Related papers: Harmonic Order Parameters for Characterizing Compl…
In recent years, a new class of mixed finite elements -- compatible-strain mixed finite elements (CSMFEs) -- has emerged that uses the differential complex of nonlinear elasticity. Their excellent performance in benchmark problems, such as…
We use an operational approach to discuss ways to measure the higher-order cross-correlations between optical and matter-wave fields. We pay particular attention to the fact that atomic fields actually consist of composite particles that…
In the present study, we focus on the parity of the order parameters and clarify the order formation process in a system including two order parameters. Each order parameter shows each different parity under a gauge transformation, namely…
In this paper, we present a robust spherical harmonics approach for the classification of point cloud-based objects. Spherical harmonics have been used for classification over the years, with several frameworks existing in the literature.…
The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
Since the dawn of quantum theory, coherence was attributed as a key to understand the weirdness of fundamental concepts like the wave-particle duality and the Stern-Gerlach experiment. Recently, based on a resource theory approach, the…
Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from…
Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
We present an efficient machine learning framework for detection and classification of nanoparticles on surfaces that are detected in the far-field with Coherent Fourier Scatterometry (CFS). We study silicon wafers contaminated with…
Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…
Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as…
Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple…
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the…
We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…