Lie algebra cohomology and group structure of gauge theories

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{\dagger}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other charge $Q^{\dagger}$.Comment: 24 pages, RevTex, Revised version submitted to J. Math. Phy

Emergent Geometry and Quantum Gravity

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of symplectic structure \omega in terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page

Optically mediated nonlinear quantum optomechanics

We consider theoretically the optomechanical interaction of several mechanical modes with a single quantized cavity field mode for linear and quadratic coupling. We focus specifically on situations where the optical dissipation is the dominant source of damping, in which case the optical field can be adiabatically eliminated, resulting in effective multimode interactions between the mechanical modes. In the case of linear coupling, the coherent contribution to the interaction can be exploited e.g. in quantum state swapping protocols, while the incoherent part leads to significant modifications of cold damping or amplification from the single-mode situation. Quadratic coupling can result in a wealth of possible effective interactions including the analogs of second-harmonic generation and four-wave mixing in nonlinear optics, with specific forms depending sensitively on the sign of the coupling. The cavity-mediated mechanical interaction of two modes is investigated in two limiting cases, the resolved sideband and the Doppler regime. As an illustrative application of the formal analysis we discuss in some detail a two-mode system where a Bose-Einstein condensate is optomechanically linearly coupled to the moving end mirror of a Fabry-P\'erot cavity.Comment: 11 pages, 8 figure

Charge states and magnetic ordering in LaMnO3/SrTiO3 superlattices

We investigated the magnetic and optical properties of [(LaMnO3)n/(SrTiO3)8]20 (n = 1, 2, and 8) superlattices grown by pulsed laser deposition. We found a weak ferromagnetic and semiconducting state developed in all superlattices. An analysis of the optical conductivity showed that the LaMnO3 layers in the superlattices were slightly doped. The amount of doping was almost identical regardless of the LaMnO3 layer thickness up to eight unit cells, suggesting that the effect is not limited to the interface. On the other hand, the magnetic ordering became less stable as the LaMnO3 layer thickness decreased, probably due to a dimensional effect.Comment: 17 pages including 4 figures, accepted for publication in Phys. Rev.

Nanopillar Arrays on Semiconductor Membranes as Electron Emission Amplifiers

A new transmission-type electron multiplier was fabricated from silicon-on-insulator (SOI) material by integrating an array of one dimensional (1D) silicon nanopillars onto a two dimensional (2D) silicon membrane. Primary electrons are injected into the nanopillar-membrane system from the flat surface of the membrane, while electron emission from the other side is probed by an anode. The secondary electron yield (SEY) from nanopillars is found to be about 1.8 times that of plane silicon membrane. This gain in electron number is slightly enhanced by the electric field applied from the anode. Further optimization of the dimensions of nanopillars and membrane and application of field emission promise an even higher gain for detector applications and allow for probing of electronic/mechanical excitations in nanopillar-membrane system excited by incident particles or radiation.Comment: 4 figure

Electronic interferometer capacitively coupled to a quantum dot

We theoretically study electron interference in a ballistic electronic interferometer capacitively coupled to a quantum dot. The visibility of the interference is reduced when the dot has degenerate ground states with different excess charges. The degree of the reduction depends on system parameters such as the strength of the capacitive coupling, and the dependence is analyzed in the regime where the dwell time of electrons in the dot is much longer than the electron flight time through the interferometry region coupled to the dot. The result is consistent with recent experimental data.Comment: 4 pages, 2 figure

Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

Effect of sintering temperature under high pressure in the uperconductivity for MgB2

We report the effect of the sintering temperature on the superconductivity of MgB2 pellets prepared under a high pressure of 3 GPa. The superconducting properties of the non-heated MgB2 in this high pressure were poor. However, as the sintering temperature increased, the superconducting properties were vastly enhanced, which was shown by the narrow transition width for the resistivity and the low-field magnetizations. This shows that heat treatment under high pressure is essential to improve superconducting properties. These changes were found to be closely related to changes in the surface morphology observed using scanning electron microscopy.Comment: 3 Pages including 3 figure

Towards A Background Independent Quantum Gravity

We recapitulate the scheme of emergent gravity to highlight how a background independent quantum gravity can be defined by quantizing spacetime itself.Comment: 25 pages, 2 figures, Proceedings of 7th International Conference "Quantum Theory and Symmetries" (QTS-7) in Prague, Czech Republic, August, 201