Mathematical Physics

An elastica knot is defined in terms of the Frenet-Serret curvature $\kappa(s,t)$ as a function of the arclength $s$ along the spatial curve ${\bf r}(s,t)$ at a fixed time $t$, which is a solution of the curvature differential equation…

We propose a geometric--analytic framework for equilibrium statistical mechanics on infinite-dimensional Hamiltonian systems. In situations where no suitable $\sigma$-additive invariant measure is available, we use \emph{normalized means},…

We show that, for a metric graph equipped with the Laplacian operator $\Delta=-\frac{d^2}{dx^2}$, the graph trace formula admits a new interpretation in terms of quantum probability and curvature. Our approach is based on a notion of graph…

We study quantum superintegrability for two interacting non-relativistic spin-$\frac12$ particles in three-dimensional Euclidean space. The Hamiltonian contains a central potential together with spin-orbit, spin-spin, tensor, and quadratic…

We continue the study initiated by Kilin ({\em Reg. Chaot. Dyn.} 4, (1999)) and by Mart\'inez and Sim\'o ({\em Celest. Mech. Dynam. Astronom.} 128, (2017)) on the classification and stability of the relative equilibria of the restricted…

The Bender--Brody--M\"uller (BBM) Hamiltonian was proposed as a non-Hermitian Hilbert--P\'olya operator. We analyze the Hilbert completion induced, on the standard half-line $L^2$ core, by BBM's candidate metric $\hat\eta=\sin^2(\hat…

We consider the Sachdev--Ye--Kitaev model of $N$ Majorana fermions with random $q$-body interactions. For $q=4$, we show that as $N\to \infty$ through even integers, the largest eigenvalue of the model satisfies \[…

This three-part series establishes a parameter-free, topological classification of multi-field instability in granular continua, extending Maxwell's rigidity count to dynamic, non-equilibrium processes. Part 1 (Foundations): a discrete…

We investigate integrable exclusion Markov processes constructed from set-theoretical solutions of the Yang-Baxter Equation (YBE) that generalise the multi-species Symmetric Simple Exclusion Process (SSEP). We first introduce the process…

The quality of an image observed through a scattering layer, such as a shower curtain, depends strongly on the relative position of the scattering layer between the object and the observer. This well-known phenomenon is commonly referred to…

We investigate the transformation of Killing-Yano (KY) $p$-forms under Abelian T-duality in the presence of a non-trivial three-form torsion. Using a torsionful, metric-compatible connection and the Buscher rules of T-duality, we derive…

As an application of the generalized principal bundle theory to covariant Lagrangian field theories, we aim at the development of an instance of generalized gauge theories, with the prospect of a unifying language for Yang-Mills theories…

This paper is concerned with the construction of the bosonic universal character (UC) hierarchy, whose tau functions are investigated within the framework of charged free bosons. The Lie algebra corresponding to the bosonic UC hierarchy is…

We study an inverse problem for generalized Runcorn's theorem motivated by an apparent paradox of lunar magnetism. In mathematical terms, we characterize square-integrable complex functions $f$ such that $$ \int_{\{ x\in\mathbb{R}^n : a…

We investigate entropy production and nonequilibrium transport in a class of random dynamical systems modeling a Knudsen gas confined to a compartmented container. The system consists of a single particle undergoing random billiard motion,…

Following approach of Iorgov--Lisovyy--Teschner, we construct solutions of the (modified) Riemann--Hilbert problem using conformal blocks of $(1,k)$ Virasoro models. For $k>1$ case, the solution of this Riemann--Hilbert problem is not…

We present a column adsorption model that couples a Pseudo-First-Order (PFO) kinetic formulation with the Sips isotherm framework. Using a traveling wave approximation, we derive analytical solutions for specific operating conditions.…

We investigate generalized topological recursion on compact spectral curves admitting exponential, and more generally essential, singularities as ramification points. Exploiting the global formulation of generalized topological recursion,…

The master T-operator is a generating function for transfer matrices and a tau-function of the modified KP (mKP) hierarchy. It is conventionally introduced through a Schur-function expansion whose coefficients are fused transfer matrices…

Under the framework of time-independent Hamiltonian mechanics on the cotangent bundles $T^*Q$ of the configuration spaces $Q$ of mechanical systems, we introduce the concept of fouling map as a non-invertible generalization of the so-called…