Communications in Mathematical Physics最新文献

In our article [arxiv:1511.05226], we studied the commutant (mathcal {C}'subset operatorname {Bim}(R)) of a unitary fusion category (mathcal {C}), where R is a hyperfinite factor of type (mathrm II_1), (mathrm II_infty ), or (mathrm III_1), and showed that it is a bicommutant category. In other recent work [arxiv:1607.06041, arxiv:2301.11114] we introduced the notion of a (unitary) anchored planar algebra in a (unitary) braided pivotal category (mathcal {D}), and showed that they classify (unitary) module tensor categories for (mathcal {D}) equipped with a distinguished object. Here, we connect these two notions and show that finite depth objects of (mathcal {C}') are classified by connected finite depth unitary anchored planar algebras in (mathcal {Z}(mathcal {C})). This extends the classification of finite depth objects of (operatorname {Bim}(R)) by connected finite depth unitary planar algebras.

In this paper, we investigate the long-time behavior of solutions to the two-dimensional Navier–Stokes equations with initial data evolving under the influence of the planar Couette flow. We focus on general perturbations, which may be large and of low regularity, including singular configurations such as point vortices, and show that the vorticity asymptotically approaches a constant multiple of the fundamental solution of the corresponding linearized vorticity equation after a long-time evolution determined by the relative Reynolds number.

We extend methods of Ding and Smart (Invent Math 219(2):467–506, 2020) which showed Anderson localization for certain random Schrödinger operators on (ell ^2(mathbb {Z}^2)) via a quantitative unique continuation principle and Wegner estimate. We replace the requirement of identical distribution with the requirement of a uniform bound on the essential range of potential and a uniform positive lower bound on the variance of the variables giving the potential. Under those assumptions, we recover the unique continuation and Wegner lemma results, using Bernoulli decompositions and modifications of the arguments therein. This leads to a localization result at the bottom of the spectrum.

The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched Rényi entropy of quantum channels. For that, we generalize the results of Devetak et al. (Commun Math Phys 266(1):37–63, 2006) to multi-index Schatten norms. As an application, we strengthen the additivity statement of Van Himbeeck and Brown (A tight and general finite-size security proof for quantum key distribution, 2025) thus allowing the analysis of time-adaptive quantum cryptographic protocols. In addition, we establish chain rules for Rényi conditional entropies that are similar to the ones used for the generalized entropy accumulation theorem of Metger et al. (Commun Math Phys 405(11):261, 2024).

We construct families of rotationally symmetric toroidal domains in ({mathbb {R}}^3) for which the eigenfields associated to the first (positive) Ampèrian curl eigenvalue are symmetric, and others for which no first eigenfield is symmetric. This implies, in particular, that minimizers of the celebrated Woltjer’s variational principle do not need to inherit the rotational symmetry of the domain. This disproves the folk wisdom that the eigenfields corresponding to the lowest curl eigenvalue must be symmetric if the domain is.

We study “V-shaped” solutions to the KPZ equation, those having opposite asymptotic slopes (theta ) and (-theta ), with (theta >0), at positive and negative infinity, respectively. Answering a question of Janjigian, Rassoul-Agha, and Seppäläinen, we show that the spatial increments of V-shaped solutions cannot be statistically stationary in time. This completes the classification of statistically time-stationary spatial increments for the KPZ equation by ruling out the last case left by those authors. To show that these V-shaped time-stationary measures do not exist, we study the location of the corresponding “viscous shock,” which, roughly speaking, is the location of the bottom of the V. We describe the limiting rescaled fluctuations, and in particular show that the fluctuations of the shock location are not tight, for both stationary and flat initial data. We also show that if the KPZ equation is started with V-shaped initial data, then the long-time limits of the time-averaged laws of the spatial increments of the solution are mixtures of the laws of the spatial increments of (xmapsto B(x)+theta x) and (xmapsto B(x)-theta x), where B is a standard two-sided Brownian motion.

