Quaternion Electromagnetism and the Relation with 2-Spinor Formalism

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary 'i' should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotationComment: Version published in journal Universe (2019

The temperature dependence of the local tunnelling conductance in cuprate superconductors with competing AF order

Based on the $t-t'-U-V$ model with proper chosen parameters for describing the cuprate superconductors, it is found that near the optimal doping at low temperature ($T$), only the pure d-wave superconductivity ($d$SC) prevails and the antiferromagnetic (AF) order is completely suppressed. At higher $T$, the AF order with stripe modulation and the accompanying charge order may emerge, and they could exist above the $d$SC transition temperature. We calculate the local differential tunnelling conductance (LDTC) from the local density of states (LDOS) and show that their energy variations are rather different from each other as $T$ increases. Although the calculated modulation periodicity in the LDTC/LDOS and bias energy dependence of the Fourier amplitude of LDTC in the "pseudogap" region are in good agreement with the recent STM experiment [Vershinin $et al.$, Science {\bf 303}, 1995 (2004)], we point out that some of the energy dependent features in the LDTC do not represent the intrinsic characteristics of the sample

Schwinger-Dyson Approach to Color Superconductivity in Dense QCD

The problem of color superconductivity in dense QCD is reconsidered in the improved rainbow approximation to the Schwinger-Dyson equation. The effect of the unscreened magnetic modes of gluons on the value of the color condensate is studied. In particular, it is shown that, at sufficiently large values of the chemical potential, these modes lead to the enhancement of the superconducting order parameter. The interplay between the instanton induced interaction and the one-gluon induced one in color superconductivity is discussed.Comment: REVTeX: 13 pages + 1 figure (new). Sec. 5 is revised, the old Sec. 6 is removed, a new Appendix is added. The final version accepted for publication in Phys. Rev.

High-Mobility Few-Layer Graphene Field Effect Transistors Fabricated on Epitaxial Ferroelectric Gate Oxides

The carrier mobility \mu of few-layer graphene (FLG) field-effect transistors increases ten-fold when the SiO_2 substrate is replaced by single-crystal epitaxial Pb(Zr_0.2Ti_0.8)O_3 (PZT). In the electron-only regime of the FLG, \mu reaches 7x10^4 cm^2/Vs at 300K for n = 2.4x10^12/cm^2, 70% of the intrinsic limit set by longitudinal acoustic (LA) phonons; it increases to 1.4x10^5 cm^2/Vs at low temperature. The temperature-dependent resistivity \rho(T) reveals a clear signature of LA phonon scattering, yielding a deformation potential D = 7.8+/-0.5 eV.Comment: 5 pages, 4 figure

Entanglement conditions for two-mode states: Applications

We examine the implications of several recently derived conditions [Hillery and Zubairy, Phys. Rev. Lett. 96, 050503 (2006)] for determining when a two-mode state is entangled. We first find examples of non-Gaussian states that satisfy these conditions. We then apply the entanglement conditions to the study of several linear devices, the beam splitter, the parametric amplifier, and the linear phase-insensitive amplifier. For the first two, we find conditions on the input states that guarantee that the output states are entangled. For the linear amplifier, we determine in the limit of high and no gain, when an entangled input leads to an entangled output. Finally, we show how application of two two-mode entanglement conditions to a three-mode state can serve as a test of genuine three-mode entanglement.Comment: 7 pages, no figures, replaced with published versio