Mott physics in 2p2p electron dioxygenyl magnet : O2_{2}MMF6_{6} (MM=Sb, Pt)

We have investigated electronic structures and magnetic properties of O$_{2}$$M$F$_{6}$ ($M$=Sb, Pt), which are composed of two building blocks of strongly correlated electrons: O$_{2}^{+}$ dioxygenyls and $M$F$_{6}^{-}$ octahedra, by employing the first-principles electronic structure band method. For O$_{2}$SbF$_{6}$, as a reference system of O$_{2}$PtF$_{6}$, we have shown that the Coulomb correlation of O(2$p$) electrons drives the Mott insulating state. For O$_{2}$PtF$_{6}$, we have demonstrated that the Mott insulating state is induced by the combined effects of the Coulomb correlation of O(2$p$) and Pt(5$d$) electrons and the spin-orbit (SO) interaction of Pt(5$d$) states. The role of the SO interaction in forming the Mott insulating state of O$_{2}$PtF$_{6}$ is similar to the case of Sr$_{2}$IrO$_{4}$ that is a prototype of a SO induced Mott system with J$_{eff}=1/2$.Comment: 5 pages, 6 figure

Robustness analysis of magnetic torquer controlled spacecraft attitude dynamics

This paper describes a systematic approach to the robustness analysis of linear periodically time-varying (LPTV) systems. The method uses the technique known as Lifting to transform the original time-varying uncertain system into linear fractional transformation (LFT) form. The stability and performance robustness of the system to structured parametric uncertainty can then be analysed non-conservatively using the structured singular value μ. The method is applied to analyse the stability robustness of an attitude control law for a spacecraft controlled by magnetic torquer bars, whose linearised dynamics can naturally be written in linear periodically time-varying form. The proposed method allows maximum allowable levels of uncertainty, as well as worst-case uncertainty combinations to be computed. The destabilising effect of these uncertain parameter combinations is verified in time-domain simulations

Verbal paired associates and the hippocampus: The role of scenes

It is widely agreed that patients with bilateral hippocampal damage are impaired at binding pairs of words together. Consequently, the verbal paired associates (VPA) task has become emblematic of hippocampal function. This VPA deficit is not well understood and is particularly difficult for hippocampal theories with a visuospatial bias to explain (e.g., cognitive map and scene construction theories). Resolving the tension among hippocampal theories concerning the VPA could be important for leveraging a fuller understanding of hippocampal function. Notably, VPA tasks typically use high imagery concrete words and so conflate imagery and binding. To determine why VPA engages the hippocampus, we devised an fMRI encoding task involving closely matched pairs of scene words, pairs of object words, and pairs of very low imagery abstract words. We found that the anterior hippocampus was engaged during processing of both scene and object word pairs in comparison to abstract word pairs, despite binding occurring in all conditions. This was also the case when just subsequently remembered stimuli were considered. Moreover, for object word pairs, fMRI activity patterns in anterior hippocampus were more similar to those for scene imagery than object imagery. This was especially evident in participants who were high imagery users and not in mid and low imagery users. Overall, our results show that hippocampal engagement during VPA, even when object word pairs are involved, seems to be evoked by scene imagery rather than binding. This may help to resolve the issue that visuospatial hippocampal theories have in accounting for verbal memory

Antiferromagnetic and structural transitions in the superoxide KO2 from first principles: A 2p-electron system with spin-orbital-lattice coupling

KO2 exhibits concomitant antiferromagnetic (AFM) and structural transitions, both of which originate from the open-shell 2p electrons of O$_{2}^{-}$ molecules. The structural transition is accompanied by the coherent tilting of O$_{2}^{-}$ molecular axes. The interplay among the spin-orbital-lattice degrees of freedom in KO2 is investigated by employing the first-principles electronic structure theory and the kinetic-exchange interaction scheme. We have shown that the insulating nature of the high symmetry phase of KO2 at high temperature (T) arises from the combined effect of the spin-orbit coupling and the strong Coulomb correlation of O 2p electrons. In contrast, for the low symmetry phase of KO2 at low T with the tilted O$_{2}^{-}$ molecular axes, the band gap and the orbital ordering are driven by the combined effects of the crystal-field and the strong Coulomb correlation. We have verified that the emergence of the O 2p ferro-orbital ordering is essential to achieve the observed AFM structure for KO2

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

Role of non-magnetic disorder on the stability of U(1) spin liquid : A renormalization group study

Recently Hermele et. al claimed that the infrared (IR) fixed point of non-compact $QED_3$ is stable against instanton excitations in the limit of large flavors of massless Dirac fermions [cond-mat/0404751]. We investigate an effect of non-magnetic disorder on the deconfined quantum critical phase dubbed U(1) spin liquid ($U1SL$) in the context of quantum antiferromagnet. In the case of weak disorder the IR fixed point remains stable against the presence of both the instanton excitations and non-magnetic disorder and thus the $U1SL$ is sustained. In the case of strong disorder the IR fixed point becomes unstable against the disorder and the Anderson localization is expected to occur. We argue that in this case deconfinement of spinons does not occur since the Dirac fermion becomes massive owing to the localization