Mathematical theory on multi-layer high contrast acoustic subwavelength resonatorsSubwavelength resonance is a vital acoustic phenomenon in contrasting media. The narrow bandgap width of single-layer resonator has prompted the exploration of multi-layer metamaterials as an…Youjun Deng, Lingzheng Kong, Hongjie Li et al.·Nov 13, 2024SaveLearn
A study on the Belinski-Khalatnikov-Lifshitz scenario through quadrics of kinetic energyA detailed description of the asymptotic behaviour in the Belinski-Khalatnikov-Lifshitz (BKL) scenario is presented through a simple geometric picture illustrating the geometry of their ordinary…Piotr P. Goldstein·Nov 12, 2024SaveLearn
Superintegrability and Coulomb-Oscillator DualityThis review is devoted to the problem of Coulomb (dyon)-oscillator duality in non-relativistic quantum mechanics, which is based on the so-called non-bijective quadratic transformations, i.e.…Levon G. Mardoyan·Nov 12, 2024SaveLearn
A Theoretical Review of Area Production Rates as Test Statistics for Detecting Nonequilibrium Dynamics in Ornstein-Uhlenbeck ProcessesA stochastic process is at thermodynamic equilibrium if it obeys time-reversal symmetry; forward and reverse time are statistically indistinguishable at steady state. Non-equilibrium processes break…Alexander Strang·Nov 12, 2024SaveLearn
Dualities for characteristic polynomial averages of complex symmetric and self dual non-Hermitian random matricesEnsembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand,…Peter J. Forrester·Nov 11, 2024SaveLearn
Conservation Law and Trace Anomaly for the Stress Energy Tensor of a Self-Interacting Scalar FieldWe consider a self-interacting, massive, real scalar field on a four-dimensional globally hyperbolic spacetime and the associated stress-energy tensor. Using techniques proper of the algebraic…Beatrice Costeri, Claudio Dappiaggi, Michele Goi·Nov 11, 2024SaveLearn
Generalized Airy polynomials, Hankel determinants and asymptoticsWe further study the orthogonal polynomials with respect to the generalized Airy weight based on the work of Clarkson and Jordaan [ J. Phys. A: Math. Theor. 54 (2021) 185202]. We prove…Chao Min, Pixin Fang·Nov 11, 2024SaveLearn
Derivation of the Maxwell-Schr\"odinger and Vlasov-Maxwell Equations from Non-Relativistic QEDWe study the spinless Pauli-Fierz Hamiltonian in a semiclassical mean-field limit of many fermions. For appropriate initial conditions, we prove, in the trace norm topology of reduced density…Nikolai Leopold·Nov 11, 2024SaveLearn
The Ground State Energy of Heavy Atoms: Leading and Subleading AsymptoticsWe study atomic ground state energies for neutral atoms as the nuclear charge Z is large in the no-pair formalism. We show that for a large class of projections defining the underlying Dirac sea --…Long Meng, Heinz Siedentop·Nov 11, 2024SaveLearn
Near linearity of the macroscopic Hall current response in infinitely extended gapped fermion systemsWe consider an infinitely extended system of fermions on a d-dimensional lattice with (magnetic) translation-invariant short-range interactions. We further assume that the system has a locally…Marius Wesle, Giovanna Marcelli, Tadahiro Miyao et al.·Nov 11, 2024SaveLearn
Families of Kuramoto models and bounded symmetric domainsWe define the families of Kuramoto models (KM) related to bounded symmetric domains. The families include the Lohe unitary model and the spherical models as special cases. Our approach is based on…M. Olshanetsky·Nov 11, 2024SaveLearn
Generalized Eigenspaces and Pseudospectra of Nonnormal and Defective Matrix-Valued Dynamical SystemsWe consider nonnormal matrix-valued dynamical systems with discrete time. For an eigenvalue of matrix, the number of times it appears as a root of the characteristic polynomial is called the…Saori Morimoto, Makoto Katori, Tomoyuki Shirai·Nov 10, 2024SaveLearn
