An Example of Banach and Hilbert manifold: the universal Teichm\"uller spaceFor s >32, the group of Sobolev class s diffeomorphisms of the circle is a smooth manifold modeled on the space of Sobolev class s sections of the tangent bundle of the circle. It is a…Alice Barbara Tumpach·Mar 27, 2023SaveLearn
Recovering the shape of a quantum caterpillar tree by two spectraWe show how to find the shape of an equilateral caterpillar tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm-Liouville equation on this tree. We prove that in…Dmytro Kaliuzhnyi-Verbovetskyi, Vyacheslav Pivovarchik·Mar 26, 2023SaveLearn
An inside view of the tensor productGiven a vector-space ~V~ which is the tensor product of vector-spaces A and B, we reconstruct A and B from the family of simple tensors ab within V. In an application to…Rafael D. Sorkin·Mar 26, 2023SaveLearn
Limit theorems for the cubic mean-field Ising modelWe study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two…Pierluigi Contucci, Emanuele Mingione, Godwin Osabutey·Mar 25, 2023SaveLearn
Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological RecursionsVia Andersen-Borot-Orantin's geometric recursion, a twist of the topological recursion was proposed, and a recursion for the Masur-Veech polynomials was uncovered. The purpose of this article is to…Hiroyuki Fuji, Masahide Manabe·Mar 24, 2023SaveLearn
Two-term asymptotics of the exchange energy of the electron gas on symmetric polytopes in the high-density limitWe derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This…Thiago Carvalho Corso·Mar 24, 2023SaveLearn
The Lp-boundedness of wave operators for fourth order Schr\"odinger operators on R4We prove that the wave operators of scattering theory for the fourth order Schr\"odinger operators 2 + V(x) in R4 are bounded in Lp( R4) for the set of p's of…Artbazar Galtbayar, Kenji Yajima·Mar 24, 2023SaveLearn
Friedrichs Diagrams -- Bosonic and FermionicWe give a mathematically precise review of a diagrammatic language introduced by Friedrichs in order to simplify computations with creation and annihilation operator products. In that language, we…Morris Brooks, Sascha Lill·Mar 24, 2023SaveLearn
Bitangent planes of surfaces and applications to thermodynamicsThe classical van der Waals equation, applied to one or two mixing fluids, and the Helmholtz (free) energy function A yield, for fixed temperature T, a curve in the plane R2 (one…Peter Giblin, Graham Reeve·Mar 24, 2023SaveLearn
On the structure of graded Poisson color algebrasIn this paper we introduce the class of graded Poisson color algebras as the natural generalization of graded Poisson algebras and graded Poisson superalgebras. For an arbitrary abelian…Valiollah Khalili·Mar 24, 2023SaveLearn
Phase Transitions in the Hubbard Model on the Square LatticeWe study the low temperature properties of the two-dimensional weakly interacting Hubbard model on 2 with renormalized chemical potential μ=2-μ0, μ0=10-10 fixed, in which case…Zhituo Wang·Mar 23, 2023SaveLearn
Integrable systems of finite type from F-cohomological field theories without unitOne of many manifestations of a deep relation between the topology of the moduli spaces of algebraic curves and the theory of integrable systems is a recent construction of Arsie, Lorenzoni, Rossi,…Alexandr Buryak, Danil Gubarevich·Mar 23, 2023SaveLearn
Typical Macroscopic Long-Time Behavior for Random HamiltoniansWe consider a closed macroscopic quantum system in a pure state t evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces…Stefan Teufel, Roderich Tumulka, Cornelia Vogel·Mar 23, 2023SaveLearn
The families of Hamiltonians sharing common symmetry structureWe describe a general procedure which allows to construct, starting from a given Hamiltonian, the whole family of new ones sharing the same set of unparameterized trajectories in phase space. The…Cezary Gonera, Joanna Gonera, Artur Jasiński et al.·Mar 23, 2023SaveLearn
Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising ChainsThe monotonicity of the scalar curvature of the state space equipped with the Bogoliubov-Kubo-Mori metric under more mixing a state is an important conjecture called the Petz conjecture. From the…Takemi Nakamura·Mar 21, 2023SaveLearn
Noncommutative integration, quantum mechanics, Tannaka's theorem for compact groupoids and examplesWe consider topological groupoids in finite and also in a compact settings. In the initial sections, we introduce definitions of typical observables and we studied them in the context of statistical…Artur O. Lopes, Marcos Sebastian, Victor Vargas·Mar 21, 2023SaveLearn
Unitarity of the SoV Transform for SL(2, C) Spin ChainsWe prove the unitarity of the separation of variables transform for SL(2, C) spin chains by a method based on the use of Gustafson integrals.Alexander N. Manashov·Mar 20, 2023SaveLearn
Almost flat highest weights and application to Wilson loops on compact surfacesWe derive new formulas for the expectation and variance of Wilson loops for any contractible simple loop on a compact orientable surface of genus 1 and higher, in the model of two-dimensional…Thibaut Lemoine·Mar 20, 2023SaveLearn
A Completion of Quantum MechanicsA proposal of how to complete non-relativistic quantum mechanics to a physically meaningful, mathematically precise and logically coherent theory is reviewed. Our proposal leads to a general,…Jürg Fröhlich, Zhou Gang, Alessandro Pizzo·Mar 20, 2023SaveLearn
Lattice Green functions for pedestrians: Exponential decayThe exponential decay of lattice Green functions is one of the main technical ingredients of the Baaban's approach to renormalization. We give here a self-contained proof, whose various…Wojciech Dybalski, Alexander Stottmeister, Yoh Tanimoto·Mar 19, 2023SaveLearn
On non-strictly hyperbolic systems and models of natural sciences reducible to themWe show that many important natural science models in their mathematical formulation can be reduced to non-strictly hyperbolic systems of the same kind. This allows the same methods to be applied to…Olga Rozanova·Mar 19, 2023SaveLearn
Non-linear Electrodynamics derived from the Kaluza-Klein TheoryThe lagrangian of the Kaluza-Klein theory, in its simplest five-dimensional version, should include not only the scalar curvature R, but also the quadratic Gauss-Bonnet invariant. The general…Richard Kerner·Mar 19, 2023SaveLearn
Spin Calogero-Moser periodic chains and two dimensional Yang-Mills theory with cornersQuantum Calogero-Moser spin system is a superintegable system with the spectrum of commuting Hamiltonians that can be described entirely in terms of representation theory of corresponding simple Lie…Nicolai Reshetikhin·Mar 19, 2023SaveLearn
Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactionsWe study the Schroedinger operators Hλμ(K), with K ∈ T2 the fixed quasi-momentum of the particles pair, associated with a system of two identical fermions on the two-dimensional lattice…Saidakhmat N. Lakaev, Alexander K. Motovilov, Saidakbar Kh. Abdukhakimov·Mar 18, 2023SaveLearn
Some perturbation results for quasi-bases and other sequences of vectorsWe discuss some perturbation results concerning certain pairs of sequences of vectors in a Hilbert space and producing new sequences which share, with the original ones, reconstruction…Fabio Bagarello, Rosario Corso·Mar 17, 2023SaveLearn