Transport and Conductance in Fibonacci Graphene Superlattices with Electric and Magnetic Potentials

We investigate the electron transport and conductance properties in Fibonacci quasi-periodic graphene superlattices with electrostatic barriers and magnetic vector potentials.It is found that a new Dirac point appears in the band structure of graphene superlattice and the position of the Dirac point is exactly located at the energy corresponding to the zero-averaged wave number.The magnetic and electric potentials modify the energy band structure and transmission spectrum in entirely diverse ways.In addition,the angular-dependent transmission is blocked by the potential barriers at certain incident angles due to the appearance of the evanescent states.The effects of lattice constants and different potentials on angular-averaged conductance are also discussed.     

QCD Dirac spectrum and components of the gauge field

We analyze the relation between the Dirac spectrum and the gauge field in SU(3) lattice QCD. We focus on how a certain component of the gauge field is related to the Dirac spectrum. First, we consider momentum components of the gauge field. It turns out that the broad momentum region is relevant for the low-lying Dirac spectrum and topological charges. The connection with chiral random matrix theory is also discussed. Second, we consider an SU(2) subgroup component of the SU(3) gauge field. The SU(2) subgroup component behaves like the SU(2) gauge field in the low-lying Dirac spectrum.     

The Dirac equation in Schwarzschild black hole coupled to a stationary electromagnetic field

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzschild solution to an external, stationary electromagnetic field. The set of equations representing the uncharged Dirac particle in the Newman–Penrose formalism is decoupled into a radial and an angular parts. We obtain exact analytical solutions of the angular equations. We manage to obtain the radial wave equations with effective potentials. Finally, we study the potentials by plotting them as a function of radial distance and examine the effect of the twisting parameter and the frequencies on the potentials.     

The nonlinear Dirac equation in Bose-Einstein condensates: Foundation and symmetries

We show that Bose-Einstein condensates in a honeycomb optical lattice can be described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i.e., Poincaré covariance, the nonlinear Dirac equation for Bose-Einstein condensates breaks this symmetry. We present a rigorous derivation of the nonlinear Dirac equation from first principles. We provide a thorough discussion of all symmetries broken and maintained.     

Overlap valence quarks on a twisted mass sea: A case study for mixed action lattice QCD

We discuss a lattice QCD mixed action investigation employing Wilson maximally twisted mass sea and overlap valence fermions. Using four values of the lattice spacing, we demonstrate that the overlap Dirac operator assumes a point-like locality in the continuum limit. We also show that by adopting suitable matching conditions for the sea and valence theories a consistent continuum limit for the pion decay constant and light baryon masses can be obtained. Finally, we confront results for sea–valence mixed meson masses and the valence scalar correlator with corresponding expressions of chiral perturbation theory. This allows us to extract low energy constants of mixed action chiral perturbation which characterize the strength of unitarity violations in our mixed action setup.     

有限空间中经典场的正则量子化

从离散的角度研究带边界的1+1维经典标量场和Dirac场的正则量子化问题. 与以往不同的是, 这里将时间和空间两个变量同时进行变步长的离散, 应用变步长离散的变分原理, 得到离散形式的运动方程、边界条件和能量守恒的表达式. 然后, 根据Dirac理论, 将边界条件当作初级约束, 将边界条件和内在约束统一处理. 研究表明, 采用此方法, 不仅在每个离散的时空格点上能够建立起Dirac括号, 从而可以完成该模型的正则量子化;而且, 该方法还保持了离散情况下的能量守恒.     

Cold atom simulation of interacting relativistic quantum field theories

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.     

On the Geometry of the Dirac Matter with the Fermionic Potentials and its Quantum Properties

We consider the torsional completion of gravity with electrodynamics for Dirac matter fields; we will see that these Dirac matter field equations will develop torsionally-induced non-linear interactions, which can be manipulated in order to be rearranged in the form of self-fermion potentials of a specific structure: we will see that this structure is formally equivalent to the one arising from quantum properties.     