We introduce a class of generalized tube algebras which describe how finite, non-invertible global symmetries of bosonic 1+1d QFTs act on operators which sit at the intersection point of a collection of boundaries and interfaces. We develop a 2+1d symmetry topological field theory (SymTFT) picture of boundaries and interfaces which, among other things, allows us to deduce the representation theory of these algebras. In particular, we initiate the study of a character theory, echoing that of finite groups, and demonstrate how many representation-theoretic quantities can be expressed as partition functions of the SymTFT on various backgrounds, which in turn can be evaluated explicitly in terms of generalized half-linking numbers. We use this technology to explain how the torus and annulus partition functions of a 1+1d QFT can be refined with information about its symmetries. We are led to a vast generalization of Ishibashi states in CFT: to any multiplet of conformal boundary conditions which transform into each other under the action of a symmetry, we associate a collection of generalized Ishibashi states, in terms of which the twisted sector boundary states of the theory and all of its orbifolds can be obtained as linear combinations. We derive a generalized Verlinde formula involving the characters of the boundary tube algebra which ensures that our formulas for the twisted sector boundary states respect open-closed duality. Our approach does not rely on rationality or the existence of an extended chiral algebra; however, in the special case of a diagonal RCFT with chiral algebra V and modular tensor category (mathcal {C}), our formalism produces explicit closed-form expressions—in terms of the F-symbols and R-matrices of (mathcal {C}), and the characters of V—for the twisted Cardy states, and the torus and annulus partition functions decorated by Verlinde lines.

We construct finite energy blow-up solutions for the radial self-dual Chern–Simons–Schrödinger equation with a continuum of blow-up rates. Our result stands in stark contrast to the rigidity of blow-up of (H^{3}) solutions proved by the first author for equivariant index (m ge 1), where the soliton-radiation interaction is too weak to admit the present blow-up scenarios. It is optimal (up to an endpoint) in terms of the range of blow-up rates and the regularity of the asymptotic profiles, in view of the authors’ previous proof of (H^{1}) soliton resolution for the self-dual Chern–Simons–Schrödinger equation in any equivariance class. Our approach is a backward construction combined with modulation analysis, starting from prescribed asymptotic profiles and deriving the corresponding blow-up rates from their strong interaction with the soliton. In particular, our work may be seen as an adaptation of the method of Jendrej–Lawrie–Rodriguez (developed for energy critical equivariant wave maps) to the Schrödinger case. However, the Schrödinger nature of the equation (in particular, the lack of finite speed of propagation) and the optimal range (up to the (H^{1})-endpoint) of our blow-up construction give rise to new challenges. Notably, the construction of (approximate) radiation from the prescribed asymptotic profile is one of our key novelties and might be of independent interest.

We prove that for any initial data on a genus zero spectral curve the corresponding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles.

We show that the category of (C_1)-cofinite modules for the universal (N=1) super Virasoro vertex operator superalgebra (mathcal {S}(c,0)) at any central charge c is locally finite and admits the vertex algebraic braided tensor category structure of Huang–Lepowsky–Zhang. For central charges (c^{mathfrak {ns}}(t)=frac{15}{2}-3(t+t^{-1})) with (tnotin mathbb {Q}), we show that this tensor category is semisimple, rigid, and slightly degenerate, and we determine its fusion rules. For central charge (c^{mathfrak {ns}}(1)=frac{3}{2}), we show that this tensor category is rigid and that its simple modules have the same fusion rules as (textrm{Rep},mathfrak {osp}(1vert 2)), in agreement with earlier fusion rule calculations of Milas. Finally, for the remaining central charges (c^{mathfrak {ns}}(t)) with (tin mathbb {Q}^times ), we show that the simple (mathcal {S}(c^{mathfrak {ns}}(t),0))-module (mathcal {S}_{2,2}) of lowest conformal weight (h^{mathfrak {ns}}_{2,2}(t)=frac{3(t-1)^2}{8t}) is rigid and self-dual, except possibly when (t^{pm 1}) is a negative integer or when (c^{mathfrak {ns}}(t)) is the central charge of a rational (N=1) superconformal minimal model. As (mathcal {S}_{2,2}) is expected to generate the category of (C_1)-cofinite (mathcal {S}(c^{mathfrak {ns}}(t),0))-modules under fusion, rigidity of (mathcal {S}_{2,2}) is the first key step to proving rigidity of this category for general (tin mathbb {Q}^times ).