Baker-Akhiezer function for the deformed root system BC(l,1) and bispectralityWe show that a Sergeev-Veselov difference operator of rational Macdonald-Ruijsenaars (MR) type for the deformed root system BC(l,1) preserves a ring of quasi-invariants in the case of non-negative…Iain McWhinnie, Liam Rooke, Martin Vrabec·Jun 2, 2024SaveLearn
Capped Vertex Functions for Hilbn (C2)We obtain explicit formulas for capped descendent vertex functions of Hilbn(C2) for descendents given by the exterior algebra of the tautological bundle. This formula provides a…Jeffrey Ayers, Andrey Smirnov·Jun 1, 2024SaveLearn
Monodromies of Second Order q-difference Equations from the WKB ApproximationThis paper studies the space of monodromy data of second order q-difference equations through the framework of WKB analysis. We compute the connection matrices associated to the Stokes phenomenon…Fabrizio Del Monte, Pietro Longhi·May 31, 2024SaveLearn
Mesoscopic and Macroscopic Entropy Balance Equations in a Stochastic Dynamics and Its Deterministic LimitEntropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By…Hong Qian, Zhongwei Shen·May 31, 2024SaveLearn
On the equilibrium measure for the Lukyanov integralIn 2000, Lukyanov conjectured that a certain ratio of N-fold integrals should provide access, in the large-N regime, to the ground state expectation value of the exponential of the Sinh-Gordon…Charlie Dworaczek Guera, Karol K. Kozlowski·May 31, 2024SaveLearn
A mathematical justification for nonlinear constitutive relations between stress and linearized strainWe present an asymptotic framework that rigorously generates nonlinear constitutive relations between stress and linearized strain for elastic bodies. Each of these relations arises as the leading…K. R. Rajagopal, C. Rodriguez·May 31, 2024SaveLearn
Lecture on the combinatorial algebraic method for computing algebraic integralsConsider an algebraic equation P(x,y)=0 where P∈ C[x,y] (or F[x,y] with F⊂ C a subfield) is a bivariate polynomial, it defines a plane algebraic…Bertrand Eynard·May 31, 2024SaveLearn
On the nested algebraic Bethe ansatz for spin chains with simple g-symmetryWe propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with g-symmetry for any simple Lie algebra g. Starting the nesting process…Allan John Gerrard·May 30, 2024SaveLearn
On Low-Rank Multiplicity-Free Fusion CategoriesThis thesis explains the methods and algorithms we used to obtain explicit F symbols, R symbols, and pivotal coefficients of all multiplicity-free pivotal fusion categories up to rank 7. The thesis…Gert Vercleyen·May 30, 2024SaveLearn
A Proof of L2-Boundedness for Magnetic Pseudodifferential Super Operators via Matrix Representations With Respect to Parseval FramesA fundamental result in pseudodifferential theory is the Calder\'on-Vaillancourt theorem, which states that a pseudodifferential operator defined from a H\"ormander symbol of order 0 defines a…Gihyun Lee, Max Lein·May 30, 2024SaveLearn
Equivalence between non-commutative harmonic oscillators and two-photon quantum Rabi modelsWe prove that the non-commutative harmonic oscillator on L2(R)2 introduced by Parmeggiani and Wakayama is equivalent to the two-photon quantum Rabi model, and they are…Ryosuke Nakahama·May 30, 2024SaveLearn
Mixed radix numeration bases: Horner's rule, Yang-Baxter equation and Furstenberg's conjectureMixed radix bases in numeration is a very old notion but it is rarely studied on its own or in relation with concrete problems related to number theory. Starting from the natural question of the…Damien Simon·May 30, 2024SaveLearn
Asymptotics for automorphisms of quantum systems on the latticeWe study the behaviour of continuous automorphism groups of quantum spin systems on the lattice. Whereas the shift is norm asymptotically abelian continuous automorphism groups can lead only to…Heide Narnhofer·May 30, 2024SaveLearn
Spectral flow and Levinson's theorem for Schr\"o dinger operatorsWe use spectral flow to present a new proof of Levinson's theorem for Schr\"odinger operators on Rn with smooth compactly supported potential. Our proof is valid in all dimensions and…Angus Alexander, Adam Rennie·May 29, 2024SaveLearn
Causal Fermion Systems as an Effective Collapse TheoryIt is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are…Felix Finster, Johannes Kleiner, Claudio F. Paganini·May 29, 2024SaveLearn
The adhesive contact problem for a piecewise-homogeneous orthotropic plate with an elastic patchA piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedgeshaped, which meets the interface at a right angle and is loaded with tangential and normal forces is…Nugzar Shavlakadze, Nana Odishelidze, Francisco Criado-Aldeanueva·May 28, 2024SaveLearn
Quantum Integrable Systems on a Classical Integrable BackgroundIn this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show…Andrii Liashyk, Nicolai Reshetikhin, Ivan Sechin·May 28, 2024SaveLearn
The investigation of singular integro-differential equations relating to adhesive contact problems of the theory of viscoelasticityThe exact and approximate solutions of singular integro-differential equations relating to the problems of interaction of an elastic thin finite or infinite non-homogeneous patch with a plate are…Nugzar Shavlakadze, Nana Odishelidze, Francisco Criado-Aldeanueva·May 27, 2024SaveLearn
The torus plateau for the high-dimensional Ising modelWe consider the Ising model on a d-dimensional discrete torus of volume rd, in dimensions d>4 and for large r, in the vicinity of the infinite-volume critical point βc. We prove that…Yucheng Liu, Romain Panis, Gordon Slade·May 27, 2024SaveLearn
Boundary conditions and the two-point function plateau for the hierarchical ||4 model in dimensions 4 and higherWe obtain precise plateau estimates for the two-point function of the finite-volume weakly-coupled hierarchical ||4 model in dimensions d 4, for both free and periodic boundary…Jiwoon Park, Gordon Slade·May 27, 2024SaveLearn
A Mathematical Theory of Integer Quantum Hall Effect in PhotonicsThis paper investigates interface modes in a square lattice of photonic crystal composed of gyromagnetic particles with C4v point group symmetry. The study shows that Dirac or linear degenerate…Jiayu Qiu, Hai Zhang·May 27, 2024SaveLearn
Commutator-based operator splitting for linear port-Hamiltonian systemsIn this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian…Marius Mönch, Nicole Marheineke·May 27, 2024SaveLearn
Anderson localized states for the quasi-periodic nonlinear Schr\"odinger equation on ZdWe establish large sets of Anderson localized states for the quasi-periodic nonlinear Schr\"odinger equation on Zd, thus extending Anderson localization from the linear (cf. Bourgain…Yunfeng Shi, W. -M. Wang·May 27, 2024SaveLearn
The three-point Gaudin model and branched coverings of the Riemann sphereWe study the three-point quantum sl2-Gaudin model. In this case the compactification of the parameter space is M0,4(C), which is the Riemann sphere. We analyze…Natalia Amburg, Ilya Tolstukhin·May 26, 2024SaveLearn
On the M.Kac problem with augmented dataLet be a bounded plane domain. As is known, the spectrum 0<λ1<λ2≤slant… of its Dirichlet Laplacian L=-[H2() H10()]…M. I. Belishev, A. F. Vakulenko·May 26, 2024SaveLearn