Static non-reciprocity in mechanical metamaterials

Reciprocity is a fundamental principle governing various physical systems, which ensures that the transfer function between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity have been mostly considered in dynamic systems, for electromagnetic, acoustic and mechanical wave propagation associated with spatio-temporal variations. Here we show that it is possible to strongly break reciprocity in static systems, realizing mechanical metamaterials that, by combining large nonlinearities with suitable geometrical asymmetries, and possibly topological features, exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. In addition to extending non-reciprocity and isolation to statics, our work sheds new light on the understanding of energy propagation in non-linear materials with asymmetric crystalline structures and topological properties, opening avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.Comment: 19 pages, 3 figures, Supplementary information (11 pages and 5 figures

Designing perturbative metamaterials from discrete models

Identifying material geometries that lead to metamaterials with desired functionalities presents a challenge for the field. Discrete, or reduced-order, models provide a concise description of complex phenomena, such as negative refraction, or topological surface states; therefore, the combination of geometric building blocks to replicate discrete models presenting the desired features represents a promising approach. However, there is no reliable way to solve such an inverse problem. Here, we introduce ‘perturbative metamaterials’, a class of metamaterials consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model with individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing two-dimensional elastic metamaterials that realize Veselago lenses, zero-dispersion bands and topological surface phonons. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal and photonic metamaterials composed of weakly interacting unit cells

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the noninteger degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spinchains provides strong analytical evidences corroborating our results

A measure for spatial dependence in natural stochastic textures

Random textures differ from natural textures because they lack structure. Structure is a concept that is difficult to formalize, but we generally observe that it is associated with spatial dependence between adjacent pixels. Completely random textures, in fact, are characterized by independent pixels, while natural textures show some local dependence. In this paper, we propose a measure for such local dependence. The texture is scanned on a random walk path and the pixels values encountered are collected in form of a time-series. The statistical properties of the time-series are used to characterize the spatial dependence of the texture. We assume that the proposed measure can be used to help the model textures, to set the size of operating windows in texture synthesis algorithms, and to compute a simple indicator of texture scale. Moreover, we show how the measure can be linked to texture perception