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

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

Vibrational spectroscopy of NO^+(H_2O)_n: Evidence for the intracluster reaction NO^+(H_2O)_n→H_3O^+(H_2O)_(n-2)(HONO) at n≥4

Infrared spectra of mass‐selected clusters NO^+(H_2O)_n for n=1 to 5 were recorded from 2700 to 3800 cm^(−1) by vibrational predissociation spectroscopy. Vibrational frequencies and intensities were also calculated for n=1 and 2 at the second‐order Møller–Plesset (MP2) level, to aid in the interpretation of the spectra, and at the singles and doubles coupled cluster (CCSD) level energies of n=1 isomers were computed at the MP2 geometries. The smaller clusters (n=1 to 3) were complexes of H_2O ligands bound to a nitrosonium ion NO^+ core. They possessed perturbed H_2O stretch bands and dissociated by loss of H_2O. The H_2O antisymmetric stretch was absent in n=1 and gradually increased in intensity with n. In the n=4 clusters, we found evidence for the beginning of a second solvation shell as well as the onset of an intracluster reaction that formed HONO. These clusters exhibited additional weak, broad bands between 3200 and 3400 cm^(−1) and two new minor photodissociation channels, loss of HONO and loss of two H_2O molecules. The reaction appeared to go to completion within the n=5 clusters. The primary dissociation channel was loss of HONO, and seven vibrational bands were observed. From an analysis of the spectrum, we concluded that the n=5 cluster rearranged to form H_3O^+(H_2O)_3(HONO), i.e., an adduct of the reaction products

Dynamical effects of the nanometer-sized polarized domains in Pb(Zn1/3Nb2/3)O3

Recent neutron scattering measurements performed on the relaxor ferroelectric Pb[(Zn1/3Nb2/3)0.92Ti0.08]O3 (PZN-8%PT) in its cubic phase at 500 K, have revealed an anomalous ridge of inelastic scattering centered ~0.2 A-1 from the zone center (Gehring et al., Phys. Rev. Lett. 84, 5216 (2000)). This ridge of scattering resembles a waterfall when plotted as a phonon dispersion diagram, and extends vertically from the transverse acoustic (TA) branch near 4 meV to the transverse optic (TO) branch near 9 meV. No zone center optic mode was found. We report new results from an extensive neutron scattering study of pure PZN that exhibits the same waterfall feature. We are able to model the dynamics of the waterfall using a simple coupled-mode model that assumes a strongly q-dependent optic mode linewidth Gamma1(q) that increases sharply near 0.2 A-1 as one approaches the zone center. This model was motivated by the results of Burns and Dacol in 1983, who observed the formation of a randomly-oriented local polarization in PZN at temperatures far above its ferroelectric phase transition temperature. The dramatic increase in Gamma1 is believed to occur when the wavelength of the optic mode becomes comparable to the size of the small polarized micro-regions (PMR) associated with this randomly-oriented local polarization, with the consequence that longer wavelength optic modes cannot propagate and become overdamped. Below Tc=410 K, the intensity of the waterfall diminishes. At lowest temperatures ~30 K the waterfall is absent, and we observe the recovery of a zone center transverse optic mode near 10.5 meV.Comment: 8 pages, 9 figures (one color). Submitted to Physical Review

Quasi-degenerate self-trapping in one-dimensional charge transfer exciton

The self-trapping by the nondiagonal particle-phonon interaction between two quasi-degenerate energy levels of excitonic system, is studied. We propose this is realized in charge transfer exciton, where the directions of the polarization give the quasi-degeneracy. It is shown that this mechanism, unlike the conventional diagonal one, allows a coexistence and resonance of the free and self-trapped states even in one-dimensional systems and a quantitative theory for the optical properties (light absorption and time-resolved luminescence) of the resonating states is presented. This theory gives a consistent resolution for the long-standing puzzles in quasi-one-dimensional compound A-PMDA.Comment: accepted to Phys. Rev. Letter

Soft Phonon Anomalies in the Relaxor Ferroelectric Pb(Zn_1/3Nb_2/3)_0.92Ti_0.08O_3

Neutron inelastic scattering measurements of the polar TO phonon mode dispersion in the cubic relaxor Pb(Zn_1/3Nb_2/3)_0.92Ti_0.08O_3 at 500K reveal anomalous behavior in which the optic branch appears to drop precipitously into the acoustic branch at a finite value of the momentum transfer q=0.2 inverse Angstroms, measured from the zone center. We speculate this behavior is the result of nanometer-sized polar regions in the crystal.Comment: 4 pages, 4 figure