On the Ergodicity of Renormalized Translation-Invariant Nelson-Type SemigroupsWe present a simple functional integration based proof that the semigroups generated by the ultraviolet-renormalized translation-invariant non- and semi-relativistic Nelson Hamiltonians are…Benjamin Hinrichs, Fumio Hiroshima·Dec 12, 2024SaveLearn
Formal Languages and TQFTs with DefectsA construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is…Luisa Boateng, Matilde Marcolli·Dec 12, 2024SaveLearn
On the spectrum of the Landau Hamiltonian perturbed by a periodic electric potential V∈ Hs loc( R2; R), s > 0We prove that in a Sobolev space Hs ( R2; R), s > 0, of periodic functions with a given period lattice , there exists a dense Gδ -set $…L. I. Danilov·Dec 12, 2024SaveLearn
Towards kinetic equations of open systems of active soft matterThe chapter presents some new approaches to describing the collective behavior of complex systems of mathematical biology based on the evolution equations of observables such as open systems. This…V. I. Gerasimenko·Dec 12, 2024SaveLearn
Highest weight vectors, shifted topological recursion and quantum curvesWe extend the theory of topological recursion by considering Airy structures whose partition functions are highest weight vectors of particular W-algebra representations. Such highest…Raphaël Belliard, Vincent Bouchard, Reinier Kramer et al.·Dec 12, 2024SaveLearn
Formal justification of a continuum relaxation model for one-dimensional moir\'e materialsMechanical relaxation in moir\'e materials is often modeled by a continuum model where linear elasticity is coupled to a stacking penalty known as the Generalized Stacking Fault Energy (GSFE). We…Jingzhi, Zhou, Alexander B. Watson·Dec 12, 2024SaveLearn
On the equivalence of AQFTs and prefactorization algebrasThis paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new…Marco Benini, Victor Carmona, Alastair Grant-Stuart et al.·Dec 10, 2024SaveLearn
Tube Category, Tensor Renormalization and Topological HolographyOcneanu's tube algebra provides a finite algorithm to compute the Drinfeld center of a fusion category. In this work we reveal the universal property underlying the tube algebra. Take a base category…Tian Lan·Dec 10, 2024SaveLearn
Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via ContoursFollowing seminal work by J. Fr\"ohlich and T. Spencer on the critical exponent α=2, we give a proof via contours of phase transition in the one-dimensional long-range ferromagnetic Ising…Lucas Affonso, Rodrigo Bissacot, Henrique Corsini et al.·Dec 10, 2024SaveLearn
Extended Landen's formulas and double product theta functionsFor an arbitrary positive integer p, Landen's formula is extended to express theta function with modulus pτ by p product of theta functions with τ, which is applied to several examples.…Kiyoshi Sogo·Dec 8, 2024SaveLearn
Theory of general theta relations, addition formulas, and theta constants identitiesJacobi's theta relations among quartic products of theta functions are generalized to those of arbitrary n products. Igusa's procedure of derivation is extended to prove such general theta…Kiyoshi Sogo·Dec 8, 2024SaveLearn
Generalized Buchdahl equations as Lie-Hamilton systems from the 'book' and oscillator algebras: Quantum deformations and their general solutionWe revisit the nonlinear second-order differential equations x(t)=a (x )x(t)2+b(t)x(t) where a(x) and b(t) are arbitrary functions on their argument from the perspective…Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz, Francisco J. Herranz·Dec 8, 2024SaveLearn
Extreme Gibbs measures for a Hard-Core-SOS model on Cayley treesWe investigate splitting Gibbs measures (SGMs) of a three-state (wand-graph) hardcore SOS model on Cayley trees of order k ≥ 2 . Recently, this model was studied for the hinge-graph with $ k =…R. M. Khakimov, M. T. Makhammadaliev, U. A. Rozikov·Dec 8, 2024SaveLearn
Lower and upper bounds for configurations of points on a sphereWe present a new proof (based on spectral decomposition) of a bound originally proved by Sidelnikov~\, for the frame potentials Σij ( Pi · Pj ) on a…Paolo Amore, Ricardo A. Sáenz·Dec 8, 2024SaveLearn
Multivector (MV) functions in Clifford algebras of arbitrary dimension: Defective MV caseExplicit formulas to calculate MV functions in a basis-free representation are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on analysis of the roots of…A. Acus, A. Dargys·Dec 7, 2024SaveLearn
The Gauss Circle Problem and Fourier QuasicrystalsThe Gauss circle problem asks for an approximation to the number of lattice points of Z2 contained in Br, the disk of radius r centered at the origin. Upper, lower, and average…Roni A. Edwin, Allen Lin·Dec 7, 2024SaveLearn
Poisson structures in the Banach setting: comparison of different approachesIn this paper we examine various approaches to the notion of Poisson manifold in the context of Banach manifolds. Existing definitions are presented and differences between them are explored and…Tomasz Goliński, Praful Rahangdale, Alice Barbora Tumpach·Dec 6, 2024SaveLearn
Diagonal invariants and genus-zero Hurwitz Frobenius manifoldsThe Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of…Alessandro Proserpio, Ian A. B. Strachan·Dec 6, 2024SaveLearn
Extensions of the Brascamp-Lieb Inequality and the Dipole GasThis paper is concerned with lattice field models in dimension at least 2. The action is a uniformly convex function of the gradient of the field. The main result Theorem 1.4 proves that…Joseph G. Conlon, Michael Dabkowski·Dec 6, 2024SaveLearn
Linearization of Newton's second lawThe geometric linearization of nonlinear differential equation is a robust method for the construction of analytic solutions. The method is related to the existence of Lie symmetries which can be…Andronikos Paliathanasis·Dec 6, 2024SaveLearn
Simplicial Cheeger-Simons models and simplicial higher abelian gauge theoryA pair (K,K') consisting of a smooth triangulation K of a compact smooth oriented Riemannian manifold M and a sufficiently fine subdivision K' determines a finite-dimensional Cheeger--Simons…Jyh-Haur Teh·Dec 6, 2024SaveLearn
Exact solution of the Izergin-Korepin Gaudin model with periodic and open boundariesWe study the Izergin-Korepin Gaudin models with both periodic and open integrable boundary conditions, which describe quantum systems exhibiting novel long-range interactions. Using the Bethe ansatz…Xiaotian Xu, Pei Sun, Xin Zhang et al.·Dec 6, 2024SaveLearn
Fermionic quantum walkers coupled to a bosonic reservoirWe analyse the discrete-time dynamics of a model of non-interacting fermions coupled to an infinite reservoir formed by a bosonic quantum walk on Z. This dynamics consists of consecutive…Olivier Bourget, Alain Joye, Dominique Spehner·Dec 6, 2024SaveLearn
Spectral theory for periodic vector NLS equationsWe consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation. The spectrum of the operator covers…Evgeny Korotyaev·Dec 6, 2024SaveLearn
Enlargement of symmetry groups in physics: a practitioner's guideWigner's classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective…Lehel Csillag, Julio Marny Hoff da Silva, Tudor Patuleanu·Dec 6, 2024SaveLearn