283 papers
This paper reformulates the Chern character in topological K-theory using Fermi points of Fredholm operators to generalize spectral flow and provide elementary proofs for the evenness of the edge index and the bulk-edge correspondence in four-dimensional time-reversal symmetric topological insulators (class AI).
This paper establishes a comprehensive theory of multiary graded polyadic algebras by extending classical group-graded algebras to higher-arity structures, introducing multiary group gradings, and uncovering unique phenomena such as higher power gradings and specific arity compatibility constraints through results like quantization rules and a First Isomorphism Theorem.
This paper provides a complete characterization of -positivity and Schmidt numbers for linear maps and bipartite states with symplectic group symmetries, yielding new constructions of optimal indecomposable maps, high-degree PPT entangled states, and resolutions to the PPT-squared conjecture and a Pal-Vertesi conjecture.
This paper presents a polynomial-time algorithm that provides an exact, suboptimal solution for decomposing arbitrary two-body Hamiltonians into local unitary transformations of an Ising Hamiltonian, thereby enabling scalable digital-analog quantum simulation without the need for computationally expensive numerical optimization.
This paper proves that the classification of two-dimensional symmetry-protected topological states by the cohomology group is complete for the specific subset of states that can be prepared from a product state via a symmetric entangler.
This paper introduces hysteretic squashed entanglement (), a robust conditional entanglement monotone for mixed many-body states that effectively filters out classical contributions to detect genuine quantum correlations and quantify topological order in systems like the transverse-field Ising model.
This paper establishes a universal structural principle showing that smoothing optimizers are clipped probability vectors, which enables the derivation of optimal, state-independent bounds relating smoothed quantum divergences of arbitrary orders, including the hypothesis testing divergence.
This paper establishes that circle graph states are closed under local unitary equivalence, demonstrates their correspondence to planar code states to prove the classical simulability of measurement-based quantum computation on them, and shows that counting LU-equivalent graph states is -hard.
This paper presents a quantum numerical scheme for solving anisotropic diffusion and convection equations that utilizes vector-norm analysis to achieve an exponential reduction in the required number of time-steps compared to previous operator-norm bounds.
This paper constructs fractional Sobolev spaces with variable orders on arbitrary time scales and their product domains, establishing their functional-analytic properties and trace frameworks to derive Euler-Lagrange equations for variational problems involving variable-order Riemann-Liouville and Caputo fractional operators.
This paper establishes global well-posedness in the critical energy space and proves almost periodicity in time for the half-wave maps equation on the one-dimensional torus by leveraging its integrable Lax pair structure to derive explicit solution formulae and a general stability principle that extends to matrix-valued cases and companion results on the real line.
This paper demonstrates that a canonical extension of generalized Dynkin diagrams generates families of Kac-Moody groups, such as the series relevant to string theory, which satisfy homological stability and exhibit emergent structures upon stabilization, utilizing homotopy decompositions of their classifying spaces.
This paper demonstrates that the infinite random Heisenberg XXZ spin- chain exhibits slow, logarithmic information propagation characteristic of many-body localization within any arbitrary fixed energy interval, provided the interaction and disorder parameters fall within a regime determined solely by that energy interval.
This paper clarifies the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces used in Cartan Neural Networks by proving that only Kähler spaces support Gibbs distributions, explicitly characterizing their generalized temperature spaces via adjoint orbits, and demonstrating the equivalence between various information and thermodynamical geometries while establishing the covariance of these distributions under the full symmetry group.
This paper investigates the Cauchy problem for a nonlinear damped Schrödinger equation involving the Riemann zeta function, establishing the uniqueness of distributional solutions, proving the existence of global solutions via regularization and compactness arguments, and demonstrating that solutions in the one-dimensional case vanish in finite time.
This paper introduces spectral Barron spaces within the framework of quantum harmonic analysis, establishes their fundamental properties such as completeness and continuous embeddings, and applies these results to prove the existence and uniqueness of solutions for a Schrödinger-type equation.
This paper classifies and analyzes exactly solvable one-dimensional complex Schrödinger operators related to the Gauss hypergeometric equation, organizing them into three geometric families (spherical, hyperbolic, and deSitterian) to compute their spectra and Green functions while establishing transmutation identities and linking them to symmetric manifolds.
This paper investigates the limit shapes and fluctuations of random Young diagrams arising from symplectic group duality by deriving semiclassical orthogonal polynomials via Christoffel transformation from Krawtchouk polynomials and analyzing their asymptotic behavior through an integral representation, thereby overcoming the lack of a free-fermionic representation available in the general linear case.
This paper proves that the infinite system-size free energy of quantum -spin glasses in a transverse magnetic field converges to that of the quantum random energy model as , achieved by combining non-commutative analytical techniques with the geometry of extreme negative deviations in classical -spin glasses.
This paper investigates the robustness of topological phases on aperiodic lattices by constructing *-homomorphisms between groupoid and coarse-geometric models, demonstrating that strong phases are detected by position spectral triples while phases arising from stacking along Delone sets are inherently weak in the coarse-geometric sense.