Symmetry Preservation in Hamiltonian Systems: Simulation and LearningThis work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of…Miguel Vaquero, Jorge Cortés, David Martín de Diego·Aug 30, 2023SaveLearn
Spectral statistics of interpolating random circulant matrix and its applications to random circulant graphsWe consider a versatile matrix model of the form A+i B, where A and B are real random circulant matrices with independent but, in general, nonidentically distributed…Sunidhi Sen, Himanshu Shekhar, Santosh Kumar·Aug 30, 2023SaveLearn
Derivation of the Vlasov-Maxwell system from the Maxwell-Schr\"odinger equations with extended chargesWe consider the Maxwell-Schr\"odinger equations in the Coulomb gauge describing the interaction of extended fermions with their self-generated electromagnetic field. They heuristically emerge as…Nikolai Leopold, Chiara Saffirio·Aug 30, 2023SaveLearn
Differential Equations for Approximate Solutions of Painlev\'e Equations: Application to the Algebraic Solutions of the Painlev\'e-III ( D7) EquationIt is well known that the Painlev\'e equations can formally degenerate to autonomous differential equations with elliptic function solutions in suitable scaling limits. A way to make this…Robert J. Buckingham, Peter D. Miller·Aug 30, 2023SaveLearn
Uncertainty relation for non-Hermitian operatorsIn this paper we discuss some aspects of the Heisenberg uncertainty relation, mostly from the point of view of non self-adjoint operators. Some equivalence results, and some refinements of the…Fabio Bagarello·Aug 30, 2023SaveLearn
Form factor of local operators in the generalized algebraic Bethe ansatzWe consider an XYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to the singlet states in the limit of free…G. Kulkarni, N. A. Slavnov·Aug 30, 2023SaveLearn
On the properties of the density matrix of the sln+1-invariant modelWe present an ansatz of generalizing the construction of recursion relations for the correlation functions of the sl2-invariant fundamental exchange model in the thermodynamic limit by…Henrik Juergens, Hermann Boos·Aug 29, 2023SaveLearn
Stress tensor bounds on quantum fieldsThe singular behaviour of quantum fields in Minkowski space can often be bounded by polynomials of the Hamiltonian H. These so-called H-bounds and related techniques allow us to handle pointwise…Ko Sanders·Aug 29, 2023SaveLearn
Relations between generalised Wishart matrices, the Muttalib--Borodin model and matrix spherical functionsGeneralised uncorrelated Wishart matrices are formed out of rectangular standard Gaussian data matrices with a certain pattern of zero entries. Development of the theory in the real and complex cases…Peter J. Forrester·Aug 29, 2023SaveLearn
A Brillouin torus decomposition for two-dimensional topological insulatorsTwo-band Chern insulators are topologically classified by the Chern number, c, which is given by the integral of the Berry curvature of the occupied band over the Brillouin torus. The curvature…F. Kordon, J. Fernández, P. Roura-Bas·Aug 28, 2023SaveLearn
Compact-form solution to the time-dependent Schr\"odinger equation with an arbitrary potentialWe obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as…Ivan Gonoskov·Aug 27, 2023SaveLearn
Trace formulas revisited and a new representation of KdV solutions with short-range initial dataWe put forward a new approach to Deift-Trubowitz type trace formulas for the 1D Schrodinger operator with potentials that are summable with the first moment (short-range potentials). We prove that…Alexei Rybkin·Aug 25, 2023SaveLearn
Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic setsIn discrete schemes, weak KAM solutions may be interpreted as approximations of correctors for some Hamilton-Jacobi equations in the periodic setting. It is known that correctors may not exist in the…Eduardo Garibaldi, Samuel Petite, Philippe Thieullen·Aug 24, 2023SaveLearn
A limit of nonplanar 5-body central configurations is nonplanarMoeckel (1990), Moeckel and Sim\'o (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that…Alain Albouy, Antonio Carlos Fernandes·Aug 24, 2023SaveLearn
The regularization of Dotsenko--Fateev integralsWe discuss the regularization of certain hypergeometric integrals appearing in 2D CFT, a step needed in the construction of the BPZ minimal models via the Coulomb gas formalism. The method is a…Ethan Sussman·Aug 24, 2023SaveLearn
Polynomial algebras from commutants: Classical and Quantum aspects of A3We review some aspects of the Racah algebra R(n), including the closure relations, pointing out their role in superintegrability, as well as in the description of the symmetry algebra for several…Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette et al.·Aug 24, 2023SaveLearn
The secular equation for elastic surface waves under non standard boundary conditions of impedance type: A perspective from linear algebraThe study of elastic surface waves under impedance boundary conditions has become an intensive field of research due to their potential to model a wide range of problems. However, even when the…Fabio Vallejo·Aug 23, 2023SaveLearn
Solving first order differential equations presenting elementary functionsWe have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have established solid…L. G. S. Duarte, L. A. C. P. da Mota, A. B. M. M. Queiroz·Aug 23, 2023SaveLearn
Solving the matrix exponential function for special orthogonal groups SO(n) and the exceptional G2In this work the matrix exponential function is solved analytically for the special orthogonal groups SO(n) up to n=9. The number of occurring k-th matrix powers gets limited to $0≤ k ≤…Norbert Kaiser·Aug 23, 2023SaveLearn
Nijenhuis operators on 2D pre-Lie algebras and 3D associative algebrasIn this paper, we describe all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras. As an application, using these operators, we obtain…Xiaoguang Zou, Xiang Gao, Chuangchuang Kang et al.·Aug 23, 2023SaveLearn
Exact linear representations of the nonlinear Cauchy problems and their smooth solutionsThe paper establishes conditions under which there are exact linear representations of nonlinear partial differential equations (Cauchy problems). By introducing a certain linear operator A, it is…Yu. N. Kosovtsov·Aug 23, 2023SaveLearn
The ghost algebra and the dilute ghost algebraWe introduce the ghost algebra, a two-boundary generalisation of the Temperley-Lieb (TL) algebra, using a diagrammatic presentation. The existing two-boundary TL algebra has a basis of string…Madeline Nurcombe·Aug 23, 2023SaveLearn
Validit\'e de la th\'eorie cin\'etique des gaz: au-del\`a de l'\'equation de Boltzmann [d'apr\`es T. Bodineau, I. Gallagher, L. Saint-Raymond, S. Simonella]Obtaining a rigorous justification of the kinetic theory of gases from Newton's second law of dynamics for a large number of identical spheres interacting by elastic binary collisions, is a problem…François Golse·Aug 23, 2023SaveLearn
Probability of a single currentThe Riemann surface associated with counting the current between two states of an underlying Markov process is hyperelliptic. We explore the consequences of this property for the time-dependent…Sylvain Prolhac·Aug 22, 2023SaveLearn
From the chiral model of TBG to the Bistritzer--MacDonald modelWe analyse the splitting of exact flat bands in the chiral model of the twisted bilayer graphene (TBG) when the AA'/BB' coupling of the full Bistritzer--MacDonald model is taken into account. The…Simon Becker, Maciej Zworski·Aug 22, 2023SaveLearn