Causal Fermion Systems: An Introduction to Fundamental Structures, Methods and ApplicationsThis textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general…Felix Finster, Sebastian Kindermann, Jan-Hendrik Treude·Nov 10, 2024SaveLearn
Duality, asymptotic charges and higher form symmetries in p-form gauge theoriesThe surface charges associated with p-form gauge fields in the Bondi patch of D-dimensional Minkowski spacetime are computed. We show that, under the Hodge duality between the field strengths of…Federico Manzoni·Nov 8, 2024SaveLearn
On Unitary 2-Group SymmetriesGlobal internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions…Thomas Bartsch·Nov 7, 2024SaveLearn
Existence and Uniqueness of Solutions to the Generalized Hydrodynamics EquationThe generalized hydrodynamics (GHD) equation is the equivalent of the Euler equations of hydrodynamics for integrable models. Systems of hyperbolic equations such as the Euler equations usually…Friedrich Hübner, Benjamin Doyon·Nov 7, 2024SaveLearn
Many-body physics and resolvent algebrasSome advantages of the algebraic approach to many body physics, based on resolvent algebras, are illustrated by the simple example of non-interacting bosons which are confined in compact regions with…Detlev Buchholz, Jakob Yngvason·Nov 7, 2024SaveLearn
Introducing Multidimensional Dirac-Hestenes EquationIt is easier to investigate phenomena in particle physics geometrically by exploring a real solution to the Dirac-Hestenes equation instead of a complex solution to the Dirac equation. The current…S. V. Rumyantseva, D. S. Shirokov·Nov 6, 2024SaveLearn
On the Kostant-Souriau prequantization of scalar fields with polysymplectic structuresIn this paper, I present a novel, purely differential geometric approach to the quantization of scalar fields, with a special focus on the familiar case of Minkowski spacetimes. This approach is…Tom McClain·Nov 6, 2024SaveLearn
The Lorentz Gas in a Mean-Field Potential: Weak Coupling and Diffusive RegimeWe investigate the diffusive scaling of the Lorentz gas in the presence of an external force of mean-field type. In the weak coupling regime and for diffusive time scales, the test particle's law…Dominik Nowak·Nov 6, 2024SaveLearn
Nondeterministic particle systemsWe consider systems of n particles that move with constant velocity between collisions. Their total momentum but not necessarily their kinetic energy is preserved at collisions. As there are no…Andreas Knauf, Manuel Quaschner·Nov 6, 2024SaveLearn
Energy transport in a free Euler-Bernoulli beam in terms of Schr\"odinger's wave functionThe Schr\"odinger equation is not frequently used in the framework of the classical mechanics, though historically this equation was derived as a simplified equation, which is equivalent to the…Serge N. Gavrilov, Anton M. Krivtsov, Ekaterina V. Shishkina·Nov 6, 2024SaveLearn
Large Scale Response of Gapless 1d and Quasi-1d SystemsWe consider the transport properties of non-interacting, gapless one-dimensional quantum systems and of the edge modes of two-dimensional topological insulators, in the presence of time-dependent…Marcello Porta, Harman Preet Singh·Nov 6, 2024SaveLearn
Generalized exchange operators for a system of spin-1 particlesThe irreps (SU(2), H,U) of SU(2) of dimension (2S+1)N, i.e. operators acting on the space H= HN= C(2S+1)N of N identical particles with spin S, are described…Charlie Jeudy, Michel Rouleux·Nov 6, 2024SaveLearn
Fool's crowns, trumpets, and SchwarzianFor a Riemann surface with holes, we propose a variant of the action on a circum\-ference-P boundary component with n bordered cusps attached (a "fool's crown") that is decoration-invariant and…Leonid O. Chekhov·Nov 6, 2024SaveLearn