Classical relativistic nonholonomic mechanics and time-dependent G-Chaplygin systems with affine constraintsWe study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent G-Chaplygin systems…Bozidar Jovanovic·Jul 7, 2024SaveLearn
Kac-Ward solution of the 2D classical and 1D quantum Ising modelsWe give a rigorous derivation of the free energy of (i) the classical Ising model on the triangular lattice with translation-invariant coupling constants, and (ii) the one-dimensional quantum Ising…Georgios Athanasopoulos, Daniel Ueltschi·Jul 7, 2024SaveLearn
"Pentagonal Algebra" and Four-Simplex EquationSome idea, which leads to a non-trivial solution of the quantum four-simplex equation, is exposed in this paper. We call this idea "pentagonal algebra". Few examples of the realisation of this idea…Sergey Sergeev·Jul 7, 2024SaveLearn
The Fermionic Entanglement Entropy of Causal Diamonds in Two-Dimensional Minkowski SpaceThe fermionic Rényi entanglement entropy is studied for causal diamonds in two-dimensional Minkowski spacetime. Choosing the quasi-free state describing the Minkowski vacuum with an ultraviolet…Felix Finster, Magdalena Lottner, Albert Much et al.·Jul 7, 2024SaveLearn
Surface waves in randomly perturbed discrete modelsWe study the propagation of surface waves across structured surfaces with random, localized inhomogeneities. A discrete analogue of Gurtin-Murdoch model is employed and surface elasticity, in…Josselin Garnier, Basant Lal Sharma·Jul 6, 2024SaveLearn
On non-uniqueness of phase retrieval in multidimensionsWe give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are…Roman Novikov, Tianli Xu·Jul 6, 2024SaveLearn
Coupled Stochastic-Statistical Equations for Filtering Multiscale Turbulent SystemsWe present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed…Di Qi, Jian-Guo Liu·Jul 5, 2024SaveLearn
Global Spectral Gap in Bosonic Molecular HamiltoniansWe consider a neutral bosonic molecule in the Born-Oppenheimer approximation without spin and assume the physically obvious assertion that a neutral molecule prefers to break into smaller neutral…Sebastian Gherghe·Jul 5, 2024SaveLearn
A spring pair method of finding saddle points using the minimum energy path as a compassFinding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle…Gang Cui, Kai Jiang·Jul 5, 2024SaveLearn
Chernoff's product formula: Semigroup approximations with non-uniform time intervalsOften, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's…J. Z. Bernád, A. B. Frigyik·Jul 5, 2024SaveLearn
Representation Structure of the SL(2, C) Acting in the Hilbert Space of the Quantum Coulomb FieldWe give a complete description of the representation of SL(2,C) acting in the Hilbert space of the quantum Coulomb field and a constructive consistency proof of the axioms of the quantum…J. Wawrzycki, T. Wawrzycki·Jul 5, 2024SaveLearn
Conformally covariant probabilities, operator product expansions, and logarithmic correlations in two-dimensional critical percolationThe large-scale behavior of two-dimensional critical percolation is expected to be described by a conformal field theory (CFT). Moreover, this putative CFT is believed to be of the logarithmic type,…Federico Camia, Yu Feng·Jul 5, 2024SaveLearn
Convergence Rates for the Trotter Splitting for Unbounded OperatorsWe study convergence rates of the Trotter splitting eA+L = n ∞ (eL/n eA/n)n in the strong operator topology. In the first part, we use complex interpolation theory to…Simon Becker, Niklas Galke, Robert Salzmann et al.·Jul 4, 2024SaveLearn
Cohomological field theories and generalized Seiberg-Witten equationsWe introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the formalism to the…Shuhan Jiang, Jürgen Jost·Jul 4, 2024SaveLearn
Stochastic Processes: From Classical to QuantumThe main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from…Soon Hoe Lim·Jul 4, 2024SaveLearn
A Hamiltonian formalism for general variational problems, with applications to first order gravity with basisThe present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational…Guadalupe Quijón, Santiago Capriotti·Jul 4, 2024SaveLearn
Regularity of the (N-1)-particle electronic reduced density matrix for molecules with fixed nuclei and N electronsWe consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions, fixed nuclei, and N electrons (N>1). Near appropriate electronic collisions, we…Thierry Jecko, Camille Noûs·Jul 4, 2024SaveLearn
Holomorphic Functional Calculus approach to the Characteristic Function of Quantum ObservablesWe show how Cauchy's Integral Formula and the ideas of Dunford's Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier…Andreas Boukas·Jul 4, 2024SaveLearn
Helicity is a topological invariant of massless particles: C=-2hThere is an elementary but indispensable relationship between the topology and geometry of massive particles. The geometric spin s is related to the topological dimension of the internal space V…Eric Palmerduca, Hong Qin·Jul 3, 2024SaveLearn
Optimal synchronisation to a limit cycleIn the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic, trajectory -- the limit cycle -- after infinite time. Here, we drive…C. Ríos-Monje, C. A. Plata, D. Guéry-Odelin et al.·Jul 3, 2024SaveLearn
Feynman checkers: through the looking-glassFeynman gave a famous elementary introduction to quantum theory by discussing the thin-film reflection of light. We make his discussion mathematically rigorous, keeping it elementary, using his other…Fedor Ozhegov, Mikhail Skopenkov, Alexey Ustinov·Jul 3, 2024SaveLearn
Quantum states as countable convex combination of pure states with bounded energyWe give response to the question: in infinite dimension states,given a state with energy bounded by E, we can write the state as a countable convex combination of pure states with energy bounded by…Juan Pablo Lopez·Jul 2, 2024SaveLearn
The Symplectic Schur ProcessWe define a measure on tuples of partitions, called the symplectic Schur process, that should be regarded as the right analogue of the Schur process of Okounkov-Reshetikhin for the Cartan type C. The…Cesar Cuenca, Matteo Mucciconi·Jul 2, 2024SaveLearn
Quantum KdV hierarchy and shifted symmetric functionsWe study spectral properties of the quantum Korteweg-de Vries hierarchy defined by Buryak and Rossi. We prove that eigenvalues to first order in the dispersion parameter are given by shifted…Jan-Willem van Ittersum, Giulio Ruzza·Jul 2, 2024SaveLearn
A mathematical definition of complex adaptive system as interaction spaceWe define a mathematical notion of complex adaptive system by following the original intuition of G.K. Zipf about the principle of least effort, an intuitive idea which is nowadays informally…Paolo Giordano·Jul 2, 2024SaveLearn