318 papers
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 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 rigorously establishes the gap property for linearized operators associated with the cubic nonlinear Schrödinger equation in three dimensions by proving, via a new comparison-based approach, that the interval contains no eigenvalues and that no resonances exist at the bottom of the essential spectrum, even in the fully non-radial case.
This paper demonstrates that twisted sectors in the vanishing cohomology of one-parameter deformations of Calabi-Yau type Fermat polynomial singularities, along with the genus zero Gromov-Witten generating series of the corresponding varieties, are components of automorphic forms for certain triangular groups, utilizing mixed Hodge structures, the Riemann-Hilbert correspondence, and genus zero mirror symmetry.
This paper investigates fluctuations in Coulomb gases under specific external potentials, proving that particle counts near spectral outposts follow an asymptotic Heine distribution while those near disconnected droplet components exhibit discrete normal fluctuations, ultimately characterizing general linear statistics as a sum of Gaussian and oscillatory discrete Gaussian fields.
This paper establishes a bridge between homotopy type theory and information theory by defining probability types, demonstrating that homotopy cardinality respects dependent sums but not products, and deriving Shannon entropy and its chain rule as the homotopy cardinality of specific types constructed via deloopings of finite cyclic groups.
The paper proposes the Branched Hilbert Subspace Interpretation (BHSI), a minimalist framework that explains quantum measurement as a unitary branching of the local Hilbert space into decoherent subspaces, thereby avoiding both wave function collapse and parallel worlds while preserving the Born rule and offering testable predictions for phenomena like the double-slit experiment and quantum teleportation.
This paper investigates the asymptotic symmetry structure of Jackiw-Teitelboim supergravity within a BF framework, demonstrating how the dilaton supermultiplet dynamically reduces the affine symmetry to a specific subalgebra with an abelian ideal, thereby providing a consistent bulk-based framework for studying boundary dynamics beyond the Schwarzian regime.
This paper establishes a non-unitary version of the Bisognano-Wichmann property and proves Haag duality for nets of smeared Wightman fields by deriving Tomita-Takesaki-like results directly from Wightman axioms, thereby extending these fundamental algebraic quantum field theory concepts to non-unitary theories where traditional Hilbert space functional analysis tools are unavailable.
This paper provides an explicit description of the phase space stratification for Calogero-Moser-Sutherland systems associated with , demonstrating that each positive-dimensional symplectic stratum is symplectomorphic to and admits natural action-angle coordinates.
This paper proves that the discrete Dirichlet-to-Neumann operator uniquely determines edge conductivities on multi-dimensional hypercubic lattices (dimension three or higher) by employing a novel slicing technique, thereby extending the classical two-dimensional uniqueness result of Curtis and Morrow.
This paper defines a compactification of the parameter space for the quantum multiplication of hypertoric varieties, following deConcini and Gaiffi, and demonstrates how to extend this multiplication to the compactified space.
This paper introduces an intrinsic deformation of smooth function algebras on compact Riemannian manifolds via spectral channel twisting, establishes conditions for its extension to Sobolev algebras and associativity, and demonstrates that classical strict deformations arising from abelian group actions are unified as specific instances of this framework.
This paper extends the probabilistic construction of Kähler-Einstein metrics to Fano manifolds with non-discrete automorphism groups by introducing Gibbs polystability and symmetry-breaking via moment map constraints, conjecturing its equivalence to metric existence and the emergence of unique metrics in the large-N limit, while proving these results for log Fano curves and deriving a strengthened logarithmic Hardy-Littlewood-Sobolev inequality with optimal stability constants.
This paper proves that for finite-dimensional quantum systems undergoing single-branch collapse dynamics without information erasure, operational irreversibility is structurally impossible because every physically admissible collapse selector contains a forward-invariant subset of states that can be connected with arbitrarily high precision and negligible energy cost, thereby establishing islands of quasi-reversibility.
This paper establishes an up-to-constant estimate for the critical two-point function restricted to a half-space in high-dimensional Bernoulli percolation (), thereby completing prior work by Chatterjee, Hanson, and Sosoe and resolving a specific question posed by Hutchcroft, Michta, and Slade.
This paper establishes three distinct representations for the flat space wavefunction derived from a graph , proving their correctness by linking the wavefunction to the canonical form of the cosmological polytope and confirming a conjecture regarding its partial fraction decomposition in terms of connected subgraphs.
This paper establishes a general mathematical framework for variational problems in quantum thermodynamics with measurement constraints, leveraging non-commutative optimal transport to analyze dual formulations and zero-temperature limits while tailoring the approach to quantum state tomography and developing convergent computational algorithms.
This paper investigates the motion of compressible, inviscid fluid on a rotating sphere by presenting hodograph equations that yield a class of solutions parameterized by two arbitrary functions, providing explicit examples, describing blow-up curves, and analyzing limiting cases of rotation speeds.
This paper demonstrates that while the "spectral density" derived from Gurau's resolvent trace yields valid probability measures on average for certain random tensor ensembles, it fails to correspond to a probability measure for individual deterministic tensors, thereby proving it is not a pointwise-defined probability distribution.