Local Electronic Structure around a Single Impurity in an Anderson Lattice Model for Topological Kondo Insulators

Shortly after the discovery of topological band insulators, the topological Kondo insulators (TKIs) have also been theoretically predicted. The latter has ignited revival interest in the properties of Kondo insulators. Currently, the feasibility of topological nature in SmB$_6$ has been intensively analyzed by several complementary probes. Here by starting with a minimal-orbital Anderson lattice model, we explore the local electronic structure in a Kondo insulator. We show that the two strong topological regimes sandwiching the weak topological regime give rise to a single Dirac cone, which is located near the center or corner of the surface Brillouin zone. We further find that, when a single impurity is placed on the surface, low-energy resonance states are induced in the weak scattering limit for the strong TKI regimes and the resonance level moves monotonically across the hybridization gap with the strength of impurity scattering potential; while low energy states can only be induced in the unitary scattering limit for the weak TKI regime, where the resonance level moves universally toward the center of the hybridization gap. These impurity induced low-energy quasiparticles will lead to characteristic signatures in scanning tunneling microscopy/spectroscopy, which has recently found success in probing into exotic properties in heavy fermion systems.Comment: 8 pages with 4 eps figures embedded, references update

Berry phase in graphene: a semiclassical perspective

We derive a semiclassical expression for the Green's function in graphene, in which the presence of a semiclassical phase is made apparent. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. These phases coincide for the perfectly linear Dirac dispersion relation. They differ however when a gap is opened at the Dirac point. We furthermore present several applications of our semiclassical formalism. In particular we provide, for various configurations, a semiclassical derivation of the electron's Landau levels, illustrating the role of the semiclassical ``Berry-like'' phas

Renormalization Group in Quantum Mechanics

We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of the well known pathologies which appear in quantum field theory due to the sharp cutoff. We show that for an arbitrary background path the usual local form of the action is not preserved by the flow. To cure this problem we consider a more general action than usual which is stable by the renormalization group flow. It allows us to obtain a new consistent renormalization group equation for the action.Comment: 20 page

Large-scale bottleneck effect in two-dimensional turbulence

The bottleneck phenomenon in three-dimensional turbulence is generally associated with the dissipation range of the energy spectrum. In the present work, it is shown by using a two-point closure theory, that in two-dimensional turbulence it is possible to observe a bottleneck at the large scales, due to the effect of friction on the inverse energy cascade. This large-scale bottleneck is directly related to the process of energy condensation, the pile-up of energy at wavenumbers corresponding to the domain size. The link between the use of friction and the creation of space-filling structures is discussed and it is concluded that the careless use of hypofriction might reduce the inertial range of the energy spectrum

Rank penalized estimation of a quantum system

We introduce a new method to reconstruct the density matrix $\rho$ of a system of $n$-qubits and estimate its rank $d$ from data obtained by quantum state tomography measurements repeated $m$ times. The procedure consists in minimizing the risk of a linear estimator $\hat{\rho}$ of $\rho$ penalized by given rank (from 1 to $2^n$), where $\hat{\rho}$ is previously obtained by the moment method. We obtain simultaneously an estimator of the rank and the resulting density matrix associated to this rank. We establish an upper bound for the error of penalized estimator, evaluated with the Frobenius norm, which is of order $dn(4/3)^n /m$ and consistency for the estimator of the rank. The proposed methodology is computationaly efficient and is illustrated with some example states and real experimental data sets

A Test of the Collisional Dark Matter Hypothesis from Cluster Lensing

Spergel & Steinhardt proposed the possibility that the dark matter particles are self-interacting, as a solution to two discrepancies between the predictions of cold dark matter models and the observations: first, the observed dark matter distribution in some dwarf galaxies has large, constant-density cores, as opposed to the predicted central cusps; and second, small satellites of normal galaxies are much less abundant than predicted. The dark matter self-interaction would produce isothermal cores in halos, and would also expel the dark matter particles from dwarfs orbiting within large halos. However, another inevitable consequence of the model is that halos should become spherical once most particles have interacted. Here, I rule out this model by the fact that the innermost regions of dark matter halos in massive clusters of galaxies are elliptical, as shown by gravitational lensing and other observations. The absence of collisions in the lensing cores of massive clusters implies that any dark matter self-interaction is too weak to have affected the observed density profiles in the dark-matter dominated dwarf galaxies, or to have eased the destruction of dwarf satellites in galactic halos. If $s_x$ is the cross section and $m_x$ the mass of the dark matter particle, then s_x/m_x < 10^{-25.5} \cm^2/\gev.Comment: to appear in ApJ, January 1 200

Appearance of Gauge Fields and Forces beyond the adiabatic approximation

We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix valued quantum Hamiltonians. The results are illustrated by several physical relevant examples

Higgs mechanism in a light front formulation

We give a simple derivation of the Higgs mechanism in an abelian light front field theory. It is based on a finite volume quantization with antiperiodic scalar fields and a periodic gauge field. An infinite set of degenerate vacua in the form of coherent states of the scalar field that minimize the light front energy, is constructed. The corresponding effective Hamiltonian descibes a massive vector field whose third component is generated by the would-be Goldstone boson. This mechanism, understood here quantum mechanically in the form analogous to the space-like quantization, is derived without gauge fixing as well as in the unitary and the light cone gauge.Comment: 9 page

Continuum limit of self-driven particles with orientation interaction

We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator

Some Applications of the Lee-Yang Theorem

For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h, for Re h > 0 or Re h < 0. A survey of models known to have the Lee-Yang property is given. We conclude by describing various applications of the aforementioned analyticity in h.Comment: 16 page