Noncommutative geometry of the quantum clock

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.     

Decoherence of quantum Brownian motion in noncommutative space

The decoherence of a harmonic oscillator under two-dimensional quantum Brownian motion on a noncommutative plane is investigated. The interaction with the environment is considered by two separate models so-called coupled and uncoupled. The two-dimensional master equation and its noncommutative counterpart are derived for both employed models. The rate of the linear entropy (predictability sieve) is chosen as a criterion to investigate the purity in the presence of the space noncommutativity. Besides, a two-dimensional charged harmonic oscillator on a plane which is imposed by a perpendicular magnetic field is introduced as a realization of our model. Therefore, our approach provides a formalism to investigate the influence of the magnetic field on the decoherence of the pure states. We show that in the high magnetic field limit the rate of the decoherence will be decreased.     

A new characterization of the Berger sphere in complex projective space

We give a complete classification of Lagrangian immersions of homogeneous 3-manifolds (the Berger spheres, the Heisenberg group ${\text{Nil}}_3$, the universal covering of the Lie group $\text{PSL}(2,\mathbb{R})$ and the Lie group ${\text{Sol}}_3$) in 3-dimensional complex space forms. As a corollary, we get a new characterization of the Berger sphere in complex projective space.     

Trigonally-compressed octahedral geometry of hexaamminecobalt(III) complex cation in aqueous solution investigated from the electronic spectra

Electronic spectra of hexaamminecobalt(III) complex cation in aqueous solution were analyzed to obtain spectral components. Subsequently, based on the spectral components, the coordination geometry around the cobalt(III) ion was investigated, using the reverse angular overlap model method. The result indicates that the geometry is a trigonally compressed octahedron with the polar angle of 57.9?±?1.0° under D_3d symmetry, where the polar angle is the angle between the trigonal axis and the Co–N bond. From this angle, the top and side N–Co–N bond angles are calculated as 94.4° and 85.6°, respectively. The density functional theory computation supported this trigonally compressed structure in aqueous solution.