The conic-gearing image of a complex number and a spinor-born surface geometry

Quaternion (Q-) mathematics formally contains many fragments of physical laws; in particular, the Hamiltonian for the Pauli equation automatically emerges in a space with Q-metric. The eigenfunction method shows that any Q-unit has an interior structure consisting of spinor functions; this helps us to represent any complex number in an orthogonal form associated with a novel geometric image (the conic-gearing picture). Fundamental Q-unit-spinor relations are found, revealing the geometric meaning of spinors as Lam\'e coefficients (dyads) locally coupling the base and tangent surfaces.Comment: 7 pages, 1 figur

Cooper Pairs with Broken Parity and Time-Reversal Symmetries in D-wave Superconductors

Paramagnetic effects are shown to result in the appearance of a triplet component of order parameter in a vortex phase of a d-wave superconductor in the absence of impurities. This component, which breaks both parity and time-reversal symmetries of Cooper pairs, is expected to be of the order of unity in a number of modern superconductors such as organic, high-Tc, and some others. A generic phase diagram of such type-IV superconductors, which are singlet ones at H=0 and characterized by singlet-triplet mixed Copper pairs with broken time-reversal symmetry in a vortex phase, is discussed.Comment: 10 pages, 1 figures, Phys. Rev. Lett., submitted (July 25 2005

Tetrahedron Reflection Equation

Reflection equation for the scattering of lines moving in half-plane is obtained. The corresponding geometric picture is related with configurations of half-planes touching the boundary plane in 2+1 dimensions. This equation can be obtained as an additional to the tetrahedron equation consistency condition for a modified Zamolodchikov algebra.Comment: 10 pages, LaTe

Toward equilibrium ground state of charge density waves in rare-earth tritellurides

We show that the charge density wave (CDW) ground state below the Peierls transition temperature, $T_{CDW}$, of rare-earth tritellurides is not at its equilibrium value, but depends on the time where the system was kept at a fixed temperature below $T_{CDW}$. This ergodicity breaking is revealed by the increase of the threshold electric field for CDW sliding which depends exponentially on time. We tentatively explain this behavior by the reorganization of the oligomeric (Te$_x$)$^{2-}$ sequence forming the CDW modulation.Comment: 10 pages, 5 figures, accepted in PR