Rotation angles of a rotating disc as the holonomy of the Hopf fibrationWe address the fundamental question of how rotation angles arise in classical rigid body motion from a geometric viewpoint. As a fundamental kinematical setting, we consider a rotating-disc model. We…Takuya Matsumoto·Dec 4, 2025SaveLearn
Edge Hamiltonian for Free Fermion Quantum Hall ModelsWe investigate a proposal of Kitaev for a microscopic construction of a Hamiltonian intended to describe the edge dynamics of a quantum Hall system. We show that the construction works in the setting…Simon Du, Martin Fraas, Abi Gopal et al.·Dec 4, 2025SaveLearn
Cumulant expansions of operator groups of quantum many-particle systemsThe article presents a method of cluster expansions for groups of operators associated with the von Neumann equations for states and the Heisenberg equations for observables, aiming to construct…V. I. Gerasimenko, I. V. Gapyak·Dec 4, 2025SaveLearn
An elementary approach to Wehrl-type entropy bounds in quantitative formWe consider the problem of the stability (with sharp exponent) of the Lieb--Solovej inequality for symmetric SU(N) coherent states, which was obtained only recently by the authors. Here, we propose…Fabio Nicola, Federico Riccardi, Paolo Tilli·Dec 3, 2025SaveLearn
Invariant density statistical quantifiers and a temperature for the logistic mapIn this work, we study the dynamics of the logistic map based on a probabilistic characterization in terms of the invariant density. We analyze the relevant regimes of the dynamics (regular,…Ignacio Sebastián Gomez, Guilherme Vieira Brito Junior, Samuel Silva Santos et al.·Dec 3, 2025SaveLearn
Instantaneous Sobolev Regularization for Dissipative Bosonic DynamicsWe investigate quantum Markov semigroups on bosonic Fock space and identify a broad class of infinite-dimensional dissipative evolutions that exhibit instantaneous Sobolev-regularization. Motivated…Pablo Costa Rico, Paul Gondolf, Tim Möbus·Dec 3, 2025SaveLearn
Single-walled carbon nanotubes: the Bloch theory, reciprocal tubes, and a tight-binding approximationThe electronic structure of a graphene sheet is altered when it is rolled up to form a single-walled carbon nanotube (SWCNT), and the curvature effects for small radius nanotubes become significant.…Yuri A. Antipov·Dec 3, 2025SaveLearn
Optical Caustics as Lagrangian Singularities: Classification and Geometric StructureThis paper develops a rigorous mathematical framework for light propagation by constructing the optical phase space with its symplectic structure and the extended phase space with its contact…Rongqi Shang, Donglin Ma·Dec 3, 2025SaveLearn
The magnetic inverse problem for two stacked layers of sourcesWe present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic…Michael T. M. Woodley, Thomas Coussens, William Evans et al.·Dec 3, 2025SaveLearn
Solutions to Open WDVV Equations for the Universal Whitham HierarchyIn this paper, we construct a pair of solutions to the open WDVV equations associated with the infinite-dimensional Frobenius manifolds that underlie the genus-zero universal Whitham hierarchy, and…Shilin Ma·Dec 3, 2025SaveLearn
A discontinuous Galerkin approach for simulating graphene-based electron devices via the Boltzmann transport equationElectron devices based on graphene have lately received a considerable interest; in fact, they could represent the ultimate miniaturization, since the active area is only one atom tick. However, the…Giovanni Nastasi, Vittorio Romano·Dec 2, 2025SaveLearn
Three-dimensional third medium contact model for hyperelastic contact and pneumatically actuated systemsThis work presents a comprehensive three-dimensional third-medium contact framework for modeling complex contact interactions in hyperelastic solids and pneumatically actuated systems. The proposed…Bing-Bing Xu, Tianju Xue, Peter Wriggers·Dec 2, 2025SaveLearn
A Mathematical Introduction to Geometric QuantizationThese notes are based on a series of lectures by Kadri \.Ilker Berktav from May 2024 to November 2024, providing a detailed exposition of geometric quantization formalism and its essential…Kadri İlker Berktav, Burak Oğuz, Ömer Önder et al.·Dec 2, 2025SaveLearn
Symmetry transformation group arising from the Laplace-Runge-Lenz vectorThe Kepler problem in classical mechanics exhibits a rich structure of conserved quantities, highlighted by the Laplace--Runge--Lenz (LRL) vector. Through Noether's theorem in reverse, the LRL vector…Stephen C. Anco, Mahdieh Gol Bashmani Moghadam·Dec 2, 2025SaveLearn
On mathematical aspects of surface correction via ion beam etchingMotivated by the ion beam dwell time calculation problem in Ion Beam Figuring we suggest a mathematical framework for solving a specific type of inverse problems, which appear in various areas of…W. Pauls·Dec 2, 2025SaveLearn
Quantum Boltzmann dynamics and bosonized particle-hole interactions in fermion gasesIn this paper, we study a cold gas of N 1 weakly interacting fermions. We describe the time evolution of states that are perturbations of the Fermi ball, and analyze the dynamics in…Esteban Cárdenas, Thomas Chen·Dec 2, 2025SaveLearn
Three Dixon-Rosenfeld PlanesRosenfeld postulated ``generalized'' projective planes, which exploit a correspondence between rank-one idempotents of Jordan algebras J3(A) and points of projective planes…David Chester, Alessio Marrani, Daniele Corradetti et al.·Dec 1, 2025SaveLearn
Cancellation Identities and RenormalizationWe construct a manifest gauge invariant renormalization framework by first introducing a perturbative BRST Feynman graph complex and then combining it with Connes--Kreimer renormalization theory: To…David Prinz·Dec 1, 2025SaveLearn
The Lieb-Robinson condition and the Fr\'echet topologyWe define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the…Sven Bachmann, Giuseppe De Nittis, Julián Gómez·Dec 1, 2025SaveLearn
A novel chain of Lie algebras and its coalgebra symmetryWe study a novel n(n+1)/2-dimensional non-semisimple Lie algebra gn, a generalisation of both sl2(K) and the two-photon Lie algebra h6. We…Giorgio Gubbiotti, Danilo Latini, Bert van Geemen·Dec 1, 2025SaveLearn
Continuity inequalities for sandwiched R\'enyi and Tsallis conditional entropies with application to the channel entropy continuityFor the sandwiched R\'enyi entropy the conditional entropy can be defined two ways: Hα(A|B), Hα(A|B). In the limiting case,…Anna Vershynina·Dec 1, 2025SaveLearn
Augmentation and Bulk Edge Correspondence for one dimensional aperiodic tight binding operatorsWe consider a particular class of 1D aperiodic models with the aim to understand how their internal degrees of freedom contribute to their topological invariants and the possible relations…Johannes Kellendonk, Lorenzo Scaglione·Dec 1, 2025SaveLearn
Robustness and resilience of dynamical networks in biology and epidemiologyNatural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is…Daniele Proverbio, Rami Katz, Giulia Giordano·Dec 1, 2025SaveLearn
Statistical Properties of the Rooted-Tree Encoding of NWe prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a…Pierluigi Contucci, Claudio Giberti, Godwin Osabutey et al.·Dec 1, 2025SaveLearn
Around the semi-classical limit of boundary Liouville conformal field theoryLiouville conformal field theory describes a random geometry that fluctuates around a deterministic one: the unique solution of the problem of finding, within a given conformal class, a Riemannian…Baptiste Cerclé·Dec 1, 2025SaveLearn