相关论文: A phonon irreducible representations calculator

A general method is presented to unfold band structures of first-principles super-cell calculations with proper spectral weight, allowing easier visualization of the electronic structure and the degree of broken translational symmetry. The…

An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and…

This manuscript puts forward and verifies an analytical approach to design phononic crystals that feature a bandgap at the lowest possible frequencies. This new approach is verified against numerical optimization. It rests on the exact form…

Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced eigenstates in addition to the degenerate energy. Also different from a typical EP, the…

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…

Phonons play a crucial role in many properties of solid state systems, such as thermal and electrical conductivity, neutron scattering and associated effects or superconductivity. Hence, it is expected that topological phonons will also…

We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our…

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

We show that two-dimensional phononic crystals exhibit Dirac cone dispersion at k=0 by exploiting dipole and quadrupole accidental degeneracy. While the equi-frequency surface of Dirac cone modes is isotropic, such systems exhibit…

We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…

We introduce SP$\mathbb{Q}$R, a new Mathematica package for the division and elimination of variables from polynomial systems. SP$\mathbb{Q}$R works by sampling and reconstructing results over finite fields, in an analogous manner to many…

In the field of phononics, periodic patterning controls vibrations and thereby the flow of heat and sound in matter. Bandgaps arising in such phononic crystals realize low-dissipation vibrational modes and enable applications towards…

Novel physical concepts that originate from quantum mechanics, such as non-Hermitian systems (dealing mostly with PT and anti-PT symmetry) and bound states in the continuum (BICs), have attracted great interest in the optics and photonics…

Time-resolved spectroscopy is an important tool for unraveling the minute details of structural changes of molecules of biological and technological significance. The nonlinear femtosecond signals detected for such systems must be…

Plane-based Geometric Algebra (PGA) has revealed points in a $d$-dimensional pseudo-Euclidean space $\mathbb{R}_{p,q,1}$ to be represented by $d$-blades rather than vectors. This discovery allows points to be factored into $d$ orthogonal…

The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules…

We prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R. As applications, we give…

Topological non-trivial band structures are the core problem in the field of topological materials. In this paper, we investigate the topological band structure in a system with controllable Dirac points from the perspective of wave packet…

This expository article supplies the mathematical background underpinning the braid representation calculator introduced in arXiv:2212.00831; those representations describe the sets of logic gates available to a topological quantum computer…

Let G be a finite group. By Riemann's Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic…