303 papers
This paper establishes the area law for the entanglement entropy of free fermions in non-random ergodic fields by proving uniform eigenfunction localization and exponential decay of correlators for quasiperiodic, limit-periodic, and subshift-generated potentials, thereby extending previous results that were limited to random systems.
This paper investigates the thermodynamic limit of Bogoliubov's theory for a weakly interacting dilute Bose gas in infinite volume by utilizing heat kernel formulations and trace estimates to establish that while the limiting behavior cannot be strictly controlled by the area term, it can be approximated arbitrarily closely.
This paper utilizes Arnold's geometric approach and matrix theory to prove the Lyapunov stability and establish a rigidity condition for steady states in Zeitlin's discretized 2-D Euler model, thereby validating its reliability for studying stationary solutions and highlighting connections between matrix theory and nonlinear PDE techniques.
This paper establishes the local-in-time existence of strong solutions to the gravity water wave kinetic equation by rigorously deriving a sharper bound for the collision kernel's growth in the highly non-local regime and utilizing this improved estimate to overcome the associated singular integral challenges.
This paper establishes a conformal lower bound for weighted Dirac eigenvalues on compact spin manifolds with chiral boundary conditions in terms of the relative Yamabe constant, proving that equality is achieved if and only if the manifold is conformally equivalent to a hemisphere supporting a Killing spinor.
This paper extends semi-classical instanton analysis to a symmetric quartic potential with four degenerate minima, deriving energy splittings and Rabi oscillations for distinct tunneling pathways that show excellent agreement with numerical results while revealing a critical coupling regime where the discrete symmetry melts into a continuous symmetry.
This paper establishes Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies by employing a novel dynamical rigidity argument.
The paper refutes the claim that Hilbert spaces are unphysical due to unbounded operators, arguing instead that infinite expectation values are not problematic and that replacing Hilbert spaces with Schwartz spaces would introduce greater theoretical issues by excluding meaningful Hamiltonian evolutions.
This paper presents a novel QR decomposition-based compression scheme combined with a tailored preconditioner and volume integral equations to enable fast and accurate iterative solutions for electromagnetic scattering from large-scale metasurfaces composed of thousands of sub-wavelength scatterers.
This paper refutes the "all-or-nothing" expectation for local commuting charges in non-Hermitian bosonic chains by constructing explicit counterexamples with selective k-local charges, thereby demonstrating the limited universality of the Grabowski–Mathieu integrability test and providing a complete classification of such models.
This paper demonstrates that quantum cellular automata constitute the degree-zero component of a coarse homology theory, thereby providing a formal framework that explains why the space of such automata forms an Omega-spectrum.
This paper analytically derives and proves a tight quantum speed limit for the charging of an -qubit Dicke quantum battery, establishing that the minimum time to reach a normalized ergotropy is bounded by , where the bound is saturated at small ergotropy values and governed by a unique composite figure of merit.
This paper introduces a symmetry-resolved framework that decomposes high-dimensional Liouvillian dynamics into low-dimensional invariant sectors to systematically identify and characterize exceptional points in realistic open quantum systems, accompanied by a numerical diagnostic metric for quantifying their proximity.
This paper establishes a framework of Courant algebroid relations to connect Dirac structures, spinors, and generalised complex/Kähler geometries, demonstrating how these relations induce T-duality in supersymmetric sigma-models and remain compatible with Type II supergravity equations.
This study presents the first explicit reconstruction of a Loewner driving function from the expanding boundaries of a growing slime mold, demonstrating that its growth front exhibits emergent Brownian-like conformal dynamics and establishing a quantitative framework linking morphogenesis to stochastic geometry.
This paper establishes that for the three-dimensional degenerate compressible Navier-Stokes equations with nonlinear viscosity coefficients depending on density, smooth solutions can develop finite-time implosions at the origin provided the viscosity power-law exponent falls below a specific threshold determined by the adiabatic exponent, a result proven through novel pointwise density estimates and weighted high-order energy methods that demonstrate the viscous terms are insufficient to suppress the convective implosion mechanism.
This paper provides a complete local description of the moduli space of dynamical spherically symmetric black hole spacetimes near the Reissner-Nordström family, characterizing the black hole threshold as the extremal leaf of a foliation and establishing universal scaling laws with a critical exponent of $1/2$ alongside the activation of Aretakis instability for threshold solutions.
This paper derives the Hamiltonian formulation for axisymmetric magnetohydrodynamics on the three-sphere and extends Zeitlin's matrix model to three dimensions, creating the first discrete 3D MHD model that preserves the underlying Lie–Poisson geometric structure.
This paper extends the framework of invariant reduction for partial differential equations to handle geometric structures that are rescaled rather than strictly invariant by symmetries, establishing a shift rule that explains the emergence or loss of invariance in reduced systems and enabling the geometric construction of exact solutions without relying on integrability structures like Lax pairs.
This paper establishes the equivalence between path integral and stochastic quantizations for generic scalar Euclidean quantum field theories by providing two novel proofs based on Taylor interpolations indexed by forests: one operating at the level of individual Feynman expansion terms and the other directly at the path integral level without requiring a full perturbative expansion.