Mathematical Physics

We associate height function models to a range of generalized two-dimensional XY models and prove that delocalisation of the height function model rules out exponential decay of the nematic order parameter in the primal spin model. The…

Reconstructing unknown electromagnetic sources from far-field radiation patterns is a fundamental inverse problem with broad applications in biomedical imaging, non-destructive testing, and telecommunications. In practical settings,…

We consider a quantum system on the real line obeying a deformed Heisenberg algebra originally proposed by Wigner in 1950. Its explicit coordinate representation was provided by Yang in 1951 and in essence is identical in form with Dunkl's…

Let $\{0, 1\}^n$ be the Boolean cube, endowed with the probability product measure, where ${\Bbb P}(1)=p$ and ${\Bbb P}(0)=q$ with $0 < p \leq q=1-p$. Let $\phi_i: \{0, 1\}^n \longrightarrow {\Bbb C}$ be $1$-Lipschitz functions in the…

We give an analytic construction of a tau function for the $q$-difference sixth Painlev\'e equation ($q$PVI) as a Fredholm determinant through the general Riemann-Hilbert problem associated with it. We show that the tau function is an…

In this paper, we mainly investigate the overtaking collision problem between a dispersive shock wave (DSW) and a rarefaction wave (RW) propagating in the same direction in the defocusing Hirota equation framework. Based on the Whitham…

In this paper, we focus on the analytical description of the interaction between a rarefaction and dispersive shock wave across both convex and non-convex cases, with particular attention to the effect of the non-convexity, within the…

We numerically investigate selection criteria for dissipative weak solutions of the compressible Euler equations. Using the Kelvin-Helmholtz problem as a benchmark, we compare four standard numerical schemes - the viscous finite volume…

We introduce a non-commutative Laplace transform between functionals on path space and formal series in a tensor algebra, under which a natural convolution of path functionals becomes an algebraic product of series. Applying it to a random…

We study a Purcell three-link microswimmer whose joints are \emph{odd-elastic}: the torsional stiffness is non-Hermitian, its antisymmetric part $k_o$ injecting mechanical work so that the internal elastic drift is non-conservative. Our…

For integers $N\ge0$ and $n\ge2$, let \[ \Delta_N^{(n)} =\left\{\alpha\in\mathbb Z_{\ge 0}^n: \alpha_1+\cdots+\alpha_n=N\right\}. \] We formulate a discrete unique-continuation problem on this lattice simplex. Given an integer $R\ge1$,…

Analytic calculations of zero- and single-scale quantities in perturbative quantum field theory result into special numbers and functions, the first of which have been revealed during the last decades. These are generalizations of the…

Imaginary Liouville theory was recently proposed as a path integral construction of a non-rational conformal field theory (CFT) with central charge less than one (Usciati et al. 2026). In the present work, we establish Ward identities and…

This work investigates the $q$-deformation of $(r,s)$-Airy structures and their realization via $q$-difference operators, providing a bridge between quantum spectral curves and integrable systems. We construct an all-order $q$-WKB solution…

Here, we investigate the motion of a thin circular quantum vortex filament near the infinite planar surface. The fluid surrounding this surface moves with a non-zero velocity $\bf{v}$, which is parallel to the surface. We study the specific…

A model governing quasi-unidirectional wave propagation at the surface of a shallow layer of water is derived from Euler equations by long wave asymptotics together with Hamiltonian reduction techniques. The balance between nonlinearity,…

Generalised continuum theories couple the macroscopic deformation and the micro-/meso-scopic deformation of an underlying micro-structure. They can account for internal length-scale effects and higher-order mechanical loadings absent from…

We present a novel approach to the superintegrability of collective Hamiltonians invariant under a Hamiltonian action of a connected semisimple compact Lie group, $G$, on a symplectic manifold, $M$. By exploiting a Hamiltonian torus action…

Topological $K$-theory supplies the decisive stable classification principle for gapped free-fermion phases in Euclidean crystals once symmetry and stabilization are fixed. In hyperbolic band theory, by contrast, it is less decisive for the…

Curl forces are position-dependent, non-conservative, and non-dissipative forces that, in general, cannot be derived from an ordinary potential energy. Consequently, their equations of motion do not, in general, follow from a standard…