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We prove that the probability that a sum of independent random variables in $\mathbb{R}^d$ with bounded densities lies in a ball is maximized by taking uniform distributions on balls. This in turn generalizes a result by Rogozin on the maximum density of such sums on the line., Comment: 4 pages; typos corrected

We fabricated GaAs/AlGaAs quantum dots by droplet epitaxy method, and obtained the geometries of the dots from scanning transmission electron microscopy data. Post-thermal annealing is essential for the optical activation of quantum dots grown by droplet epitaxy. We investigated the emission energy shifts of the dots and underlying superlattice by post-thermal annealing with photoluminescence and cathodoluminescence measurements, and specified the emissions from the dots by selectively etching the structure down to a lower layer of quantum dots. We studied the influences of the degree of annealing on the optical properties of the dots from the peak shifts of the superlattice, which has the same composition as the dots, since the superlattice has uniform and well-defined geometry. Theoretical analysis provided the diffusion length dependence of the peak shifts of the emission spectra.

In the attosecond (as) streaking of Cu 3s core-level photoemission of copper dihalides, we predict theoretically that the satellite ($3d^9$) is emitted later than the main line ($3d^{10}L^{-1}$; $L$: ligand). The emission time delay is originated from the electron correlation between the core level and 3d shell, which leads to the difference in core-hole screening between satellite and main lines. Further, we find that the time delay corresponds to a quantification of the extrinsic loss of photoemission., Comment: 4 pages, 5 figures

We demonstrate optical control of the LO phonon-plasmon coupled (LOPC) modes in GaAs by using a femtosecond pump-pulse pair. The relaxation time of the plasmon-like LOPC mode significantly depends on the separation time (\Delta t) of the pump-pulse pair. Especially it is maximized when \Delta t becomes simultaneously comparable to the half period of the longitudinal optical (LO) phonon oscillation and resonant to the 3/4 period of the plasmon-like LOPC oscillation. We attribute these observations to the modification of carrier-LO phonon scattering and ballistic motion of the plasmon-like LOPC mode., Comment: 5 pages, 4 figures, submitted to Journal of Applied Physics

We study the dynamics of spins in the canted antiferromagnetic hematite nanoparticles $\alpha$-Fe$_2$O$_3$. The system includes an antiferromagnetic exchange ($J$) between two sublattices as well as the potential dominated by a uniaxial anisotropy and dissipates through the thermally triggered spin-phonon mechanism. The exchange $J$ is found to reduce the superparamagnetic relaxation and drive the incoherent relaxation of transverse spins in the low temperature. Dynamical properties are semi-quantitatively understood within a role of the exchange interaction $J$ and agree well with recent inelastic neutron scattering experiments., Comment: 4 pages (4 figures)

Dynamics of classical Heisenberg spins, ${\bf S}_i=({\bf s}_i,S_{iz})$, on the Kagom\'{e} lattice has been studied. An ideal Heisenberg Kagom\'{e} antiferromagnet is known to remain disordered down to T=0 due to the macroscopic degeneracy of the ground state. Through the study, however, we find that ${\bf S}_i$ and their planar components ${\bf s}_i$ behave in a qualitatively different way and especially planar spins (${\bf s}_i$) show the exotic glass-like transition in the very low temperature $T\sim 0.003J$ ($J$: spin exchange). The glassy behaviors of ${\bf s}_i$ would be found to be driven by the spin-nematic fluctuations, different from ordinary spin glasses by disorders or anisotropies., Comment: 4 pages, 5 figures

The electronic structure of La0.7Ce0.3MnO3 (LCeMO) thin film has been investigated using photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). The Ce 3d core-level PES and XAS spectra of LCeMO are very similar to those of CeO2, indicating that Ce ions are far from being trivalent. A very weak 4f resonance is observed around the Ce 4d $\to$ 4f absorption edge, suggesting that the localized Ce 4f states are almost empty in the ground state. The Mn 2p XAS spectrum reveals the existence of the Mn(2+) multiplet feature, confirming the Mn(2+)-Mn(3+) mixed-valent states of Mn ions in LCeMO. The measured Mn 3d PES/XAS spectra for LCeMO agrees reasonably well with the calculated Mn 3d PDOS using the LSDA+U method. The LSDA+U calculation predicts a half-metallic ground state for LCeMO., Comment: 7 pages, 7 figures

