33 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 establishes Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies by employing a novel dynamical rigidity argument.
This paper demonstrates that for point perturbations of the Laplacian on a compact Riemannian manifold, the high-frequency eigenfunctions exhibit semiclassical measures invariant under the geodesic flow, provided the scatterers satisfy a non-focality condition ensuring that returning geodesics form a set of zero measure.
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 establishes an asymptotic expansion in inverse powers of time for the correlation functions of isometric extensions of volume-preserving Anosov flows defined on Abelian covers of closed manifolds.
This paper revisits the Friedrichs model to derive precise asymptotic results, including the Breit-Wigner formula and spectral concentration, for resonances near embedded eigenvalues, while also establishing exact properties for sojourn time, scattering amplitude, and time delay in the context of rank-one perturbations of the Laplacian.
This paper establishes universal eigenvalue estimates and derives bounds for the gaps between consecutive eigenvalues for coupled systems of second- and fourth-order elliptic differential equations in divergence form, encompassing operators such as the Lamé, Laplacian, and bi-Laplacian.
This paper unconditionally proves the quantum unique ergodicity conjecture for Pitale lifts on hyperbolic 4-manifolds by employing a novel amplification method with favorable geometric properties to overcome the challenges posed by non-temperedness.
This paper investigates the Rumin differentials within irreducible unitary representations of the (2,3,5) nilpotent Lie group, computing their spectra and zeta-regularized determinants for Schrödinger representations while evaluating the analytic torsion for generic representations.
This paper establishes that geodesic disks are the unique domains maximizing the first non-trivial Neumann eigenvalue among all simply connected regions of the sphere with a fixed area.
This paper establishes that for a generic set of finite-dimensional irreducible representations of the fundamental group of a surface's unit tangent bundle, the twisted Ruelle zeta function either vanishes at zero with an order determined by the genus or equals the Reidemeister--Turaev torsion, thereby extending Fried's conjecture to generic acyclic representations and confirming the constancy of the vanishing order for untwisted zeta functions across a dense set of Anosov metrics.
This paper investigates the regularization and completeness of root functions for operator-differential expressions involving bounded invertible and finite-dimensional operators, demonstrating how such forms can regularize singular differential expressions with negative Sobolev space coefficients and establishing completeness under specific Volterra operator and boundary conditions.
This paper generalizes Backhausz and Szegedy's result on the infinite regular tree by proving that the Gaussian wave is the unique typical process with Green's function covariance for any infinite tree of finite cone type satisfying mild expansion, thereby establishing the convergence of local eigenvector distributions to the Gaussian wave for random bipartite biregular graphs and generic configuration models.