math-ph papers | Gist.Science

Quadratic Bureau-Guillot systems with the first and second Painlevé transcendents in the coefficients. Part I: geometric approach and birational equivalence

This paper revisits quadratic Bureau-Guillot systems containing first and second Painlevé transcendent coefficients, utilizing Okamoto's geometric approach and iterative polynomial regularisation to establish their birational equivalence, resolve the Painlevé equivalence problem for non-rational meromorphic coefficients, and identify a Hamiltonian formulation for one of the systems.

Marta Dell'Atti, Galina FilipukWed, 11 Ma🌀 nlin

Asymmetric simple exclusion process with tree-like network branches

Motivated by proton transport in solid oxides, this paper extends the asymmetric simple exclusion process to a one-dimensional backbone with tree-like branches, deriving the exact stationary distribution and analyzing how specific network geometries influence transport properties through hypergeometric series.

Yuki Ishiguro, Yasunobu AndoWed, 11 Ma🔢 math-ph

Fine asymptotics of the magnetization of the annealed dilute Curie-Weiss model

This paper establishes sharp cumulant bounds for the magnetization in the annealed dilute Curie-Weiss model under high-temperature conditions with an external magnetic field, thereby proving a central limit theorem with convergence rates, a moderate deviation principle, concentration inequalities, and mod-Gaussian convergence for the regime where $p^3 N^2 \to \infty$ .

Fabian Apostel, Hanna Döring, Kristina SchubertWed, 11 Ma🔢 math-ph

Canonical Criterion for Third-Order Transitions

This paper establishes a fluctuation-based canonical framework for identifying third-order phase transitions through a cumulant-ratio criterion that links to microcanonical classifications, avoids density-of-states reconstruction, and applies to both equilibrium and nonequilibrium systems.

Fangfang Wang, Wei Liu, Kai Qi, Zidong Cui, Ying Tang, Zengru DiWed, 11 Ma🔢 math-ph

Non-invertible symmetries and selection rules for RG flows of coset models

This paper introduces a method utilizing local data to classify superselection sectors and topological defect lines in two-dimensional conformal field theories, thereby establishing a unified framework for deriving selection rules governing renormalization group flows in coset and parafermion models.

Valentin Benedetti, Paul Fendley, Javier M. MaganWed, 11 Ma⚛️ hep-th

Dynamics and interaction of solitons in the BPS limit and their internal modes

This thesis investigates the dynamics and interactions of solitons (kinks, oscillons, vortices, and sphalerons) in one- and two-dimensional models by employing effective collective coordinate models to introduce radiation modes, generalize moduli space metrics with vibrational degrees of freedom, identify semi-BPS sphalerons, and propose a dynamic stabilization mechanism driven by internal modes.

S. Navarro-ObregónWed, 11 Ma🌀 nlin

Structure and Representation Theory of basic simple $\mathbb{Z}_2\times \mathbb{Z}_2$ -graded color Lie algebras

This paper adapts methods from complex semisimple Lie algebra theory to establish a root theory for basic simple $\mathbb{Z}_2 \times \mathbb{Z}_2$ -graded color Lie algebras, enabling the classification of their finite-dimensional representations through highest weight and complete reducibility theorems under the assumption of a self-centralizing Cartan subalgebra.

Spyridon Afentoulidis-AlmpanisWed, 11 Ma🔢 math-ph

A Dynamical Approach to Non-Extensive Thermodynamics

This paper develops a non-extensive thermodynamic formalism for one-sided shifts by introducing $q$ -entropy and $q$ -pressure concepts, proving the existence and uniqueness of $q$ -equilibrium states for Lipschitz potentials, and establishing connections between these generalized structures and classical Ruelle transfer operators.

Artur O. Lopes, Paulo VarandasWed, 11 Ma🔢 math-ph

Hydrodynamics as cospans of field theories into the BF theory

This paper proposes a categorical framework for hydrodynamics by modeling the approximation of a microscopic theory as a cospan of differential graded manifolds that connects the microscopic and hydrodynamic descriptions through a $BF$ theory encoding the conservation laws of currents.

Simon Jonsson, Hyungrok KimWed, 11 Ma⚛️ hep-th

Intertwining Markov Processes via Matrix Product Operators

This paper introduces a generalized matrix product operator framework to establish global duality transformations between distinct one-dimensional boundary-driven Markov processes, demonstrating that the symmetric simple exclusion process with out-of-equilibrium boundaries is exactly dual to an equilibrium system where the Gibbs-Boltzmann measure effectively captures non-equilibrium physics.

