On Physical Components of Tensors in Elasticity and InelasticityWidely used in mechanics and mathematical physics, physical components remove the inherent coordinate-dependent scaling in curvilinear coordinates, yielding components of consistent physical…Souhayl Sadik, Arash Yavari·Aug 15, 2026SaveLearn
The Okinawa Lectures on EntropyAfter a historical introduction, the most important classical and quantum entropies are introduced as constructions in classical and quantum probability theory. Classical entropies are studied from…Klaas Landsman·Aug 14, 2026SaveLearn
A semiclassical limit of reduced Hartree-Fock theory at positive temperatureIt is established that the reduced Hartree-Fock grand potential at positive temperature converges in the semiclassical limit to a Thomas-Fermi grand potential. In particular, a density-potential dual…Dominic Shillingford·Aug 14, 2026SaveLearn
Form factors of field exponentials in the 1+1 dimensional Sine-Gordon modelThis work provides explicit expressions, in all sectors of the Fock space: soliton, antisoliton and breather, for the fundamental building blocks -the form factors- of the generalised integral…Karol K. Kozlowski, Alex Simon·Aug 14, 2026SaveLearn
Symmetry Emergence in Self-Organized CriticalityWe 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…Ernesto Lupercio, Mikhail Shkolnikov·Aug 13, 2026SaveLearn
Hidden Dyson Universality in Inverse-Spectral GeometryDyson 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…Momo Hayashi, Kazumitsu Sakai·Aug 13, 2026SaveLearn
Proper condensates versus the Onsager-Penrose criterion: A friendly debate on Bose-Einstein condensationThis 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.…Detlev Buchholz·Aug 13, 2026SaveLearn
On Toeplitz determinants with slow Fourier decayWe study Toeplitz determinants Tn(ef) for f whose Fourier coefficients satisfy fk=O(|k|-1). This regime extends beyond H1/2 and includes symbols with Fisher-Hartwig…Nedialko Bradinoff, Maurice Duits·Aug 13, 2026SaveLearn
Exact analytical solution for the non-selfadjoint problem of Maxwell--Cattaneo--Vernotte heat conduction with heat-transfer boundary conditionThe 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…Mátyás Szücs, Tamás Fülöp·Aug 13, 2026SaveLearn
Transparent Boundary Conditions for the Heat Equation on Metric GraphsWe 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…Jasur Matrasulov, Jambul Yusupov, Matthias Ehrhardt·Aug 13, 2026SaveLearn
A discrete Smorodinsky--Winternitz II superintegrable systemWe 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…Pierre-Antoine Bernard, Vutha Vichhea Chea, Luc Vinet·Aug 13, 2026SaveLearn
Notes on Electrostatics in R3A 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…Vladimir Gol'dshtein, Wolfgang H. Müller, Reuven Segev·Aug 13, 2026SaveLearn
A discrete Smorodinsky--Winternitz I superintegrable systemWe 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…Vutha Vichhea Chea, Luc Vinet·Aug 13, 2026SaveLearn
From Lie--Rinehart Algebras to F-Manifold AlgebrasFor 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 [Proposition 13.3.26]LodayVallette, the…Yufeng Pei, Yunhe Sheng·Aug 13, 2026SaveLearn
Neveu--Schwarz Irregular Vertex Operators, Decomposition Theorems, and Bilinear OperatorsWe 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…Hajime Nagoya·Aug 13, 2026SaveLearn
Dynamical uncertainty geometry for nonlinear transportUncertainty 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…Giacomo Tommei·Aug 12, 2026SaveLearn
A contiguity approach to replica symmetric marginalsWe 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…Ernesto Mordecki, Anas A. Rahman, Manuel Sáenz·Aug 12, 2026SaveLearn
PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion SystemsMany 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…Zhipeng Chang, Wenpeng Yin, Wenrui Hao·Aug 12, 2026SaveLearn
Model-Consistent Structured-Hankel Matrix Completion for 3D Sparse Multi-frequency Electromagnetic Source ReconstructionReconstruction 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…Shujaat Khan, Abdul Wahab·Aug 12, 2026SaveLearn
A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimerWe present a refined strong-coupling Birman-Schwinger analysis of the three-boson lattice Schroedinger operator on Z2 at the exceptional quasimomentum K = pi. First, we provide an exact closed-form…Mikhail Dolgopolov·Aug 12, 2026SaveLearn
Confinement transitions in half-space constrained Riesz gasesWe study a Riesz gas with interaction parameter s ∈ (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…Sung-Soo Byun, Yong-Woo Lee, Eui Yoo·Aug 12, 2026SaveLearn
Ward identities: a geometric point of view and applicationsThe 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…Baojun Wu, Shengjing Xu·Aug 12, 2026SaveLearn
Inverse characterization and non-uniqueness of the Gaussian configurational partition functionGiven a configurational partition function, in this work we investigate the inverse problem of reconstructing the one-dimensional potential. For the case of the Gaussian partition function, the…Ignacio S. Gomez·Aug 11, 2026SaveLearn
Finite nonlinear mathematical structures induced by the Tsallis q-sumThe 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…Ignacio S. Gomez·Aug 11, 2026SaveLearn
Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows. II: The two-dimensional space caseThe work is a natural continuation of that published in Stud Appl Math. 2024; 153:e12737. All possible two-components evolutions systems of (1+2)-dimensional second-order PDEs admitting an…Roman Cherniha, John R. King·Aug 11, 2026SaveLearn