Variational approach for the effects of periodic modulations on the spectrum of massless Dirac fermion

In the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic field. We analyze the influence of the lateral periodic modulations in one direction, created by these oscillating electric and magnetic fields, on Dirac like Landau levels depending on amplitudes and periods of the field modulations. We compare our theoretical results with those found within the framework of non-degenerate perturbation theory. We found that the technique presented here yields energies lower than that obtained by the perturbation calculation, and thus gives more stable solutions for the electronic spectrum of massless Dirac fermion subjected to a magnetic field perpendicular to graphene layer under the influence of additional periodic potentials.     

Unquenched complex dirac spectra at nonzero chemical potential: two-color QCD lattice data versus matrix model

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses.     

Stability and decay of the Dirac vacuum in external gauge fields

We consider various gauge fields coupled to the free Dirac equation according to symmetry principles. The gauge fields are treated as classical, unquantized fields. Sufficiently strong time-independent fields may give rise to spontaneous particle creation and to the decay of the symmetric Dirac vacuum into a new ground state with broken symmetry. The vacuum stability of the Dirac field is studied for the cases of external electromagnetic (U(1)), gravitational (Poincaré group including torsion) and Yang-Mills (SU(2)) potentials.     

Random walk construction of spinor fields on a three-dimensional lattice

Euclidean-invariant Klein-Gordon, Dirac and massive Chern-Simons field theories are constructed in terms of a random walk with a spin factor on a three-dimensional lattice. We exactly calculate the free energy and the correlation functions which allow us to obtain the critical diffusion constant and associated critical exponents. It is pointed out that these critical exponents do not satisfy the hyper-scaling relation but the scaling inequalities. We take the continuum limit of this theory on the basis of these analyses. We check the universality of the obtained results on other lattice structures such as the triclinic lattice and the body-centered lattice.     

Generalizations of MICZ-Kepler system

We discuss the generalizations of the MICZ-Kepler system (the system describing the motion of the charged particle in the field of Dirac dyon), to the curved spaces, arbitrary potentials, and to the multidyon background.     

Electrical and optoelectronic properties of graphene Schottky contact on Si-nanowire arrays with and without H2O2 treatment

We show a methodology for how to construct Dirac points that occur at the corners of Brillouin zone as the Photonic counterparts of graphene. We use a triangular lattice with circular holes on a silicon substrate to create a Coupled Photonic Crystal Resonator Array (CPCRA) which its cavity resonators play the role of carbon atoms in graphene. At first we draw the band structure of our CPCRA using the tight-binding method. For this purpose we first designed a cavity which its resonant frequency is approximately at the middle of the first H-polarization band gap of the basis triangular lattice. Then we obtained dipole modes and magnetic field distribution of this cavity using the Finite Element Method (FEM). Finally we drew the two bands that construct the Dirac points together with the frequency contour plots for both bands and compared with the Plane Wave Expansion (PWE) and FEM results to prove the existence of Dirac point in the H-polarization band structure of lattices with air holes.     

Quasinormal frequencies of asymptotically flat two-dimensional black holes

We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrödinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.     

Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit

We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term κ. We also investigate the energy eigenvalues of the Dirac particles for the well-known Kratzer-Fues and modified Kratzer potentials which are Mie-type potentials.     

Index of a family of lattice Dirac operators and its relation to the non-Abelian anomaly on the lattice

In the continuum, a topological obstruction to the vanishing of the non-Abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac operators in 2n dimensions. In this paper an analogous result is derived for chiral fermions on the lattice in the overlap formulation. This involves deriving an index theorem for a family of lattice Dirac operators satisfying the Ginsparg-Wilson relation. The index density is proportional to Lüscher's topological field in 2n+2 dimensions.     

Single field baryogenesis

We propose a new variant of the Affleck-Dine baryogenesis mechanism in which a rolling scalar field couples directly to left- and right-handed neutrinos, generating a Dirac mass term through neutrino Yukawa interactions. In this setup, there are no explicitly CP violating couplings in the Lagrangian. The rolling scalar field is also taken to be uncharged under the B - L quantum numbers. During the phase of rolling, scalar field decays generate a nonvanishing number density of left-handed neutrinos, which then induce a net baryon number density via electroweak sphaleron transitions.