Demonstrating Entanglement by Testing Bell's Theorem in Majorana Wires

We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is viable with realistic system parameters, simple "keyboard" gating, and projective measurement. Simulation results indicate entanglement can be demonstrated with moderately accurate gate operations. In addition to providing further evidence for the existence of the Majorana bound states, our proposal could be used as an experimental stepping stone to more complicated braiding experiments.Comment: 11 pages, 8 figures, 2 table

Nonequilibrium noise correlations in a point contact of helical edge states

We investigate theoretically the nonequilibrium finite-frequency current noise in a four-terminal quantum point contact of interacting helical edge states at a finite bias voltage. Special focus is put on the effects of the single-particle and two-particle scattering between the two helical edge states on the fractional charge quasiparticle excitations shown in the nonequilibrium current noise spectra. Via the Keldysh perturbative approach, we find that the effects of the single-particle and the two-particle scattering processes on the current noise depend sensitively on the Luttinger liquid parameter. Moreover, the Fano factors for the auto- and cross correlations of the currents in the terminals are distinct from the ones for tunneling between the chiral edge states in the quantum Hall liquid. The current noise spectra in the single-particle-scattering-dominated and the two-particle-scattering-dominated regime are shown. Experimental implications of our results on the transport through the helical edges in two-dimensional topological insulators are discussed.Comment: 10 pages, 8 figure

Conformal Affine Toda Soliton and Moduli of IIB Superstring on AdS5×S5AdS_5\times S^5

In this paper we interpret the hidden symmetry of the moduli space of IIB superstring on $AdS_{5}\times S^{5}$ in terms of the chiral embedding in $AdS_{5}$, which turns to be the $\mathbb{CP}^{3}$ conformal affine Toda model. We review how the position $\mu$ of poles in the Riemann-Hilbert formulation of dressing transformation and how the value of loop parameters $\mu$ in the vertex operator of affine algebra determines the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinize the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients $\mu$ of twistor.Comment: Final version, Misprints corrected, Note adde

On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra

With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can be put together to form a single algebra which can be regarded as an elliptic deformation of the universal enveloping algebra of \hat{g}, where g is any classical simply-laced Lie algebra.Comment: LaTeX file, 9 pages. Errors in Serre relation corrected. Two references to Awata,H. et al adde

Necessary and sufficient conditions for local creation of quantum discord

We show that a local channel cannot create quantum discord (QD) for zero QD states of size $d\geq3$ if and only if either it is a completely decohering channel or it is a nontrivial isotropic channel. For the qubit case this propertiy is additionally characteristic to the completely decohering channel or the commutativity-preserving unital channel. In particular, the exact forms of the completely decohering channel and the commutativity-preserving unital qubit channel are proposed. Consequently, our results confirm and improve the conjecture proposed by X. Hu et al. for the case of $d\geq3$ and improve the result proposed by A. Streltsov et al. for the qubit case. Furthermore, it is shown that a local channel nullifies QD in any state if and only if it is a completely decohering channel. Based on our results, some protocols of quantum information processing issues associated with QD, especially for the qubit case, would be experimentally accessible.Comment: 8 page

Soliton Solutions on Noncommutative Orbifold $ T^2/Z_4

In this paper, we explicitly construct a series of projectors on integral noncommutative orbifold $T^2/Z_4$ by extended $GHS$ constrution. They include integration of two arbitary functions with $Z_4$ symmetry. Our expressions possess manifest $Z_{4}$ symmetry. It is proved that the expression include all projectors with minimal trace and in their standard expansions, the eigen value functions of coefficient operators are continuous with respect to the arguments $k$ and $q$. Based on the integral expression, we alternately show the derivative expression in terms of the similar kernal to the integral one.Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a series of corresponding solitons.Comment: 18 pages, no figure; referrences adde

Deconfined fractional electric charges in graphene at high magnetic fields

The resistance at the charge neutral (Dirac) point was shown by Checkelsky et al in Phys. Rev. B 79, 115434 (2009) to diverge upon the application of a strong magnetic field normal to graphene. We argue that this divergence is the signature for a Kekule instability of graphene, which is induced by the magnetic field. We show that the strong magnetic field does not remove the zero modes that bind a fraction of the electron around vortices in the Kekule dimerization pattern, and that quenched disorder present in the system makes it energetically possible to separate the fractional charges. These findings, altogether, indicate that graphene can sustain deconfined fractionalized electrons.Comment: 11 pages, 2 figure

Capture and sorting of multiple cells by polarization-controlled three-beam interference

For the capture and sorting of multiple cells, a sensitive and highly efficient polarization-controlled three-beam interference set-up has been developed. With the theory of superposition of three beams, simulations on the influence of polarization angle upon the intensity distribution and the laser gradient force change with different polarization angles have been carried out. By controlling the polarization angle of the beams, various intensity distributions and different sizes of dots are obtained. We have experimentally observed multiple optical tweezers and the sorting of cells with different polarization angles, which are in accordance with the theoretical analysis. The experimental results have shown that the polarization angle affects the shapes and feature sizes of the interference patterns and the trapping force

Probing the fourth generation Majorana neutrino dark matter

Heavy fourth generation Majorana neutrino can be stable and contribute to a small fraction of the relic density of dark matter (DM) in the Universe. Due to its strong coupling to the standard model particles, it can be probed by the current direct detection experiments even it is a subdominant component of the whole halo DM. Assuming that it contributes to the same fraction of the local halo DM density as that of the DM relic density, we show that the current Xenon100 data constrain the mass of the stable Majorana neutrino to be greater than the mass of the top quark. In the mass range between 200 GeV and a few hundred GeV, the effective spin-independent cross section for the neutrino elastic scattering off nucleon is insensitive to the neutrino mass and is predicted to be $\sim 1.5\times 10^{-44} cm^2$, which can be reached by the direct DM search experiments soon. In the same mass region the predicted effective spin-dependent cross section for the heavy neutrino scattering off proton is in the range $2\times 10^{-40} cm^2\sim 2\times 10^{-39} cm^2$, which is within the reach of the ongoing IceCube experiment. We demonstrate such properties in a fourth generation model with the stability of the fourth Majorana neutrino protected by an additional generation-dependent U(1) gauge symmetry.Comment: 22 pages, 5 figures, discussions on collider searches included, to appear in Phys. Rev.