At very large Reynolds numbers the Navier-Stokes equations can possess a pair of large stationary vortices. This seemingly counter-intuitive phenomenon seems to be true in two-dimensions, and is demonstrated by numerically computing many Kolmogorov flows.

The nature of the Mott transition is discussed based on recent theoretical results for the one- and two-dimensional Hubbard models. The Mott transition is characterized by freezing of the charge degrees of freedom in a single-particle excitation that leads continuously to the spin excitation of the Mott insulator. Various anomalous features observed in cuprate high-temperature superconductors are explained in a unified manner as properties of a two-dimensional system near the Mott transition.

We report structural and electronic properties of molecular layered superconductors including polar molecules in an insulating layer, κ_H-(DMEDO-TSeF)₂[Au(CN)₄](THF) and the third polymorph of the organic superconductor (BEDT-TTF)₂ Ag(CF₃)₄(TCE). For the first compound, the angular-dependent magnetoresistance shows incoherent interlayer transport. However, two closed Fermi surfaces are observed in quantum oscillation. This indicates that crystallographically independent layers have different charge densities, i.e. interlayer charge disproportionation, which is due to the electric dipole of THF. For the later compound, the crystal consists of alternating stacks of two types of donor sheets, κ- and α′-types, and the unit cell includes four donor layers. This structure is similar to another high-T_c phase, in which the unit cell contains two donor layers. The superconducting transition temperatures are approximately 11.0 and 9.5 K for the four-layered and two-layered phases, respectively. Superconductivity is attributed to the κ-type conducting layer, because the α′-type layer is in a charge-ordered state. This is in agreement with the de Haas–van Alphen oscillation, which indicates that the κ-layer with an effective half-filled band is the conducting layer. In both superconductors, the superconducting layer is sandwiched by polar insulating layers. This reminds us the Ginzburg superconducting mechanism.

Observation of the electric dipole moment (EDM) of an elementary particle is attractive as a probe of CP violation, a necessary condition to explain matter-antimatter asymmetry in universe. In particular, the precision of electron EDM (eEDM) measurements in molecules has been drastically improved nowadays. For the eEDM detection, collaborations of particle physic, atomic molecular optics (AMO), and relativistic quantum chemistry is necessary. This article reviews the basic background of EDM in particle physics, experimental strategy, and relativistic theoretical chemistry to calculate effective electric field (E_eff), a requisite to extract the value of eEDM from an experimental observable. We recently developed a program to calculate E_eff accurately and in this article, we discuss our calculated values of E_eff in YbF and HgX (X: halogen) molecules. HgX are found to be promising candidates of new eEDM experiment because of its large E_eff .