Related papers: Double crystallographic groups and their represent…
Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian…
Use of dedicated computers in spin glass simulations allows one to equilibrate very large samples (of size as large as $L=32$) and to carry out "computer experiments" that can be compared to (and analyzed in combination with) laboratory…
We present a symmetry-based framework for the analysis of excitonic states, incorporating both time-reversal and space-group symmetries. We demonstrate the use of time-reversal and space-group symmetries to obtain exciton eigenstates at…
As is well known, crystals have discrete space translational symmetry. It was recently noticed that one-dimensional crystals possibly have discrete Poincar\'{e} symmetry, which contains discrete Lorentz and discrete time translational…
Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We present a performant and rigorous algorithm for certifying that a matrix is close to being a projection onto an irreducible subspace of a given group representation. This addresses a problem arising when one seeks solutions to…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
Crystalline materials can form different structural arrangements (i.e. polymorphs) with the same chemical composition, exhibiting distinct physical properties depending on how they were synthesized or the conditions under which they…
Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…
Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this paper, we use this property for the observability analysis of nonlinear PDEs with input and output. Based on a differential-geometric…
We study periodic crystalline spin textures in spinor condensates with dipolar interactions via a systematic symmetry analysis of the low-energy effective theory. By considering symmetry operations which combine real and spin space…
One versatile route to the creation of two-dimensional crystal structures on the nanometer to micrometer scale is the self-assembly of colloidal particles at an interface. Here, we explore the crystal phases that can be expected from the…
This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The major contribution of…
A spin space group provides a suitable way to fully exploit the symmetry of a spin arrangement with a negligible spin-orbit coupling. There has been a growing interest in applying spin symmetry analysis with the spin space group in the…
Multiple clustering has gathered significant attention in recent years due to its potential to reveal multiple hidden structures of the data from different perspectives. Most of multiple clustering methods first derive feature…
Excited-state calculations, notably for quasiparticle band structures, are nowadays routinely performed within the GW approximation for the electronic self-energy. Nevertheless, certain numerical approximations and simplifications are still…
There are exactly three finite subgroups of SU(2) that act irreducibly in the spin 1 representation, namely the binary tetrahedral, binary octahedral and binary icosahedral groups. In previous papers I have shown how the binary tetrahedral…