle is represented by an antisymmetric second order tensor. Assuming the conservation of total four momentum and total…
Spectral and transport properties of high-contrast resonator systems can be described in the subwavelength regime in terms of the so-called capacitance operator. In this paper, we consider an infinitely periodic chain of high-contrast…
We resolve the hyperbolic off-center-orbit problem for the singular potential \[ V(r)=-\frac{\alpha}{(R^2-r^2)^2},\qquad \alpha>0. \] At zero energy, the Jacobi metric has constant negative curvature on both components separated by $r=R$.…
We study one-centre point interactions for the Dirichlet Laplacian on unbounded domains in dimensions two and three, with emphasis on exterior domains and special Lipschitz domains. These operators are singular perturbations constructed as…
We recast the physics discussions in the paper of Dieter Van den Bleeken \cite{svan2012bps} within the context of wall-crossing structure \`a la Kontsevich and Soibelman \cite{kontsevich2014wall}. In particular, we compare the Hesse flow…
We prove the Eigenstate Thermalisation Hypothesis (ETH), also known as Quantum Unique Ergodicity (QUE), for large $N\times N$ mean-field random matrices with general correlation structure. We identify the microcanonical ensemble and…
This paper develops the matrix-valued analogue of the reflectionless and oracle framework for Jacobi operators. Starting from matrix-valued Weyl--Titchmarsh $m$-functions on the Siegel upper half-space, we study the distance-decreasing…
We establish a new PBW basis for $\mathcal A_q$, the alternating central extension of the $q$-Onsager algebra. Terwilliger showed that the alternating generators form a PBW basis in the block order $\mathcal G<\mathcal W^-<\mathcal…
This paper introduces a transition-set morphometry for quantifying inter-scale contacts in digital sandstones. Pore volume, a medial pore-throat subsystem, and fracture porosity are treated as distinct geometric subsystems. Their…
We study high-order analogues of the classical Heun operator of Fuchs index one, \[ \dq=\sum_{i=1}^k Q_i(z)\frac{d^i}{dz^i}, \qquad \deg Q_i\le i+1, \qquad \deg Q_k=k+1. \] For a fixed degree $n$ we consider the linear Van Vleck polynomials…
We consider a very general Rosenzweig-Porter-type model, $H=H_0+\lambda W$, where $H_0$ is an arbitrary Hermitian matrix and $W$ is a standard Wigner matrix. We precisely trace the localization properties of the eigenvectors and the…
We study mesoscopic linear spectral statistics for two ensembles of random quantum graphs. These are defined by a discrete graph $G$ and a unitary-matrix-valued function $U(k)$ indexed by directed edges of $G$. The matrix function $U(k)$ is…
This paper studies the imperfect Bose gas after the Kac density law and the mean-field Euler equations have selected a condensed density with positive zero-mode excess. In this BEC regime the selected chemical potential cancels the…
We present a complete classification of integrable Yang-Baxter quantum circuits with open boundary conditions and arbitrary circuit geometries. Starting from the standard transfer-matrix construction with two types of staggered…
In this article, we consider the $r$-logarithm for defining three-parameter family of R\'{e}nyi relative entropies that are generalization of the $\alpha$-$z$-R\'{e}nyi relative entropies. All the members of $r$-deformed…
We study a small-denominator mechanism in weakly nonlinear dispersive dynamics. After Fourier decomposition, a nonlinear dispersive equation becomes an infinite system of weakly coupled oscillators. Higher-order correction terms may then…