The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated, and characterized up to a measure zero set, by means of the BombieriTaylor conjecture, for Bragg peaks, and of another conjecture that we call AubryGodrèche-Luck conjecture, for the singular continuous component. The decomposition of the Fourier transform of the weighted Dirac comb is obtained in terms of temp...

We present a coherent picture of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz invariant local Lagrangian, when combined with Green’s functions defined in terms of time ordered products, ensure causality regardless of statistics. The Feynman’s m−iǫ prescription ensures the positive energy condition regardless of statistics, and the abnorma...

We measure the temperature-dependent carrier density and resistivity of the topological surface state of thin exfoliated Bi(2)Se(3) in the absence of bulk conduction. When the gate-tuned chemical potential is near or below the Dirac point, the carrier density is strongly temperature-dependent, reflecting thermal activation from the nearby bulk valence band, while, above the Dirac point, unipola...

Using scanning tunneling spectroscopy, we study a 3D topological insulator Bi(2)Te(3) with a periodic structural deformation (buckling). The buckled surface allows us to measure the response of Dirac electrons in a magnetic field to the presence of a well-defined potential variation. We find that while the n=0 Landau level exhibits a 12 meV energy shift across the buckled structure at 7 T, the ...

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane E_{1u} lattice vibration at 6.3  μm. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the K point. We observe that lattice modulation causes anomalous carrier dynamics, with the D...

Using Dirac Notation as a powerful tool, we investigate the three classical Information Retrieval (IR) models and some their extensions. We show that almost all such models can be described by vectors in Occupation Number Representations (ONR) of Fock spaces with various specifications on, e.g., occupation number, inner product or termterm interactions. As important cases of study, Concept Fock...

Complete eigenvalue spectra of the staggered Dirac operator in quenched 4d compact QED are studied on 83 × 4 and 83 × 6 lattices. We investigate the behavior of the nearest-neighbor spacing distribution P (s) as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble...

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from the behavior of non-relativistic electrons seen in traditional atomic and impurity systems 1-3. Surprisingly, many key theoretical predictions for this ultra-relativistic regime have...

Fermi surfaces are basic objects in solid state physics and in the spectral theory of periodic operators. We define several measures connected to Fermi surfaces and study their measure theoretic properties. From this we get absence of singular continuous spectrum and of singular continuous components in the density of states for symmetric periodic elliptic differential operators acting on vecto...

Fermi surfaces are basic objects in solid state physics and in the spectral theory of periodic operators. We deene several measures connected to Fermi surfaces and study their measure theoretic properties. From this we get absence of singular continuous spectrum and of singular continuous components in the density of states for symmetric periodic elliptic diierential operators acting on vector ...