Annales Henri Poincaré最新文献

Anyons with a statistical phase parameter (alpha in (0,2)) are a kind of quasi-particles that, for topological reasons, only exist in a 1D or 2D world. We consider the dimensional reduction for a 2D system of anyons in a tight wave guide. More specifically, we study the 2D magnetic gauge picture model with an imposed anisotropic harmonic potential that traps particles much stronger in the y-direction than in the x-direction. We prove that both the eigenenergies and the eigenfunctions are asymptotically decoupled into the loose confining direction and the tight confining direction during this reduction. The limit 1D system for the x-direction is given by the impenetrable Tonks–Girardeau Bose gas, which has no dependency on (alpha ), and no trace left of the long-range interactions of the 2D model.

We show that quantum graph parameters for finite, simple, undirected graphs encode winning strategies for all possible synchronous non-local games. Given a synchronous game (mathcal {G}=(I,O,lambda )) with (|I|=n) and (|O|=k), we demonstrate what we call a weak (*)-equivalence between (mathcal {G}) and a 3-coloring game on a graph with at most (3+n+9n(k-2)+6|lambda ^{-1}({0})|) vertices, strengthening and simplifying work implied by Ji [16] for winning quantum strategies for synchronous non-local games. As an application, we obtain a quantum version of Lovász’s reduction [21] of the k-coloring problem for a graph G with n vertices and m edges to the 3-coloring problem for a graph with (3+n+9n(k-2)+6mk) vertices. Moreover, winning strategies for a synchronous game (mathcal {G}) can be transformed into winning strategies for an associated graph coloring game, where the strategies exhibit perfect zero knowledge for an honest verifier. We also show that, for “graph of the game” (X(mathcal {G})) associated with (mathcal {G}) from Atserias et al. [1], the independence number game (text {Hom}(K_{|I|},overline{X(mathcal {G})})) is hereditarily (*)-equivalent to (mathcal {G}), so that the possibility of winning strategies is the same in both games for all models, except the game algebra. Thus, the quantum versions of the chromatic number, independence number and clique number encode winning strategies for all synchronous games in all quantum models.

We consider a deformation of a family of hyperelliptic refined spectral curves and investigate how deformation effects appear in the hyperelliptic refined topological recursion as well as the (mathcal {Q})-top recursion. We then show a coincidence between a deformation condition and a quantisation condition in terms of the (mathcal {Q})-top recursion on a degenerate elliptic curve. We also discuss a relation to the corresponding Nekrasov–Shatashivili effective twisted superpotential.

We consider the Laplace–Beltrami operator with Dirichlet boundary conditions on convex domains in a Riemannian manifold ((M^n,g)) and prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small whenever (M^n) has even a single tangent plane of negative sectional curvature. In particular, the fundamental gap conjecture strongly fails for small deformations of Euclidean space which introduce any negative curvature. We also show that when the curvature is negatively pinched, it is possible to construct such domains of any diameter up to the diameter of the manifold. The proof is adapted from the argument of Bourni et al. (in: Annales Henri Poincaré, Springer, 2022), which established the analogous result for convex domains in hyperbolic space, but requires several new ingredients.

We discuss high energy properties of states for (possibly interacting) quantum fields in curved spacetimes. In particular, if the spacetime is real analytic, we show that an analogue of the timelike tube theorem and the Reeh–Schlieder property hold with respect to states satisfying a weak form of microlocal analyticity condition. The former means the von Neumann algebra of observables of a spacelike tube equals the von Neumann algebra of observables of a significantly bigger region that is obtained by deforming the boundary of the tube in a timelike manner. This generalizes theorems by Araki (Helv Phys Acta 36:132–139, 1963) and Borchers (Nuovo Cim (10) 19:787–793, 1961) to curved spacetimes.

We pursue a uniform quantization of all twists of 4-dimensional (mathcal N=4) supersymmetric Yang–Mills theory, using the BV formalism, and we explore consequences for factorization algebras of observables. Our central result is the construction of a one-loop exact quantization on (mathbb {R}^4) for all such twists and for every point in a moduli of vacua. When an action of the group (textrm{SO}(4)) can be defined—for instance, for Kapustin and Witten’s family of twists—the associated framing anomaly vanishes. It follows that the local observables in such theories can be canonically described by a family of framed (mathbb E_4) algebras; this structure allows one to take the factorization homology of observables on any oriented 4-manifold. In this way, each Kapustin–Witten theory yields a fully extended, oriented 4-dimensional topological field theory à la Lurie and Scheimbauer.

Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. It would seem that few methods can be useful in such diverse applications. However, we here present a flexible modeling tool for the limit of theories, soft inductive limits, constituting a generalization of inductive limits of Banach spaces. In this context, general criteria for the convergence of dynamics will be formulated, and these criteria will be shown to apply in the situations mentioned and more.

This article introduces the notions of asymptotic dust and asymptotic radiation equations of state. With these non-linear generalizations of the well known dust or (incoherent) radiation equations of state the perfect-fluid equations lose any conformal covariance or privilege. We analyse the conformal field equations induced with these equations of state. It is shown that the Einstein-(lambda )-perfect-fluid equations with an asymptotic radiation equation of state allow for large sets of Cauchy data that develop into solutions which admit smooth conformal boundaries in the future and smooth extensions beyond. In the case of asymptotic dust equations of state sharp results on the future asymptotic behaviour are not available yet.

We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. We prove that the central limit theorem holds for a suitably rescaled magnetization, while its violation with the typical quartic behavior appears at the critical point.

We extend the recent classification of five-dimensional, supersymmetric asymptotically flat black holes with only a single axial symmetry to black holes with Kaluza–Klein asymptotics. This includes a similar class of solutions for which the supersymmetric Killing field is generically timelike, and the corresponding base (orbit space of the supersymmetric Killing field) is of multi-centred Gibbons–Hawking type. These solutions are determined by four harmonic functions on (mathbb {R}^3) with simple poles at the centres corresponding to connected components of the horizon, and fixed points of the axial symmetry. The allowed horizon topologies are (S^3), (S^2times S^1), and lens space L(p, 1), and the domain of outer communication may have non-trivial topology with non-contractible 2-cycles. The classification also reveals a novel class of supersymmetric (multi-)black rings for which the supersymmetric Killing field is globally null. These solutions are determined by two harmonic functions on (mathbb {R}^3) with simple poles at centres corresponding to horizon components. We determine the subclass of Kaluza–Klein black holes that can be dimensionally reduced to obtain smooth, supersymmetric, four-dimensional multi-black holes. This gives a classification of four-dimensional asymptotically flat supersymmetric multi-black holes first described by Denef et al.