Communications in Mathematical Physics最新文献

Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data ((Sigma ,x,y,B)). We give a functional relation between the correlators of genus (g=0) generated by the initial data ((Sigma ,x,y,B)) and by the initial data ((Sigma ,y,x,B)), where x and y are interchanged. The functional relation is derived with the loop insertion operator by computing a functional relation for some intermediate correlators. Additionally, we show that our result is equivalent to the recent result of Borot et al. (2021) in case of (g=0). Consequently, we are providing a simplified functional relation between generating series of higher order free cumulants and moments in higher order free probability.

This paper is devoted to investigating the rotating Boussinesq equations of inviscid, incompressible flows with both fast Rossby waves and fast internal gravity waves. The main objective is to establish a rigorous derivation and justification of a new generalized quasi-geostrophic approximation in a channel domain with no normal flow at the upper and lower solid boundaries, taking into account the resonance terms due to the fast and slow waves interactions. Under these circumstances, We are able to obtain uniform estimates and compactness without the requirement of either well-prepared initial data [as in Bourgeois and Beale (SIAM J Math Anal 25(4):1023–1068, 1994. https://doi.org/10.1137/S0036141092234980)] or domain with no boundary [as in Embid and Majda (Commun Partial Differ Equ 21(3–4):619–658, 1996. https://doi.org/10.1080/03605309608821200)]. In particular, the nonlinear resonances and the new limit system, which takes into account the fast waves correction to the slow waves dynamics, are also identified without introducing Fourier series expansion. The key ingredient includes the introduction of (full) generalized potential vorticity.

Understanding the decay of correlations in time for (1+1)-dimensional polymer models in the KPZ universality class has been a challenging topic. Following numerical studies by physicists, concrete conjectures were formulated by Ferrari and Spohn [34] in the context of planar exponential last passage percolation. These have mostly been resolved by various authors. In the context of positive temperature lattice models, however, these questions have remained open. We consider the time correlation problem for the exactly solvable inverse-gamma polymer in (mathbb Z^2). We establish, up to constant factors, upper and lower bounds on the correlation between free energy functions for two polymers rooted at the origin (droplet initial condition) when the endpoints are either close together or far apart. We find the same exponents as predicted in [34]. Our arguments rely on the understanding of stationary polymers, coupling, and random walk comparison. We use recently established moderate deviation estimates for the free energy. In particular, we do not require asymptotic analysis of complicated exact formulae.

We consider ({{,mathrm{G_2},}}) manifolds with a cohomogeneity two ({{,mathrm{mathbb {T}},}}^2times {{,textrm{SU},}}(2)) symmetry group. We give a local characterization of these manifolds and we describe the geometry, including regularity and singularity analysis, of cohomogeneity one calibrated submanifolds in them. We apply these results to the manifolds recently constructed by Foscolo–Haskins–Nordström and to the Bryant–Salamon manifold of topology (/!!!S(S^3)). In particular, we describe new large families of complete ({{,mathrm{mathbb {T}},}}^2)-invariant associative submanifolds in them.

We construct invariants of colored links using equivariant bordism groups of Conner and Floyd. We employ this bordism invariant to find the first examples of topological vortex knots, the knot structure of which is protected from decaying via topologically allowed local surgeries, i.e., by reconnections and strand crossings permitted by the topology of the vortex-supporting medium. Moreover, we show that, up to the aforementioned local surgeries, each tricolored link either decays into unlinked simple loops, or can be transformed into either a left-handed or a right-handed tricolored trefoil knot.

We establish an explicit formula for the solution of the cubic Szegő equation on the real line. Using this formula, we prove that the evolution flow of this equation can be continuously extended to the whole Hardy class (H^2) on the real line.

In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra (mathfrak {gl}(m|n)). We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical (mathcal {W})-superalgebras associated with (mathfrak {gl}(m|n)) and some rectangular nilpotent elements. We use this isomorphism to construct integrable hierarchies on these rectangular (mathcal {W})-superalgebras.

We consider solutions to the generalized Surface Quasi-geostrophic equation ((gamma )-SQG) when the velocity is more singular than the active scalar function (i.e. (gamma in (0,1))). In this paper we establish strong ill-posedness in (C^{k,beta }) ((kge 1), (beta in (0,1]) and (k+beta >1+gamma )) and we also construct solutions in (mathbb {R}^2) that initially are in (C^{k,beta }cap L^2) but are not in (C^{k,beta }) for (t>0). Furthermore these solutions stay in (H^{k+beta +1-2delta }) for some small (delta ) and an arbitrarily long time.

We investigate the spectral distribution of the twisted Laplacian associated with uniform square-integrable bounded harmonic 1-form on typical hyperbolic surfaces of high genus. First, we estimate the spectral distribution by the supremum norm of the corresponding harmonic form. Subsequently, we show that the square-integrable bounded harmonic form exhibits a small supremum norm for typical hyperbolic surfaces of high genus. Based on these findings, we prove a uniform Weyl law for the distribution of real parts of the spectrum on typical hyperbolic surfaces.

We prove that the relative entropy of entanglement is additive when at least one of the two states belongs to some specific class. We show that these classes include bipartite pure, maximally correlated, GHZ, Bell diagonal, isotropic, and generalized Dicke states. Previously, additivity was established only if both states belong to the same class. Moreover, we extend these results to entanglement monotones based on the (alpha )-z Rényi relative entropy. Notably, this family of monotones includes also the generalized robustness of entanglement and the geometric measure of entanglement. In addition, we prove that any monotone based on a quantum relative entropy is not additive for general states. We also compute closed-form expressions of the monotones for bipartite pure, Bell diagonal, isotropic, generalized Werner, generalized Dicke, and maximally correlated Bell diagonal states. Our results rely on developing a method that allows us to recast the initial convex optimization problem into a simpler linear one. Even though we mostly focus on entanglement theory, we expect that some of our technical results could be useful in investigating more general convex optimization problems.