Using the quantum Monte Carlo method, we investigate the spin dynamics of itinerant electrons in the one-dimensional Hubbard system. Based on the model calculation, we have studied the spin-fluctuations in the quarter-filled metallic Hubbard ring, which is aimed at the vanadium ring or chain defined along corner-sharing tetrahedra of LiV$_2$O$_4$, and found the dramatic changes of magnetic responses and spin-fluctuation characteristics with the temperature. Such results can explain the central findings in the recent neutron scattering experiment for LiV$_2$O$_4$., Comment: 5 pages, 3 figures

The conditions behind the sudden approximation are critically examined. The fuzzy band expression is derived in detail from first principles. We go beyond the sudden approximation to account for both extrinsic losses and interference effects. In an extension of earlier work we discuss both core and valence satellites including both intrinsic and extrinsic amplitudes, and high energy excitations as well as low energy electron-hole pairs. We show how the extrinsic losses in photoemission can be connected with the electron energy loss function. This is achieved by three approximations, to connect the dynamically screened potential in the bulk solid to the loss function, to account for the surface, and lastly to extrapolate zero momentum loss data to include dispersion. The extrinsic losses are found to be weak for small loss energies. For larger loss energies the extrinsic losses can be strong and have strong interference with the intrinsic losses depending on the nature of the solid. The transition from the adiabatic to the sudden regime is discussed for atoms and localized systems and compared with the situation for solids. We argue that in solids for photoelectron energies above some 10 eV the external losses are mainly connected with spacially extended excitations. We discuss strongly correlated quasi-two-dimensional solids with Bi2212 as example, and find an asymmetric broadening of the main peak from shake up of acoustic three-dimensional plasmons. In the superconducting state the loss function is assumed to have a gap, which then leads to a peak-dip-hump structure in the photoemission spectrum. This structure is compared with a corresponding structure in tunneling., Comment: 20 pages, 13 figures

New expressions are derived for photoemission, which allow experimental electron energy loss data to be used for estimating losses in photoemission. The derivation builds on new results for dielectric response and mean free paths of strongly correlated systems of two dimensional layers. Numerical evaluations are made for $Bi_{2}Sr_{2}CaCu_{2}O_{8}$ (Bi2212) by using a parametrized loss function. The mean free path for Bi2212 is calculated and found to be substantially larger than obtained by Norman et al in a recent paper. The photocurrent is expressed as the convolution of the intrinsic approximation for the current from a specific 2D layer with an effective loss function. The observed current is the sum of such currents from the first few layers. The photo electron from a specific $CuO$ layer is found to excite low energy acoustic plasmon modes due to the coupling between the $CuO$ layers. These modes give rise to an asymmetric power law broadening of the photo current an isolated two dimensional layer would have given. We define an asymmetry index where a contribution from a Luttinger lineshape is additive to the contribution from our broadening function. Already the loss effect considered here gives broadening comparable to what is observed experimentally. A superconductor with a gapped loss function is predicted to have a peak-dip-hump lineshape similar to what has been observed, and with the same qualitative behavior as predicted in the recent work by Campuzano et al., Comment: 17 pages, 10 figures

Photoemission in the system of linear charged chains has been studied with the dipole matrix incorporated, from which its dependencies on the photoelectron momentum (${\bf k}$), photon polarization ($\hat{\bf E}$), and photon energy ($\omega$) can be explored. The used model is the three-dimensional array of noninteracting chains, which is so simple as to allow an analytic approach. Motivations of the study are for the doped CuO$_3$ chain in PrBa$_2$Cu$_3$O$_7$ and the doped static stripe phase in La$_{\rm 2-x-y}$Nd$_{\rm y}$Sr$_{\rm x}$CuO$_4$. The one-dimensional dispersion exhibiting spin-charge separation and its dependence on the momentum perpendicular to the chain and its $\hat{\bf E}$-dependency as well are discussed in PrBa$_2$Cu$_3$O$_7$. For La$_{\rm 2-x-y}$Nd$_{\rm y}$Sr$_{\rm x}$CuO$_4$, the anomalous spectral distribution formed by two sets of stripes perpendicular to each other is investigated. The geometric effects led to by the dipole transition matrix including the interference of photocurrents from different chains are found to change the simple one-dimensional feature drastically. We find these changes are consistent with experiment for the chain system PrBa$_2$Cu$_3$O$_7$, but less satisfactory for the stripe phase in La$_{\rm 2-x-y}$Nd$_{\rm y}$Sr$_{\rm x}$CuO$_4$. This means that in the stripe phase much two-dimensional characters still exist unlike the chain system., Comment: 13 pages, 7 figures

