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We propose a scheme to determine the energy-band dispersion of quasicrystals which does not require any periodic approximation and which directly provides the correct structure of the extended Brillouin zones. In the gap labelling viewpoint, this allow to transpose the measure of the integrated density-of-states to the measure of the effective Brillouin-zone areas that are uniquely determined by the position of the Bragg peaks. Moreover we show that the Bragg vectors can be determined by the stability analysis of the law of recurrence used to generate the quasicrystal. Our analysis of the gap labelling in the quasi-momentum space opens the way to an experimental proof of the gap labelling itself within the framework of an optics experiment, polaritons, or with ultracold atoms.
The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by u
We investigate the formation of a two-dimensional quasicrystal in a monodisperse system, using molecular dynamics simulations of hard sphere particles interacting via a two-dimensional square-well potential. We find that more than one stable crystall
A large set of recent experiments has been exploring topological transport in bosonic systems, e.g. of photons or phonons. In the vast majority, time-reversal symmetry is preserved, and band structures are engineered by a suitable choice of geometry,
We report an efficient algorithm for calculating momentum-space integrals in solid state systems on modern graphics processing units (GPUs). Our algorithm is based on the tetrahedron method, which we demonstrate to be ideally suited for execution in
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation gradient $math