Born-Infeld Lagrangian using Cayley-Dickson algebras

We rewrite the Born-Infeld Lagrangian, which is originally given by the determinant of a $4 \times 4$ matrix composed of the metric tensor $g$ and the field strength tensor $F$, using the determinant of a $(4 \cdot 2^n) \times (4 \cdot 2^n)$ matrix $H_{4 \cdot 2^{n}}$. If the elements of $H_{4 \cdot 2^{n}}$ are given by the linear combination of $g$ and $F$, it is found, based on the representation matrix for the multiplication operator of the Cayley-Dickson algebras, that $H_{4 \cdot 2^{n}}$ is distinguished by a single parameter, where distinguished matrices are not similar matrices. We also give a reasonable condition to fix the paramet

The Yellow Excitonic Series of Cu2O Revisited by Lyman Spectroscopy

We report on the observation of the yellow exciton Lyman series up to the fourth term in Cu2O by time-resolved mid-infrared spectroscopy. The dependence of the oscillator strength on the principal quantum number n can be well reproduced using the hydrogenic model including an AC dielectric constant, and precise information on the electronic structure of the 1s exciton state can be obtained. A Bohr radius a_{1s}=7.9 A and a 1s-2p transition dipole moment \mu_{1s-2p}= 4.2 eA were found

Study of ortho-to-paraexciton conversion in Cu2_2O by excitonic Lyman spectroscopy

Using time-resolved $1s$-$2p$ excitonic Lyman spectroscopy, we study the orthoexciton-to-paraexcitons transfer, following the creation of a high density population of ultracold $1s$ orthoexcitons by resonant two-photon excitation with femtosecond pulses. An observed fast exciton-density dependent conversion rate is attributed to spin exchange between pairs of orthoexcitons. Implication of these results on the feasibility of BEC of paraexcitons in Cu$_2$O is discussed

Coexistence and competition of local- and long-range polar orders in a ferroelectric relaxor

We have performed a series of neutron diffuse scattering measurements on a single crystal of the solid solution Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN) doped with 8% PbTiO$_3$ (PT), a relaxor compound with a Curie temperature T$_C \sim 450$ K, in an effort to study the change in local polar orders from the polar nanoregions (PNR) when the material enters the ferroelectric phase. The diffuse scattering intensity increases monotonically upon cooling in zero field, while the rate of increase varies dramatically around different Bragg peaks. These results can be explained by assuming that corresponding changes occur in the ratio of the optic and acoustic components of the atomic displacements within the PNR. Cooling in the presence of a modest electric field $\vec{E}$ oriented along the [111] direction alters the shape of diffuse scattering in reciprocal space, but does not eliminate the scattering as would be expected in the case of a classic ferroelectric material. This suggests that a field-induced redistribution of the PNR has taken place

Formation and decay of electron-hole droplets in diamond

We study the formation and decay of electron-hole droplets in diamonds at both low and high temperatures under different excitations by master equations. The calculation reveals that at low temperature the kinetics of the system behaves as in direct-gap semiconductors, whereas at high temperature it shows metastability as in traditional indirect-gap semiconductors. Our results at low temperature are consistent with the experimental findings by Nagai {\em et al.} [Phys. Rev. B {\bf 68}, 081202 (R) (2003)]. The kinetics of the e-h system in diamonds at high temperature under both low and high excitations is also predicted.Comment: 7 pages, 8 figures, revised with some modifications in physics discussion, to be published in PR

An Anomalous Phase in the Relaxor Ferroelectric Pb(Zn1/3_{1/3}Nb2/3_{2/3})O3_3

X-ray diffraction studies on a Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN) single crystal sample show the presence of two different structures. An outer-layer exists in the outer most $\sim$ 10 to 50~$\mu$m of the crystal, and undergoes a structural phase transition at the Curie temperature $T_C\approx410$ K. The inside phase is however, very different. The lattice inside the crystal maintains a cubic unit cell, while ferroelectric polarization develops below $T_C$. The lattice parameter of the cubic unit cell remains virtually a constant, i.e., much less variations compared to that of a typical relaxor ferroelectric, in a wide temperature range of 15 K to 750 K. On the other hand, broadening of Bragg peaks and change of Bragg profile line-shapes in both longitudinal and transverse directions at $T_C$ clearly indicate a structural phase transition occurring.Comment: to be submitted for PR