Letters in Mathematical Physics最新文献

Following D. Mbouna [Lett. Math. Phys. 114:54, 2024], a new method is provided to recognize and characterize a classical orthogonal polynomial sequence defined on a quadratic lattice only by the three-term recurrence relation. This characterization includes all orthogonal polynomials in the Askey scheme (including the para-Krawtchouk polynomials), covering then all those defined on linear and constant lattices. This work suggests a simple and implementable algorithm/package for some known physical problems.

For a G-crossed braided extension of a unitary modular tensor category (mathcal {C})—as in one representing a (2+1)D symmetry enriched topological order (SETO)—preservation of global on-site group symmetry after condensation by a commutative Q-system object (A in mathcal {C}) necessitates the existence of a G-equivariant structure on A. When interpreted spatially, the condensation boundary has its own internal topological symmetries. We elaborate an algebraic framework for describing the internal topological symmetries of compatible (1+1)D gapped boundaries for (2+1)D topologically ordered systems in terms of hypergroup actions. Then, we investigate the coherence of global on-site bulk symmetries and boundary symmetries. We present a categorical obstruction to the preservation of symmetry in a way which is coherent in terms of lifts of categorical actions to a certain 2-group of bulk symmetries. We give a characterization of this obstruction in the case of condensation by a Lagrangian algebra and boundary symmetries given by subalgebras of the convolution algebra associated with a Lagrangian algebra object.

In recent work, Lusztig’s positive root vectors (with respect to a distinguished choice of reduced decomposition of the longest element of the Weyl group) were shown to give a quantum tangent space for every A-series Drinfeld–Jimbo full quantum flag manifold (mathcal {O}_q(textrm{F}_n)). Moreover, the associated differential calculus (Omega ^{(0,bullet )}_q(textrm{F}_n)) was shown to have classical dimension, giving a direct q-deformation of the classical anti-holomorphic Dolbeault complex of (textrm{F}_n). Here, we examine in detail the rank two case, namely the full quantum flag manifold of (mathcal {O}_q(textrm{SU}_3)). In particular, we examine the (*)-differential calculus associated with (Omega ^{(0,bullet )}_q(textrm{F}_3)) and its noncommutative complex geometry. We find that the number of almost-complex structures reduces from 8 (that is 2 to the power of the number of positive roots of (mathfrak {sl}_3)) to 4 (that is 2 to the power of the number of simple roots of (mathfrak {sl}_3)). Moreover, we show that each of these almost-complex structures is integrable, which is to say, each of them is a complex structure. Finally, we observe that, due to non-centrality of all the non-degenerate coinvariant 2-forms, none of these complex structures admits a left (mathcal {O}_q(textrm{SU}_3))-covariant noncommutative Kähler structure.

We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we present a novel proof of the periodic table of topological insulators in one dimension. We show that edge modes necessarily arise at the junction of two materials having different topological indices. Our approach provides a systematic framework for understanding symmetry-protected modes in one dimension. It does not rely on periodic nor ergodicity and covers a wide range of operators which includes both continuous and discrete models.

Spectral decomposition with respect to the wave functions of Ruijsenaars hyperbolic system defines an integral transform, which generalizes classical Fourier integral. For a certain class of analytical symmetric functions we prove inversion formula and orthogonality relations, valid for complex valued parameters of the system. Besides, we study four regimes of unitarity, when this transform defines isomorphisms of the corresponding (L_2) spaces.

We investigate relative versions of dualizability designed for relative versions of topological field theories (TFTs), also called twisted TFTs, or quiche TFTs in the context of symmetries. In even dimensions, we show an equivalence between lax and oplax fully extended framed relative topological field theories valued in an ((infty , N)text {-}) category in terms of adjunctibility. Motivated by this, we systematically investigate higher adjunctibility conditions and their implications for relative TFTs. Our analysis leads us to identify the oplax relative TFT as the notion of choice. Finally, for fun we explore a tree version of adjunctibility and compute the number of equivalence classes thereof.

This article establishes a proof of dynamical localization for a random scattering zipper model. The scattering zipper operator is the product of two unitary by blocks operators, multiplicatively perturbed on the left and right by random unitary phases. One of the operator is shifted so that this configuration produces a random 5-diagonal by blocks unitary operator. To prove the dynamical localization for this operator, we use the fractional moments method. We first prove the continuity and strict positivity of the Lyapunov exponents in an annulus around the unit circle, which leads to the exponential decay of a power of the norm of the products of transfer matrices. We then establish an explicit formula of the coefficients of the finite resolvent in terms of the coefficients of the transfer matrices using Schur’s complement. From this, we deduce, through two reduction results, the exponential decay of the resolvent, from which we get the dynamical localization.

We introduce a notion of Lorentzian metric space which drops the boundedness condition from our previous work and argue that the properties defining our spaces are minimal. In fact, they are defined by three conditions given by (a) the reverse triangle inequality for chronologically related events, (b) Lorentzian distance continuity and relative compactness of chronological diamonds, and (c) a distinguishing condition via the Lorentzian distance function. By adding a countably generating condition, we confirm the validity of desirable properties for our spaces including the Polish property. The definition of (pre)length space given in our previous work on the bounded case is generalized to this setting. We also define a notion of Gromov–Hausdorff convergence for Lorentzian metric spaces and prove that (pre)length spaces are GH-stable. It is also shown that our (sequenced) Lorentzian metric spaces bring a natural quasi-uniformity (resp. quasi-metric). Finally, an explicit comparison with other recent constructions based on our previous work on bounded Lorentzian metric spaces is presented.

We show that the n-point, genus-g correlation functions of topological recursion on any regular spectral curve with simple ramifications grow at most like ((2g - 2 + n)!) as (g rightarrow infty ), which is the expected growth rate. This provides, in particular, an upper bound for many curve counting problems in large genus and serves as a preliminary step for a resurgence analysis.

In this work, we prove rigidity results for complete totally trapped spacelike submanifolds immersed in generalized Robertson–Walker spacetimes. In particular, we obtain uniqueness and non-existence results for totally trapped submanifolds. We use a maximum principle for the (infty )-Laplacian in order to get our results. We also present examples of totally trapped submanifolds in the Schwarzschild black hole spacetime and a surface which is trapped but it is not totally trapped in the product spacetime (-{mathbb {R}}times {mathbb {R}}times {mathbb {H}}^2).