Related papers: Double crystallographic groups and their represent…
Bipartite networks provide an effective resource for representing, characterizing, and modeling several abstract and real-world systems and structures involving binary relations, which include food webs, social interactions, and…
We analyze models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have many remarkable symmetry properties as…
Subjective classification of spiral galaxies is not sufficient for studying the effect of bars on their physical characteristics. In reality the problem is to comprehend the complex correlations in a multivariate parametric space.…
A new approximate scheme, DSUB$m$, is described for the coupled cluster method. We then apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet) spin-lattice models, namely: the $XXZ$ and the $XY$ models on the square lattice in…
The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…
Crystal structures are characterised by repeating atomic patterns within unit cells across three-dimensional space, posing unique challenges for graph-based representation learning. Current methods often overlook essential periodic boundary…
We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
Soft matters whose constituents are deformable are ubiquitous in nature especially in biological systems-including cells and their organelles-as well as in foams and emulsions. The capacity for deformation in these soft materials gives rise…
We construct integrable Hamiltonian systems with Lie bialgebras $({\bf g} , {\bf \tilde{g}})$ of the bi-symplectic type for which the Poisson-Lie groups ${\bf G}$ play the role of the phase spaces, and their dual Lie groups ${\bf {\tilde…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a…
We determine semisimple reductions of irreducible, 2-dimensional crystalline representations of the absolute Galois group $\text{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_{p^f})$. To this end, we provide explicit representatives for the…
Bloch wavefunctions in solids form a representation of crystalline symmetries. Recent studies revealed that symmetry representations in band structure can be used to diagnose the topological properties of weakly interacting materials. In…
A crystallographic arrangement is a set of linear hyperplanes satisfying a certain integrality property and decomposing the space into simplicial cones. Crystallographic arrangements were completely classified in a series of papers by…
Classical dimensional analysis has two limitations: (i) the computed dimensionless groups are not unique, and (ii) the analysis does not measure relative importance of the dimensionless groups. We propose two algorithms for estimating…
We establish Triebel-Lizorkin spaces in the Dunkl setting which are associated with finite reflection groups on the Euclidean space. The group structures induce two nonequivalent metrics: the Euclidean metric and the Dunkl metric. In this…
Branching of symplectic groups is not multiplicity-free. We describe a new approach to resolving these multiplicities that is based on studying the associated branching algebra $B$. The algebra $B$ is a graded algebra whose components…