相关论文: Isospectral and square root Cholesky photonic latt…
Second harmonic generation is a powerful tool directly connected to the symmetry of materials. Phase transitions, lattice rotations or electromagnetic coupling in multiferroic compounds can be revealed by using second harmonic…
In this paper, we prove that if the matrix of the linear system is symetric, the Cholesky decomposition can be obtained from the Gauss elimination method without pivoting, without proving that the matrix of the system is positive definite.
Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing…
The gap symmetries of superconductivity are studied in this work. It is found that the gap symmetries are simply determined by the 4-fold rotational symmetries of the coupling potential on neighbor sites. A local on-site coupling potential…
We propose a novel geometry for integrated photonic devices that can be used as isolators and polarization splitters based on engineered photonic lattices. Starting from optical waveguide arrays that mimic Fock space representation of a…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
Coalescing involves gluing one or more rooted graphs onto another graph. Under specific conditions, it is possible to start with cospectral graphs that are coalesced in similar ways that will result in new cospectral graphs. We present a…
Bipartite quantum systems from the chiral universality classes admit topologically protected zero modes at point defects. However, in two-dimensional systems these states can be difficult to separate from compacton-like localized states…
We present an algorithm where only the Cholesky basis is determined in the decomposition procedure. This allows for improved screening and a partitioned matrix decomposition scheme, both of which significantly reduce memory usage and…
We introduce a general strategy for defining distributions over the space of sparse symmetric positive definite matrices. Our method utilizes the Cholesky factorization of the precision matrix, imposing sparsity through constraints on its…
Atom arrays have emerged as a powerful platform for quantum light-matter interfaces, yet single-species arrays are constrained by in-plane symmetry, restricting polarization control. Here we investigate the cooperative optical response of…
Algorithms come with multiple variants which are obtained by changing the mathematical approach from which the algorithm is derived. These variants offer a wide spectrum of performance when implemented on a multicore platform and we seek to…
This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently…
In scenarios that stabilize the electroweak scale, the top quark is typically accompanied by partner particles. In this work, we demonstrate how extended stabilizing symmetries can yield scalar or fermionic top partners that transform as…
Supersymmetry broken geometrically in extra dimensions naturally leads to a nearly degenerate spectrum for superparticles, ameliorating the bounds from the current searches at the LHC. We present a minimal such model with a single extra…
Photonic molecules, i.e. artificial structures composed of coherently coupled optical cavities, are paradigmatic systems for investigating fundamental phenomena across photonics, quantum optics and topological physics. In recent years,…
Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
We construct families of symmetric, antisymmetric, and asymmetric solitary modes in one-dimensional bichromatic lattices with the second-harmonic-generating ($\chi ^{(2)}$) nonlinearity concentrated at a pair of sites placed at distance…
Integrated Jx photonic lattices, inspired by the quantum harmonic oscillator and due to their equidistant eigenvalue spectrum, have been proven extremely useful for various applications, such as perfect imaging and coherent transfer of…