The valence level photoemission spectra in the Anderson impurity model for Ce compounds at zero temperature are studied as a function of the photon energy $\omega$. Most of former studies on Ce compounds are based on the sudden approximation, which is valid in high energy region. For the photoemission in the adiabatic limit of low energy region, one should consider the dipole matrix elements and the hole-induced photoelectron scattering potential. We can manage it by combining the time-evolution formalism and the $1/N_f$ scheme in a large $f$-level degeneracy $N_f$. This gives the exact results as $N_f\to\infty$. In view of experiments on the valence photoemission, two contributions of $4f$- and band emissions are mixed. We study the separate $4f$ and band contributions (from Ce $5d$) and total emission including the interference between two on an equal footing with varying the photon energy. In the $4f$-emission case, we also explore the effects of hole-induced scattering potential of the photoelectron with respect to $\omega$. Its effects are found very similar to the core level photoemission in shake down case with a localized charge transfer excitation. Additionally, we examine the adiabatic-sudden transition in valence level photoemission for the present localized system through the simplified two-level model., Comment: 11 pages, 13 figures

We consider core electron photoemission in a localized system, where there is a charge transfer excitation. The system is modelled by three electron levels, one core level and two outer levels. The model has a Coulomb interaction between these levels and the continuum states into which the core electron is emitted. The model is simple enough to allow an exact numerical solution, and with a separable potential an analytic solution. We calculate the ratio r(omega) between the weights of the satellite and the main peak as a function of the photon energy omega. The transition from the adiabatic to the sudden limit takes place for quite small photoelectron kinetic energies. For such small energies, the variation of the dipole matrix element is substantial and described by the energy scale Ed. Without the coupling to the photoelectron, the corresponding ratio r0(omega) is determined by Ed and the satellite excitation energy dE. When the interaction potential with the continuum states is introduced, a new energy scale Es=1/(2Rs^2) enters, where Rs is a length scale of the interaction potential. At threshold there is typically a (weak) constructive interference between intrinsic and extrinsic contributions, and the ratio r(omega)/r0(omega) is larger than its limiting value for large omega. The interference becomes small or weakly destructive for photoelectron energies of the order Es. For larger energies r(omega)/r0(omega) therefore typically has a weak undershoot. If this undershoot is neglected, r(omega)/r0(omega) reaches its limiting value on the energy scale Es., Comment: 18 pages, latex2e, 13 eps figures

Based on the Hamiltonian of small polarons with the strong nearest neighbor repulsion, we have investigated the charge ordering phenomena observed in half-doped manganites R_{1/2}A_{1/2}MnO_3. We have explored possible consequences of the charge ordering phase in the half-doped manganites. First, we have studied the renormalization of the sound velocity around $T_{CO}$, considering the acoustic phonons coupled to the electrons participating in the charge ordering. Second, we have found a new antiferromagnetic phase induced by the charge ordering, and discussed its role in connection with the specific CE-type antiferromagnetic structure observed in half-doped manganites., Comment: 5 pages, 2 Postscript figures. To appear in Phys. Rev. B - Rapid Comm. (01Jun97)

Based on the model combining the spin double exchange and the lattice polaron, we have studied the colossal magnetoresistance phenomena observed in perovskite manganites R_{1-x}A_xMnO_3. First, effects of both the double exchange and the electron-phonon interaction on the transport property are investigated. We have evaluated the temperature dependent resistance and the magnetoresistance using the Kubo formula, and examined the crossover from tunneling to hopping regime of small polarons. Second, effects of the double exchange interaction on the lattice degree of freedom are explored. It is found that both the hardening of the phonon frequency and the reduction of the phonon damping take place with decreasing the temperature., Comment: 7 pages, 3 Postscript figures. To appear in Phys. Rev. B (01May97)