Related papers: Topological metrology and its application to optic…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic…
In the last years there have been multiple proposals in nanophotonics to mimic topological condensed matter systems. However, nanoparticles have degrees of freedom that atoms lack of, like dimensions or shape, which can be exploited to…
In geophysics, inverse modelling can be applied to a wide range of goals, including, for instance, mapping the distribution of rock physical parameters in applied geophysics and calibrating models to forecast the behaviour of natural…
The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for…
In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic…
Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…
Transmitting structured light robustly through complex random media is crucial in many applications, from sensing to communication. Unfortunately, the spatial structure of light is distorted in such media due to refractive index…
Positioning using wave signal measurements is used in several applications, such as GPS systems, structure from sound and Wifi based positioning. Mathematically, such problems require the computation of the positions of receivers and/or…
We provide a topological classification of locally constant functions over subshifts of finite type via their zero-temperature measures. Our approach is to analyze the relationship between the distribution of the zero-temperature measures…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
The nature of optical metrology is to perform efficient transfer and precise retrieval for lasers and optical signals, which is beneficial for a variety of applications ranging from optical clocking, spectroscopy, to telecommunications and…
Sensing and metrology play an important role in fundamental science and applications, by fulfilling the ever-present need for more precise data sets, and by allowing to make more reliable conclusions on the validity of theoretical models.…
Thermodynamically consistent measurements can either preserve statistics (unbiased) or preserve marginal states (non-invasive) but not both. Here we show the existence of metrological tasks which unequally favor each of the aforementioned…
We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of…
The construction of measurements suitable for discriminating signal components produced by phenomena of different types is considered. The required measurements should be capable of cancelling out those signal components which are to be…
Metasurfaces are generally designed by placing scatterers in periodic or pseudo-periodic grids. We propose and discuss design rules for functional metasurfaces with randomly placed anisotropic elements. By analyzing the focusing performance…
We find exact conditions for the enhancement or suppression of internal and/or scattered fields and the determination of their spatial distribution or angular momentum through the combination of simple fields. The incident fields can be…
This paper concerns the local study of analytic constrained differential systems (or impasse systems) of the form $A(x)\dot{x} = F(x)$, $x\in\mathbb{R}^{2}$, where $F$ is a vector field and $A$ is a matrix valued function. Using techniques…
Nonlinear topological insulators have garnered substantial recent attention as they have both enabled the discovery of new physics due to interparticle interactions, and may have applications in photonic devices such as topological lasers…