On material-uniform elastic bodies with disclinations and their homogenizationIn this note, we define material-uniform hyperelastic bodies (in the sense of Noll) containing discrete disclinations and dislocations, and study their properties. We show in a rigorous way that the…Cy Maor·Dec 18, 2024SaveLearn
Planar rooted line arrangements and an operad for factorized scatteringWe introduce two topological non- operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a…Denis Bashkirov·Dec 18, 2024SaveLearn
Local enhancement of the mean-field approximation for bosonsWe study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive…Marius Lemm, Simone Rademacher, Jingxuan Zhang·Dec 18, 2024SaveLearn
Spectrum and Lifshitz tails for the Anderson model on the Sierpinski gasket graphIn this work, we study the Anderson model on the Sierpinski gasket graph. We first identify the almost sure spectrum of the Anderson model when the support of the random potential has no gaps. We…Laura Shou, Wei Wang, Shiwen Zhang·Dec 18, 2024SaveLearn
Higher rank elliptic partition functions and multisymmetric elliptic functionsWe introduce and investigate a class of glM+1 partition functions which is an extension of the one introduced by Foda-Manabe. We characterize the partition functions by a nested…Allan John Gerrard, Kohei Motegi, Kazumitsu Sakai·Dec 18, 2024SaveLearn
On the maximal superintegrability of strongly isochronous HamiltoniansWe study strongly isochronous Hamiltonians that generate periodic time evolution with the same basic period for a dense set of initial values. We explain that all such Hamiltonians are maximally…L. Feher·Dec 18, 2024SaveLearn
A Family of Instanton-Invariants for Four-Manifolds and Their Relation to Khovanov HomologyThis article provides a review of the gauge-theoretic approach to Khovanov homology, framed in terms of a generalisation of Witten's original proposal. Concretely, the physical arguments underlying…Michael Bleher·Dec 17, 2024SaveLearn
W-algebras, Gaussian Free Fields and g-Dotsenko-Fateev integralsBased on the intrinsic connection between Gaussian Free Fields and the Heisenberg vertex algebra, we study some aspects of the correspondence between probability theory and W-algebras. This is…Baptiste Cerclé·Dec 17, 2024SaveLearn
On Haantjes tensors for second-order superintegrable systemsThe vanishing of the Haantjes tensor is an important property that has been linked, for instance, to the existence of separation coordinates and the integrability of systems of hydrodynamic type. We…Ian Marquette, Damien McLeod, Serena Scapucci et al.·Dec 17, 2024SaveLearn
Hadwiger Models: Low-Temperature Behavior in a Natural Extension of the Ising ModelAll isometrically invariant Markov (strictly local) fields on binary assignments are induced by energy functions that can be represented as linear combinations of area, perimeter, and Euler…Summer Eldridge, Benjamin Schweinhart·Dec 16, 2024SaveLearn
A Satisfiability algorithm based on Simple Spinors of the Clifford algebra of Rn,nWe refine the formulation of the Boolean satisfiability problem with n Boolean variables in Clifford algebra C(Rn,n) [3] and exploit this continuous setting to outline a…Marco Budinich·Dec 16, 2024SaveLearn
Fermi's golden rule in tunneling models with quantum waveguides perturbed by Kato class measuresIn this paper we consider two dimensional quantum system with an infinite waveguide of the width d and a transversally invariant profile. Furthermore, we assume that at a distant there is a…Sylwia Kondej, Kacper Ślipko·Dec 16, 2024SaveLearn
On the Protection Against Noise for Measurement-Based Quantum ComputationHere we establish conditions for some pairs of quantum logic gates which operate on one qubit to be protected against crosstalk.Valentin Vankov Iliev·Dec 16, 2024SaveLearn
Multi-component Hamiltonian difference operatorsIn this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classification of low order…Matteo Casati, Daniele Valeri·Dec 16, 2024SaveLearn
Unitary n-correlations with restricted support in random matrix theoryWe consider the n-correlation of eigenvalues of random unitary matrices in the alternative form that is not the tidy determinant common in random matrix theory, but rather the expression derived…Patrik Demjan, N. C. Snaith·Dec 16, 2024SaveLearn
Quantum Mechanics of Arc-Sine and Semi-Circle Distributions: A Unified ApproachThis paper continues the program of applying beyond physics the technique of probabilistic quantization and extending to the quantum mechanics associated with the arc--sine distributions our…Luigi Accardi, Tarek Hamdi, Yun Gang Lu·Dec 15, 2024SaveLearn
Polynomial potentials and nilpotent groupsThis paper deals with the partial solution of the energy-eigenvalue problem for one-dimensional Schr\"odinger operators of the form HN=X02+VN, where VN=XN2+α XN-1 is a polynomial…W. Schweiger, W. H. Klink·Dec 15, 2024SaveLearn
Pairs of Subspaces, Split Quaternions and the Modular OperatorWe revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions…Jan Naudts, Jun Zhang·Dec 15, 2024SaveLearn
Diffusion Limit of the Low-Density Magnetic Lorentz GasWe consider the magnetic Lorentz gas proposed by Bobylev et al. [4], which describes a point particle moving in a random distribution of hard-disk obstacles in R2 under the influence of a…Alessia Nota, Dominik Nowak, Chiara Saffirio·Dec 15, 2024SaveLearn
Sachs equations and plane waves III: MicrocosmsThis article examines the structure of plane wave spacetimes (of signature (1,n+1), n 2) that are homogeneous (the isometry group is transitive) and geodesically complete -- which we call…Jonathan Holland, George Sparling·Dec 14, 2024SaveLearn
The Wehrl-type entropy conjecture for symmetric SU(N) coherent states: cases of equality and stabilityLieb and Solovej proved that, for the symmetric SU(N) representations, the corresponding Wehrl-type entropy is minimized by symmetric coherent states. However, the uniqueness of the minimizers…Fabio Nicola, Federico Riccardi, Paolo Tilli·Dec 14, 2024SaveLearn
q-Series Invariants of Three-Manifolds and Knots-Quivers CorrespondenceThe Gukov-Pei-Putrov-Vafa (GPPV) conjecture is a relationship between two three-manifold invariants: the Witten-Reshetikhin-Turaev (WRT) invariant and the \(Z\) (``Z-hat'') invariant. In…Sachin Chauhan·Dec 14, 2024SaveLearn
Hankel determinant and orthogonal polynomials arising from the matrix model in 2D quantum gravityWe study the Hankel determinant and orthogonal polynomials with respect to the two-parameter weight function w(x)=w(x;t1, t2):=(-x6-t2 x4-t1 x2), x∈R, with $t1,\;…Chao Min, Yadan Ding·Dec 14, 2024SaveLearn
Quantum Indeterminacy and Polar Duality: a Probabilistic ApproachWe present a probabilistic argument supporting the application of polar duality, as discussed in our previous work, to express the indeterminacy principle of quantum mechanics. Our approach combines…Maurice de Gosson·Dec 13, 2024SaveLearn
Spectral analysis of metamaterials in curved manifoldsNegative-index metamaterials possess a negative refractive index and thus present an interesting substance for designing uncommon optical effects such as invisibility cloaking. This paper deals with…Tomáš Faikl·Dec 13, 2024SaveLearn