Letters in Mathematical Physics最新文献

Inspired by the recent paper of Baltazar and Queiroz (J Geom Anal 34:158, 2024. https://doi.org/10.1007/s12220-024-01603-y), in this article, we prove the rigidity for compact gradient Einstein-type manifolds with nonempty boundary and constant scalar curvature under a pinching condition, which is independent on the potential function. As a special case of gradient Einstein-type manifold, we also give a rigidity result of ((m,rho ))-quasi-Einstein manifold with boundary.

We investigate the count of meromorphic differentials on the Riemann sphere possessing a single zero, multiple poles with prescribed orders and fixed residues at each pole. Gendron and Tahar previously examined this problem with respect to general residues using flat geometry, while Sugiyama approached it from the perspective of fixed point multipliers of polynomial maps in the case of simple poles. In our study, we employ intersection theory on compactified moduli spaces of differentials, enabling us to handle arbitrary residues and pole orders, which provides a complete solution to this problem. We also determine interesting combinatorial properties for the solution formula as well as related intersection numbers.

We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application, we reprove and extend some theorems about eigenvalue asymptotics of Schrödinger operators with homogeneous potentials. The case of main interest is where the Weyl expression is infinite and a partially semiclassical limit occurs.

The Berezin–Karpelevich integral is a double integral over unitary matrices which plays the role of the Itzykson–Zuber integral in rectangular matrix models. We obtain a topological expansion of the Berezin–Karpelevich integral in terms of monotone Hurwitz numbers and obtain from this certain combinatorial identities.

The focus of the paper is on constructing new solutions of the generalized classical Yang-Baxter equation (GCYBE) that are not skew-symmetric. Using regular decompositions of finite-dimensional simple Lie algebras, we construct Lie algebra decompositions of (mathfrak {g}(!(x)!) times mathfrak {g}[x]/x^m mathfrak {g}[x]). The latter decompositions are in bijection with the solutions to the GCYBE. Under appropriate regularity conditions, we obtain a partial classification of such solutions. The paper is concluded with the presentations of the Gaudin-type models associated to these solutions.

We show that for a family of quantum walk models with electric fields, the spectrum is the unit circle for any irrational field. The result also holds for the associated CMV matrices defined by skew-shifts, as well as a family of the Blattner and Browne model. Generalizations to CMV matrices with skew-shifts on higher dimensional torus are also obtained.

We obtain explicit formulas for the K-theoretic capped descendent vertex functions of ({text {Hilb}}^n(mathbb {C}^2)) for descendents given by the exterior algebra of the tautological bundle. This formula provides a one-parametric deformation of the generating function for normalized Macdonald polynomials. In particular, we show that the capped vertex functions are rational functions of the quantum parameter.

One of the oldest problems in quantum information theory is to study if there exists a state with negative partial transpose which is undistillable [1]. This problem has been open for almost 30 years, and still no one has been able to give a complete answer to it. This work presents a new strategy to try to solve this problem by translating the distillability condition on the family of Werner states into a problem of partial trace inequalities, this is the aim of our first main result. As a consequence, we obtain a new bound for the 2-distillability of Werner states, which does not depend on the dimension of the system. On the other hand, our second main result provides new partial trace inequalities for bipartite systems, connecting some of them also with the separability of Werner states. Throughout this work, we also present numerous partial trace inequalities, which are valid for many families of matrices.

We deal with rigidity results for compact gradient Einstein-type manifolds with nonempty boundary. As a result, we obtain new characterizations for hemispheres and geodesic balls in simply connected space forms. In dimensions three and five, we obtain topological characterizations for the boundary and upper bounds for its area.

We discuss in this note two dual canonical operations on Dirac structures L and R—the tangent product (L star R) and the cotangent product (L circledast R). Our first result gives an explicit description of the leaves of (L star R) in terms of those of L and R, surprisingly ruling out the pathologies which plague general “induced Dirac structures.” In contrast to the tangent product, the more novel cotangent product (L circledast R) need not be Dirac even if smooth. When it is, we say that L and R concur. Concurrence captures commuting Poison structures and refines the Dirac pairs of Dorfman and Kosmann–Schwarzbach, and it is our proposal as the natural notion of “compatibility” between Dirac structures. The rest of the paper is devoted to illustrating the usefulness of tangent- and cotangent products in general, and the notion of concurrence in particular. Dirac products clarify old constructions in Poisson geometry, characterize Dirac structures which can be pushed forward by a smooth map, and mandate a version of a local normal form. Magri and Morosi’s (POmega )-condition and Vaisman’s notion of two-forms complementary to a Poisson structures are found to be instances of concurrence, as is the setting for the Frobenius–Nirenberg theorem. We conclude the paper with an interpretation in the style of Magri and Morosi of generalized complex structures which concur with their conjugates.