Communications in Mathematical Physics最新文献

We prove that in any spacetime dimension and under the null energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant surface gravity. That is, we solve the open degenerate case by showing that, if there is a complete generator, then there exists a smooth future-directed geodesic lightlike tangent field. The result can be stated as an existence result for a particular cohomological equation. The proof uses elements of ergodic theory, Hodge theory and Riemannian flow theory. We emphasize that, remarkably, these results really require only the null energy condition, whereas previous works assumed, already in the Killing or the non-degenerate cases, the stronger dominant energy condition.

We study geometric properties of trace functionals that generalize those in Zhang (Adv Math 365:107053, 2020), arising from a novel family of conditional entropies with applications in quantum information theory. Building on new convexity results for these functionals, we establish data-processing inequalities and additivity properties for our entropies, demonstrating their operational significance. We further prove completeness under duality, chain rules, and various monotonicity properties for this family. Our proofs draw on tools from complex interpolation theory, multivariate Araki-Lieb-Thirring inequalities, variational characterizations of trace functionals, and spectral pinching techniques.

A well-known conjecture in the theory of Coulomb gases and the mean-field limit of (beta )-ensembles asserts that, generically, external potentials are “off-critical” (or equivalently, “regular”). By exploiting the connection between minimizing measures and thin obstacle problems, we establish this conjecture.

We study the conditional measures of every invariant probability measure for every (C^{1+gamma }) diffeomorphism of a closed Riemannian manifold, and we show that they always admit an asymptotic local product structure. This is a direct application of the notion of tubular dimension which we introduce and study in the manuscript. As an additional application we prove a bound on any two consecutive conditional entropies in terms of volume growth.

We study the scattering of time-harmonic scalar waves by a periodic array of penetrable, high-contrast obstacles with small period, confined to a bounded Lipschitz domain. The strong contrast between the obstacles and the background induces subwavelength resonances. We derive a frequency-dependent effective model in the vanishing-period limit and prove quantitative convergence of the scattered waves in the original heterogeneous setup to those in the effective model. We also identify the limiting set of scattering resonances and establish the convergence rates. Finally, we establish the convergence rates for the far-field pattern of the scattered waves in the heterogeneous setting to that of the effective model.

We consider two-dimensional topological insulators on the cylinder, in the presence of weak quasi-periodic disorder. In the absence of disorder, we assume the presence of a single edge state on the boundary of the system, as for the Haldane model. We prove that, at large distances, the boundary correlations agree with the correlations of a renormalized, translation-invariant, massless relativistic model in (1+1) dimensions, multiplied by non-universal oscillatory factors, incommensurate with the lattice spacing. Furthermore, we compute the edge conductance and the edge susceptibility, starting from Kubo formula. We obtain explicit expressions for these response functions, completely determined by the renormalized Fermi velocity of the edge modes. In particular, we prove the quantization of the edge conductance, and the non-universality of the susceptibility. The proof relies on multiscale analysis and rigorous renormalization group methods for quasi-periodic systems, and on lattice Ward identities.

Generalized symmetries of quantum field theories can be characterized by topological defects/operators organized into a higher category. In this paper we consider the Axion-Maxwell field theory in four dimensions and, building on the construction of its topological defects by Choi, Lam, Shao, Hidaka, Nitta and Yokokura, we discuss field theoretical methods to compute some aspects of the higher structure of such category. In particular, we determine explicitly the generalized F-symbols for the non-invertible electric 1-form symmetry of the theory. Along the way, we clarify various aspects of the bottom-up worldvolume approach towards the calculus of defects.

Motivated by known examples of Joyce structures on spaces of meromorphic quadratic differentials, we consider the isomonodromic deformations of particular second-order linear ODEs with rational potential. We show the infinitesimal isomonodromic deformations are the kernel of a closed 2-form arising from the intersection pairing of an algebraic curve defined by the potential. This observation enables us to construct Joyce structures on a class of moduli spaces of meromorphic quadratic differentials on the Riemann sphere, and provides a new, geometric description of the hyper-Kähler structures of previously computed examples. We focus on the case of moduli of quadratic differentials with poles of odd orders, where we obtain a complex hyper-Kähler metric with homothetic symmetry. We also include an example corresponding to the moduli space of quadratic differentials with four simple poles, which is a version of the classical isomonodromy problem that leads to the Painlevé VI equation.