Communications in Mathematical Physics最新文献

We obtain an asymptotic for the fourth moment of truncated Eisenstein series of large Laplacian eigenvalue, verifying for the first time that the main term corresponds to Gaussian random behavior. This is a manifestation of the Random Wave Conjecture, which for Eisenstein series was formulated by Hejhal and Rackner over thirty years ago. Our innovation is to tackle the problem after introducing, at no cost, an extra averaging over the truncation parameter.

We study Kitaev’s quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of ‘localized and transportable endomorphisms’, which produce anyonic excitations from the ground state. Following the Doplicher–Haag–Roberts (DHR) sector theory from AQFT, we organize these endomorphisms into a braided monoidal category capturing the fusion and braiding properties of the anyons. We show that this category is equivalent to (textbf{Rep}_f {{mathcal {D}}}(G)), the representation category of the quantum double of G. This establishes for the first time the full DHR structure for a class of 2d quantum lattice models with non-abelian anyons.

It has been shown that in one dimension the environment viewed by the particle process (EVP process) in quasi periodic random environment is uniquely ergodic and mixing under mild additional assumptions. Here we construct an analytic quasi periodic environment on higher dimensional torus such that the EVP process is not uniquely ergodic. The stationary measures in this counterexample are necessarily atomless. We show also that the EVP process is mixing with respect to any ergodic stationary measure under some smoothness assumption.

Motivated by the fundamental role that bosonic and fermionic symmetries play in physics, we study finite (non-invertible) one-form symmetries in (2+1)d consisting of topological lines with bosonic and fermionic self-statistics. We refer to these lines as Bose–Fermi–Braided (BFB) symmetries and argue that they can be classified. Unlike the case of generic anyonic lines, BFB symmetries are closely related to groups. In particular, when BFB lines are non-invertible, they are non-intrinsically non-invertible. Moreover, BFB symmetries are, in a categorical sense, weakly group theoretical. Using this understanding, we study invariants of renormalization group flows involving non-topological QFTs with BFB symmetry.

In this paper we generalize a key result relating singular limits of certain relative entropies with index in the setting of conformal nets, which has played an important role recently in the mathematical theory of relative entropies in the context of Conformal Field Theory.

We study Schrödinger equations on (mathbb {Z}^d) and (mathbb {R}^d), (dge 2) with random potentials of strength (lambda ). Our main result gives tail bounds for the terms of the Dyson series that are effective at time scales on the order of (lambda ^{-2+varepsilon }). As corollaries, we obtain estimates on the frequency localization and spatial delocalization of approximate eigenfunctions in the spirit of Schlag et al. (J Anal Math 88(1):173–220, 2002) and Chen (J Stat Phys 120(1):279–337, 2005). These estimates also apply to Floquet states associated to time-periodic potentials. Our proof is elementary in that we use neither sophisticated harmonic analysis as in Schlag et al. (2002) nor diagrammatic arguments as in Chen (2005). Instead, we use only the noncommutative Khintchine inequality from random matrix theory combined with pointwise dispersive estimates for the free Schrödinger equation.

In the study of non-equilibrium statistical mechanics, Ruelle derived explicit formulae for entropy production of smooth dynamical systems. The vanishing or strict positivity of entropy production is determined by the entropy formula of folding type

which relates the metric entropy, folding entropy and negative Lyapunov exponents. This paper establishes the formula for all inverse SRB measures of (C^{1+alpha }) maps, including those with degeneracy (i.e., zero Jacobian). More specifically, we establish the equivalence that (mu ) is an inverse SRB measure if and only if the folding-type entropy formula holds and the Jacobian series is integrable. To overcome the degeneracy, we develop Pesin theory for general (C^{1+alpha }) maps.

We study Busemann functions, semi-infinite geodesics, and competition interfaces in the exactly solvable last-passage percolation with inhomogeneous exponential weights. New phenomena concerning geodesics arise due to inhomogeneity. These include novel Busemann functions associated with flat regions of the limit shape and thin rectangles, semi-infinite geodesics with intervals of asymptotic directions, non-trivial axis-directed geodesics, intervals with no geodesic directions, and isolated geodesic directions. We further observe a new dichotomy for competition interfaces and second-class customers in a series of memoryless continuous-time queues with inhomogeneous service rates: a second-class customer either becomes trapped or proceeds through the service stations at strictly positive speed.

We determine the structure of the Parisi measure at zero temperature for the spherical (p+s) spin glass model. We show that depending on the values of p and s, four scenarios may emerge, including the existence of 1-FRSB and 2-FRSB phases as predicted by Crisanti and Leuzzi (Private communication, 2022, Phys Rev B 73:014412, 2006). We also provide consequences for the model at low temperatures.