数学物理
We describe a mechanism of affine symmetry emergence in the maximal density regime of the prototypical model of self-organized criticality when the inverse square of the mesh of the underlying lattice is much larger than the number of…
Dyson universality typically manifests itself in local eigenvalue statistics. Here we show that its signature survives a nonlinear inverse-spectral reconstruction and reappears in the matrix geometry of the reconstructed operator. Using a…
This article contrasts the concepts of a proper condensate and the Onsager-Penrose criterion for Bose-Einstein condensation in the form of a debate between two proponents of the respective concepts. The prologue briefly introduces the two…
We study Toeplitz determinants $\det T_n(e^f)$ for $f$ whose Fourier coefficients satisfy $f_k=O(|k|^{-1})$. This regime extends beyond $H^{1/2}$ and includes symbols with Fisher-Hartwig singularities. We develop an operator-theoretic…
The most well-known beyond-Fourier heat conduction model, the Maxwell--Cattaneo--Vernotte equation is solved analytically in the presence of heat transfer boundary condition. In contrast to the corresponding Fourier problem, this boundary…
We study transparent boundary conditions (TBCs) for the time-dependent heat equation in a branching, quasi-one-dimensional domain modeled as a metric star graph. By combining the classical concept of TBCs with the theory of partial…
We construct a discrete Smorodinsky--Winternitz II superintegrable system on a triangular region of the two-dimensional square lattice. The model is built from a pair of commuting finite-difference number operators with finite spectrum…
A compact formulation of electrostatics is presented. Without using constitutive relations, including the aether relations, an expression for the potential energy of a charged region under a potential function is proposed, where the charge…
We construct a finite discrete realization of the Smorodinsky--Winternitz I superintegrable system on a triangular region of the two-dimensional square lattice. The construction is based on a pair of commuting number operators with finite…
For every Lie--Rinehart algebra, we construct an $F$-manifold algebra on the direct sum of its base algebra and module. Contrary to the assertion in \cite[Proposition 13.3.26]{LodayVallette}, the resulting structure is generally not…
We construct rank-zero irregular vertex operators for the Neveu--Schwarz algebra as linear maps between irregular Verma modules of the same rank satisfying the usual superconformal commutation relations and an irregular asymptotic…
Uncertainty in nonlinear dynamical systems is often organized by transport structures that are not apparent from posterior geometry alone. We introduce Dynamical Uncertainty Geometry (DUG), a framework that separates three ingredients that…
We develop a probabilistic cavity-contiguity framework for proving replica-symmetric convergence of local marginals in mean-field Gibbs systems. The approach is based on cavity decompositions of the Hamiltonian together with direct…
Many nonlinear models across physics, chemistry, and biology exhibit multiple solutions for the same parameters, and capturing this entire solution set is essential for understanding pattern-forming systems. Yet existing learned surrogates…
Reconstruction of 3D electromagnetic currents from sparse, multi-frequency, far-field radiation data is severely ill-posed because sparse sampling masks specific current Fourier modes and the missing spectrum enlarges the null space of the…
We study the strong-coupling Birman-Schwinger analysis of the three-boson lattice Schroedinger operator at the exceptional quasimomentum K = pi. First, we provide an exact closed-form benchmark for the fiber Fredholm determinant at a…
We study a Riesz gas with interaction parameter $s \in (d-3,d)$ in an arbitrary spatial dimension $d$, confined to a half-space by a hard wall. We prove that the equilibrium measure exhibits a dichotomy according to the interaction range.…
The work of Baverez, Guillarmou, Kupiainen, and Rhodes [BGKR24] is the starting point of this paper. It shows that analytic changes of boundary parametrizations act differentiably on Liouville amplitudes, with derivative given by Virasoro…
The configurational partition function is a central object in classical equilibrium statistical mechanics, yet its inverse characterization remains largely unexplored. In this letter, we study the inverse problem of identifying smooth…
The Tsallis $q$-sum is one of the fundamental nonlinear composition laws of nonextensive statistical mechanics. Although it has been extensively investigated in continuous settings, its implications for finite mathematical structures remain…