Two-Dimensional Linear Dependencies on the Coordinate Time-Dependent Interaction in Relativistic Non-Commutative Phase Space

In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time-dependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis-Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.     

非对易相空间Dirac oscillator的研究

在极坐标系中研究了非对易相空间中的Dirac oscillator问题.研究显示:系统的波函数可以表示为合流超几何函数,而非对易相空间Dirac oscillator的量子行为类似于朗道问题.最后,对η=0和对易极限两种特殊情况进行了简单讨论.     

Hopping Parameter Expansion Technique in Noise Method for Disconnected Quark Loops

We investigate the effectiveness of the hopping parameter expansion(HPE) combined with the Z(2) noise method in the calculation of the trace of the inverse of Wilson's Dirac operator and some other disconnected contributions.A numerical comparison of the standard deviation for the Z(2) noise method and HPE with the Z(2) noise method is carried out. It is found that there are noise reductions in all the quantities we calculated using the HPE with the Z(2) noise method. For the trace of the inverse of Wilson's Dirac operator, the HPE can reduce the statistical error by about 60%.     

Sub-Poissonian shot noise in graphene

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper.Firstly,since the Dirac equation is described as a matrix equation in phase space,it is necessary to define the Wigner function as a matrix function in spinor space.Secondly,the matrix form of the Wigner function is proven to support the Dirac equation.Thirdly,by solving the Dirac equation,energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

On the Chirality Quantum Phase Transition of the Dirac Oscillator

Dirac oscillator subjects to an external magnetic field is re-examined. We show that this model can be mapped onto different quantum optics models if one insists to introduce two kinds of phonons which associate with the excitations of Dirac oscillator and magnetic field respectively. The conclusion about chirality quantum phase transition in the paper “Chirality quantum phase transition in the Dirac oscillator” (Bermudez et al. Phys. Rev. A, 77, 063815 2008) is only valid for a specific mapped quantum optics models rather than the Dirac oscillator itself. Thus, the conclusions about chirality quantum phase transitions in this paper are not universal.     

Vielbein with Mixed Dimensions and Gravitational Global Monopole in the Planar Phase of Superfluid 3He

JETP Letters - The planar phase of superfluid 3He has Dirac points in momentum space and the analog of Dirac monopole in the real space. Here, we discuss the combined effect of Dirac point and...     

Generalized phase factors and the interaction of Dirac particles

The nonintegrable phase factor approach to interactions is generalized in the case of a Dirac particle. The results differ significantly from those obtained in the Schrödinger theory and allow Dirac particles to be characterized by two fundamental couplings.     

Non-abelian Gauge Symmetry for Fields in Phase Space: a Realization of the Seiberg-Witten Non-abelian Gauge Theory

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic presentation of the Seiberg-Witten approach is carried out for non-abelian gauge in order to guide the calculation procedures. These results are realized by starting with the Lagrangian density for the free Dirac field in phase space. Then a field strength is derived, where the non-abelian gauge group is the SU(2), corresponding to an isospin (non-abelian) field theory in phase space. An application to nucleon is then discussed.

     

Semiclassical limit of the Dirac equation and the g minus 2 experiment

A relativistic mechanics for a Dirac particle is derived as the semi-classical limit of the Dirac equation. The theory resembles ordinary mechanics, except that some of the phase space variables are four by four matrices. We are able to derive from QED the spin precession equation of Bargmann, Michel, and Telegdi and find quantum corrections for inhomogeneous fields.     

Quantum criticality between topological and band insulators in 3+1 dimensions

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.     

A geometrical interpretation of the Pauli exclusion principle in classical field theory

It is shown that classical Dirac fields with the same couplings obey the Pauli exclusion principle in the following sense: If at a certain time two Dirac fields are in different states, they can never reach the same one. This is geometrically interpreted as analogous to the impossibility of crossing of trajectories in the phase space of a dynamical system. An application is made to a model in which extended particles are represented as solitary waves of a set of several fundamental, confined nonlinear Dirac fields, with the result that the same mechanism accounts both for fermion and boson behaviors.     

Nonquantized dirac monopoles and strings in the berry phase of anisotropic spin systems

The Berry phase of an anisotropic spin system that is adiabatically rotated along a closed circuit C is investigated. It is shown that the Berry phase consists of two contributions: (i) a geometric contribution which can be interpreted as the flux through C of a nonquantized Dirac monopole, and (ii) a topological contribution which can be interpreted as the flux through C of a Dirac string carrying a nonquantized flux, i.e., a spin analogue of the Aharonov-Bohm effect. Various experimental consequences of this novel effect are discussed.     

Classical Behavior of the Dirac Bispinor

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase factors, that the fermion must have a half-integral spin. We demonstrate that this is not the case and that the identical relativistic quantum mechanics can also be derived with the phase of the fermion rotating through the same angle as does the fermion itself. Under spatial rotation and Lorentz transformation the bispinor transforms as a four-vector like the potential and Dirac current. Previous attempts to provide this form of transformational behavior have foundered because a satisfactory current could not be derived.⁽¹⁴⁾     

Low-Frequency Noise in Gate Tunable Topological Insulator Nanowire Field Emission Transistor near the Dirac Point

Low-frequency flicker noise is usually associated with material defects or imperfection of fabrication procedure.Up to now,there is only very limited knowledge about flicker noise of the topological insulator,whose topologically protected conducting surface is theoretically immune to back scattering.To suppress the bulk conductivity we synthesize antimony doped Bi_2Se_3 nanowires and conduct transport measurements at cryogenic temperatures.The low-frequency current noise measurement shows that the noise amplitude at the high-drain current regime can be described by Hooge's empirical relationship,while the noise level is significantly lower than that predicted by Hooge's model near the Dirac point.Furthermore,different frequency responses of noise power spectrum density for specific drain currents at the low drain current regime indicate the complex origin of noise sources of topological insulator.     

Shot noise in ballistic graphene

We have investigated shot noise in graphene field effect devices in the temperature range of 4.2-30 K at low frequency (f=600-850 MHz). We find that for our graphene samples with a large width over length ratio W/L, the Fano factor F reaches a maximum F ~ 1/3 at the Dirac point and that it decreases strongly with increasing charge density. For smaller W/L, the Fano factor at Dirac point is significantly lower. Our results are in good agreement with the theory describing that transport at the Dirac point in clean graphene arises from evanescent electronic states.     

Simulation and detection of dirac fermions with cold atoms in an optical lattice

We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.     

The Wigner Functions for a Spin-1/2 Relativistic Particle in the Presence of Magnetic Field

This paper provides a study of Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field. Since the Dirac equation is described as a matrix equation, it is necessary to describe the Wigner function as a matrix function in phase space. What’s more, this function is then proved to satisfy the Dirac equation with ⋆-product. Finally, by solving the ⋆-product Dirac equation, the energy levels as well as the Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field are obtained.     

与不变量有关的幺正变换方法和含时均匀电场中的量子Dirac场的演化

在推广的不变量理论的基础上,运用与不变量有关的幺正变换方法研究了含时均匀电场下的量子Dirac场的演化,求解了Dirac场的泛函Schrdinger方程,得到了方程的精确解以及对应的总相位,总相位包括动力学相和几何相(Aharonov-Anandan phase). 关键词：