Rouven Frassek, Jan de Gier, Jimin Li, Frank VerstraeteWed, 11 Ma🔢 math-ph

Pseudo-Riemmanian Lie algebras with coisotropic ideals and integrating the Laplace-Beltrami equation on Lie groups

This paper identifies a class of left-invariant pseudo-Riemannian metrics on Lie groups, characterized by coisotropic commutative ideals, for which the Laplace-Beltrami equation can be reduced to a solvable first-order PDE using noncommutative integration methods, thereby yielding explicit solutions and novel nonlocal integro-differential symmetry operators.

A. A. Magazev, I. V. ShirokovWed, 11 Ma🔢 math-ph

Weak-Coupling Limit of the Lattice Nonlinear Schrödinger Integral Equation

This paper investigates the weak-coupling limit of the lattice nonlinear Schrödinger integral equation by employing matched asymptotic expansions to derive the ground-state energy and density, revealing a logarithmic divergence linked to the Bose-Einstein distribution and uncovering a resurgent transseries structure through Wiener-Hopf analysis.

Felipe Taha Sant'AnaWed, 11 Ma🔢 math-ph

Partial Orderings of Curvature Invariants

This paper establishes a new hierarchy of pointwise inequalities among curvature invariants across various Petrov and Segre types in arbitrary dimensions, specifically demonstrating how higher-order invariants like the Zakhary–McIntosh scalars are algebraically bounded by lower-order quantities such as the Kretschmann scalar.

Ivica SmolicWed, 11 Ma⚛️ gr-qc

On Fermi's model for the scattering of a slow neutron from a bound proton

This paper mathematically validates Enrico Fermi's 1936 model for slow neutron scattering from a bound proton by proving the Limiting Absorption Principle, establishing stationary scattering theory, and deriving the scattering cross-section formula within the Born approximation.

Domenico Finco, Raffaele Scandone, Alessandro TetaWed, 11 Ma🔢 math-ph

State integral models and the tetrahedron equation

This paper demonstrates that for a specific class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichmüller TQFT, the Boltzmann weight assigned to a tetrahedron satisfies the tetrahedron equation, with the tetrahedron's dihedral angles serving as spectral parameters.

Junya YagiWed, 11 Ma🔢 math-ph

Swinging Waves in the Ablowitz-Ladik Equation

This paper constructs a novel family of exact cnoidal waves and dark solitons for the focusing and defocusing Ablowitz-Ladik equations, characterized by a "swinging" phase with nonlinear dependence on time and site number, derived via a two-point map that enables arbitrary lattice positioning and establishes explicit velocity quantization rules for waves on closed loops.

I. V. Barashenkov, Frank S. SmutsWed, 11 Ma🌀 nlin

Spectral transitions in some Rabi models

This paper employs subordinacy theory to characterize the spectral transitions from discrete to continuous spectra in several quantum Rabi models, proving the absence of singular spectrum and interior eigenvalues across all parameter ranges.

Grzegorz Swiderski, Lech ZielinskiWed, 11 Ma🔢 math-ph

Verifying Good Regulator Conditions for Hypergraph Observers: Natural Gradient Learning from Causal Invariance via Established Theorems

This paper verifies that persistent observers in causally invariant hypergraph substrates satisfy the Conant-Ashby Good Regulator Theorem, thereby necessitating internal models that lead to natural gradient descent as the unique learning rule and yielding a model-dependent closed-form formula for Vanchurin's regime parameter $\alpha$ with a quantum-classical threshold at $\kappa(F)=2$ .

Max ZhuravlevWed, 11 Ma🤖 cs.LG

Symmetry of Bounce Solutions at Finite Temperature

This paper rigorously extends the Coleman-Glaser-Martin theorem to finite temperatures, proving that the least-action saddle-point configurations for a broad class of scalar potentials are necessarily $O(D-1)$ -symmetric and spatially monotonic, thereby providing a mathematical foundation for symmetry assumptions in thermal vacuum decay and cosmological phase transitions.

Yutaro Shoji, Masahide YamaguchiWed, 11 Ma⚛️ hep-ph

Application of dual-tree complex wavelet transform for spectra background reduction

This paper introduces a universal Dual-Tree Complex Wavelet Transform (DTCWT) method for removing spectral backgrounds in experimental data, demonstrating its superior signal preservation and reduced bias compared to traditional fitting or Fourier-based techniques through applications on X-ray powder diffraction and photoluminescence spectra.

Kazimierz Skrobas, Kamila Stefanska-Skrobas, Cyprian Mieszczynski, Renata RatajczakWed, 11 Ma🔬 cond-mat.mtrl-sci

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