A Convenient Representation Theory of Lorentzian Pseudo-Tensors: P and T in O(1,3)A novel approach to the finite dimensional representation theory of the entire Lorentz group O(1,3) is presented. It is shown how the entire Lorentz group may be understood as a…Craig McRae·Jan 9, 2025SaveLearn
Mean-Field Dynamics of the Bose-Hubbard Model in High DimensionThe Bose-Hubbard model effectively describes bosons on a lattice with on-site interactions and nearest-neighbour hopping, serving as a foundational framework for understanding strong particle…Shahnaz Farhat, Denis Périce, Sören Petrat·Jan 9, 2025SaveLearn
Duality, asymptotic charges and algebraic topology in mixed symmetry tensor gauge theories and applicationsRecently the duality map between electric-like asymptotic charges of p-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality…Federico Manzoni·Jan 9, 2025SaveLearn
Properties of the one-component Coulomb gas on a sphere with two macroscopic external chargesThe one-component Coulomb gas on the sphere, consisting on N unit charges interacting via a logarithmic potential, and in the presence of two external charges each of strength proportional to N,…Sung-Soo Byun, Peter J. Forrester, Sampad Lahiry·Jan 9, 2025SaveLearn
Quantum Birkhoff Normal Form in the σ-Bruno-R\"ussmann non-resonant conditionThe aim of this paper is to construct a Gevrey quantum Birkhoff normal form for the h-differential operator Ph(t), where t∈(-12,12), in the neighborhood of the union…Huanhuan Yuan, Yixian Gao, Yong Li·Jan 9, 2025SaveLearn
Dynamical space-time ray tracing and modified horizontal ray methodThe 'vertical modes and horizontal rays' method, commonly applied for simulating acoustic wave propagation in shallow water is advanced in this research. Our approach to this method involves the use…Aleksandr Kaplun, Boris Katsnelson·Jan 7, 2025SaveLearn
A New Proof of the Sharp Gordon's Lemma: No Eigenvalues for Schr\"odinger Operators with Almost Repetition PotentialsBuilding on the work of Jitomirskaya-Simon and Jitomirskaya-Liu, who established the absence of eigenvalues for Schr\"odinger operators with almost reflective repetition potentials, we provide a new…Wencai Liu·Jan 6, 2025SaveLearn
Reconsidering Velocity Addition/Subtraction in Special RelativityWe reconsider velocity addition/subtraction in Special Relativity and re-derive its well-known non-commutative and non-associative algebraic properties in a self contained way, including various…Domenico Giulini·Jan 6, 2025SaveLearn
Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death ProcessesWe present the case-(1) multi-indexed orthogonal polynomials of a discrete variable for 8 types ((dual)(q-)Hahn, three kinds of q-Krawtchouk and q-Meixner). Based on them and the case-(1)…Satoru Odake·Jan 6, 2025SaveLearn
Mixed state topological order: operator algebraic approachWe study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided C*-tensor…Yoshiko Ogata·Jan 4, 2025SaveLearn
Embedding integrable spin models in solvable vertex models on the square latticeExploring a mapping among n-state spin and vertex models on the square lattice we argue that a given integrable spin model with edge weights satisfying the rapidity difference property can be…M. J. Martins·Jan 4, 2025SaveLearn
Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4)We consider the double-dimer model in the upper-half plane discretized by the square lattice with mesh size δ. For each point x in the upper half-plane, we consider the random variable…Mikhail Basok, Konstantin Izyurov·Jan 2, 2025SaveLearn
Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general q-Painlev\'e III3 tau functionsWe reformulate the q-difference linear system corresponding to the q-Painlev\'e equation of type A7(1)' as a Riemann-Hilbert problem on a circle. Then, we consider the Fredholm determinant…Pavlo Gavrylenko·Jan 2, 2025SaveLearn
Commutator Estimates and Quantitative Local Weyl's Law for Schr\"odinger Operators with Non-Smooth PotentialsWe analyze semi-classical Schr\"odinger operators with potentials of class C1,1/2 and establish commutator estimates for the associated projection operators in Schatten norms. These are then…Esteban Cárdenas, Laurent Lafleche·Jan 2, 2025SaveLearn
Adiabatic Solutions of the Haydys-Witten Equations and Symplectic Khovanov HomologyAn influential conjecture by Witten states that there is an instanton Floer homology of four-manifolds with corners that in certain situations is isomorphic to Khovanov homology of a given knot K.…Michael Bleher·Jan 2, 2025SaveLearn
Nearsightedness in Materials with Indirect Band GapsWe investigate the nearsightedness property in the linear tight binding model at zero Fermi-temperature. We focus on the decay property of the density matrix for materials with indirect band gaps. By…Huajie Chen, Juerong Feng, Christoph Ortner et al.·Jan 2, 2025SaveLearn
Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domainsInspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to infinity…Bernard Helffer, Ayman Kachmar, Francois Nicoleau·Jan 1, 2025SaveLearn
Lieb--Thirring inequalities for large quantum systems with inverse nearest-neighbor interactionsWe prove an analogue of the Lieb--Thirring inequality for many-body quantum systems with the kinetic operator Σi (-i)s and the interaction potential of the form Σi δi-2s…G. K. Duong, Phan Thành Nam·Jan 1, 2025SaveLearn
Trading linearity for ellipticity: a nonsmooth approach to Einstein's theory of gravity and the Lorentzian splitting theoremsWhile Einstein's theory of gravity is formulated in a smooth setting, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must…Robert J. McCann·Jan 1, 2025SaveLearn
Comment on: "Comment on "Nonperturbative calculation of Born-Infeld effects on the Schr\"odinger spectrum of the hydrogen atom"" by M. N. SmolyakovThis reply to Dr. Smolyakov's comment [2] on our PRL paper [1] was solicited by PRL on Nov. 17, 2021 and submitted to PRL on Nov. 30, 2021. Regretfully, the editors of PRL decided not to publish Dr.…H. K. Carley, M. K. -H. Kiessling·Dec 31, 2024SaveLearn
Generalized finite and affine W-algebras in type AWe construct a new family of affine W-algebras Wk(λ,μ) parameterized by partitions λ and μ associated with the centralizers of nilpotent elements in glN. The…Dong Jun Choi, Alexander Molev, Uhi Rinn Suh·Dec 31, 2024SaveLearn
On the eigenvectors of the 5D discrete Fourier transform number operator in Newtonian basisA simple analytic approach to the evaluation of the eigenvalues and eigenvectors fn of the 5D discrete number operator N5 is formulated. This approach is essentially based on the symmetry of the…Natig Atakishiyev·Dec 30, 2024SaveLearn
Lattice random walks and quantum A-period conjectureWe derive explicit closed-form expressions for the generating function CN(A), which enumerates classical closed random walks on square and triangular lattices with N steps and a signed area A,…Li Gan·Dec 30, 2024SaveLearn
Quantum tunneling and its absence in deep wells and strong magnetic fieldsWe present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for…Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein·Dec 30, 2024SaveLearn
Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equationsThe quasi-classical expansion of a multicomponent spin solution of the star-star relation with hyperbolic Boltzmann weights is investigated. The equations obtained in a quasi-classical limit provide…Andrew P. Kels·Dec 30, 2024SaveLearn