The Renormalization Group as a Stochastic Exploration ProcessThe Renormalization Group (RG) is a powerful and versatile framework for analyzing complex physical systems. Here, we reinterpret it as a stochastic process that explores physical phase spaces, scale…Denis Bernard·Aug 11, 2026SaveLearn
Emergence of fractal structures from breather interactions in the (2+1)-dimensional Konopelchenko--Dubrovsky equationFractal structures generated through nonlinear breather interactions are investigated for the (2+1)-dimensional Konopelchenko--Dubrovsky (KD) equation by means of the Hirota bilinear method. The…Snehalata Nasipuri, Prasanta Chatterjee, Saugata Dutta·Aug 11, 2026SaveLearn
Reflection Positivity in Free Fermionic TheoriesReflection positivity is one of the Osterwalder--Schrader axioms for Euclidean quantum field theory, ensuring that the reconstructed relativistic Hilbert space carries a positive-definite inner…Carl Handrack, Manfred Salmhofer·Aug 11, 2026SaveLearn
Integrability of Hamiltonian systems on COLCS ManifoldWe develop an integrability framework for Hamiltonian dynamics on con-locally conformal symplectic (COLCS) manifolds, odd-dimensional quadruples (M,Ω,θ,η) where dΩ=θΩ, a closed…Antonio J. Pan-Collantes, Xuefeng Zhao·Aug 10, 2026SaveLearn
The determinant of the Dirichlet-to-Neumann map for a surface with boundary and periods of holomorphic differentials on its doubleLet (M,g) be a smooth orientable 2d Riemannian manifold of genus g with Riemannian metric g and connected boundary Γ. Let Λ be the Dirichlet-to-Neumann map on Γ and let $…Dmitrii Korikov, Alexey Kokotov·Aug 10, 2026SaveLearn
Eigenvalue asymptotics for the one-particle density matrix and one-particle kinetic energy density operatorLet ψ( x), x ∈ R3N, be an eigenfunction of the N-particle atomic Schrödinger operator. We consider the one-particle density matrix γ(x, y) and one-particle…Søren Fournais, Alexander V. Sobolev·Aug 10, 2026SaveLearn
Theoretical analysis of the maximum range of a projectile released from a pendulumThe motion of a projectile released from a simple pendulum is analyzed, with particular emphasis on investigating the optimal release angle that maximizes the horizontal range and the corresponding…Ken Yamamoto·Aug 10, 2026SaveLearn
The L-Calculus for Causal Variational Principles: An Exterior Differential Calculus on Non-Smooth SpacesA differential calculus for causal variational principles is developed, which generalizes the exterior calculus of differential forms and some of the associated differential topological structures to…Felix Finster, Niky Kamran, Frank van der Top·Aug 9, 2026SaveLearn
Notes on the Optical-Lattice Hard-Core Bose Gas of Aizenman--Lieb--Seiringer--Solovej--YngvasonThese are detailed expository notes on the staggered optical-lattice hard-core Bose gas of Aizenman, Lieb, Seiringer, Solovej and Yngvason. They restate and expand the arguments and their principal…Yoshitsugu Sekine·Aug 9, 2026SaveLearn
New results on the domain of analyticity of the free energy for the Ising modelWe investigate the analyticity of the free energy of the Ising model in the presence of a non-zero external magnetic field, at high temperature, and at low temperature. Using the Fernandez--Procacci…Nguyen Tong Xuan, Nguyen Dang Thien Thu·Aug 9, 2026SaveLearn
Moving Frames for Lie Pseudo-groups: A Recursive ImplementationA new recursive implementation of the equivariant moving frame method for infinite-dimensional Lie pseudo-group actions is presented. It allows pseudo-group normalizations to be performed before the…Peter J. Olver, Francis Valiquette·Aug 8, 2026SaveLearn
Perturbation Theory for Time-dependent Singular Quantum SystemsWe develop a perturbative framework for time-dependent point interactions in quantum systems with purely discrete unperturbed spectrum. In two and three dimensions the point interaction is described…Kaya Güven Akbaş, Fatih Erman, O. Teoman Turgut·Aug 8, 2026SaveLearn
Analytic Integration of the Lambert W Cosmic Fluid Model H(z) FormulaThe Lambert W (LW) model for the cosmic fluid equation of state was proposed by S. Saha and K. Bamba in 2019-2020. A recent (early 2026) paper by Dubey, et al, carries out a new fit of the LW model…Ken Roberts, S. R. Valluri·Aug 8, 2026SaveLearn
Toward a Rational Extended Thermodynamics of dispersive elastic mediaWe develop a one-dimensional theory of dispersive elasticity within Rational Extended Thermodynamics, taking local first-order balance laws rather than higher spatial gradients as the fundamental…Tommaso Ruggeri, Giuseppe Saccomandi·Aug 7, 2026SaveLearn
The two-sided Bogoliubov inequality in von Neumann algebras conceptualizes the free energy--quantum correlations linkThe quantum-mechanical two-sided Bogoliubov inequality provides upper and lower bounds for the free energy required to separate a system of interacting particles into independent subsystems. The…Benedikt M. Reible, Albert Much, Rainer Verch et al.·Aug 7, 2026SaveLearn
Topological defects in reflection positive topological field theoriesTopological defects in quantum field theories are believed to assemble into higher categories with extra structure. This has been made precise for defects in 2- and 3-dimensional oriented…Lukas Müller·Aug 7, 2026SaveLearn
Effective mass density for wave propagation in periodic layered media in the elasto-acoustic transitionThis article investigates the effective mass density for acoustic and elastic wave propagation in layered media, with emphasis on its transition between these regimes. Conventionally, it is possible…Gabriel Núñez, William J. Parnell, Raphaël C. Assier·Aug 7, 2026SaveLearn
Three Generations in E7Starting from the Standard Model Lie algebra gSM = sl3 sl2 C sitting inside the complex Lie algebra e7, we show…John C. Baez·Aug 7, 2026SaveLearn
Hidden Supersymmetry in Wigner-Yang Quantum MechanicsWe 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…Georg Junker·Aug 7, 2026SaveLearn
On the convergence of the Born series for Coulomb potentialsWe provide a short proof of the convergence of the Born series on asymptotically conic manifolds, at sufficiently high energy. The potential is allowed to have multiple Coulomb singularities. This is…Ethan Sussman, Jared Wunsch·Aug 7, 2026SaveLearn
Cauchy problem for the localized wave propagation in continuous model of the one-dimensional diatomic crystalWe study the continuous model of the localized wave propagation corresponding to the one-dimensional diatomic crystal lattice. From the mathematical point of view the problem can be described in…Sergey Sergeev·Aug 7, 2026SaveLearn
Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ringWe provide explicit formulas to diagonalize the Hamiltonian for the Heisenberg-Ising XXZ spin-1/2 chain on a discrete ring. Two distinguished bases for the Hilbert space include the basis labeled by…Eric I. Corwin, Nikolaus Elsaesser, Axel Saenz·Aug 7, 2026SaveLearn
Graphene-Assisted Electrostatic Screening of Resonant Transport in Radiation-Tolerant MR-DWELL DosimetersWe propose a graphene-assisted MR-DWELL dosimeter for radiation-tolerant sensing, utilizing a dimensionless capacitance ratio to control electrostatic screening and resonant transport. By tuning the…Bigul U. Dosymova, Mikhail V. Dolgopolov·Aug 6, 2026SaveLearn
Triviality in a Non-Perturbative Second-Order Mean-Field Theory for ϕ44We introduce a second-order mean-field description of the four-dimensional Euclidean ϕ4 model within the Wilson--Polchinski renormalization-group framework. The construction is based on the…Majdouline Borji·Aug 6, 2026SaveLearn
On the synthesis of complete two-dimensional second-gradient continua: Tri-pantographic fabricsWe introduce a notion of completeness for two-dimensional second-gradient elastic continua and propose a microstructural route toward its synthesis. A continuum is said to be complete if the Hessian…Casey Rodriguez, Emilio Barchiesi, Simon R. Eugster et al.·Aug 6, 2026SaveLearn