Dynamical mean field theory of optical third harmonic generation

We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation, we observe a nontrivial approximate {\em scaling} function describing the THG spectra in all Mott insulators, independent of the gap magnitude.Comment: 4 eps figure

Shear bands in granular flow through a mixing length model

We discuss the advantages and results of using a mixing-length, compressible model to account for shear banding behaviour in granular flow. We formulate a general approach based on two function of the solid fraction to be determined. Studying the vertical chute flow, we show that shear band thickness is always independent from flowrate in the quasistatic limit, for Coulomb wall boundary conditions. The effect of bin width is addressed using the functions developed by Pouliquen and coworkers, predicting a linear dependence of shear band thickness by channel width, while literature reports contrasting data. We also discuss the influence of wall roughness on shear bands. Through a Coulomb wall friction criterion we show that our model correctly predicts the effect of increasing wall roughness on the thickness of shear bands. Then a simple mixing-length approach to steady granular flows can be useful and representative of a number of original features of granular flow.Comment: submitted to EP

Nonlinear Optical Response in two-dimensional Mott Insulators

We study the third-order nonlinear optical susceptibility $\chi^{(3)}$ and photoexcited states of two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filled Hubbard model. In the numerically exact diagonalization calculations on finite-size clusters, we find that the coupling of charge and spin degrees of freedom plays a crucial role in the distribution of the dipole-allowed states with odd parity and the dipole-forbidden states with even parity in the photoexcited states. This is in contrast with the photoexcited states in one dimension, where the charge and spin degrees of freedom are decoupled. In the third-harmonic generation (THG) spectrum, main contribution is found to come from the process of three-photon resonance associated with the odd-parity states. As a result, the two-photon resonance process is less pronounced in the THG spectrum. The calculated THG spectrum is compared with recent experimental data. We also find that $\chi^{(3)}$ with cross-polarized configuration of pump and probe photons shows spectral distributions similar to $\chi^{(3)}$ with co-polarized configuration, although the weight is small. These findings will help the analyses of the experimental data of $\chi^{(3)}$ in the 2D Mott insulators.Comment: 9 pages,5 figures,RevTeX

Nonlinear Optical Response of Spin Density Wave Insulators

We calculate the third order nonlinear optical response in the Hubbard model within the spin density wave (SDW) mean field ansatz in which the gap is due to onsite Coulomb repulsion. We obtain closed-form analytical results in one dimension (1D) and two dimension (2D), which show that nonlinear optical response in SDW insulators in 2D is stronger than both 3D and 1D. We also calculate the two photon absorption (TPA) arising from the stress tensor term. We show that in the SDW, the contribution from stress tensor term to the low-energy peak corresponding to two photon absorption becomes identically zero if we consider the gauge invariant current properly.Comment: we use \psfrag in figur

Nonlinear Optical Response Functions of Mott Insulators Based on Dynamical Mean Field Approximation

We investigate the nonlinear optical susceptibilities of Mott insulators with the dynamical mean field approximation. The two-photon absorption (TPA) and the third-harmonic generation (THG) spectra are calculated, and the classification by the types of coupling to external fields shows different behavior from conventional semiconductors. The direct transition terms are predominant both in the TPA and THG spectra, and the importance of taking all types of interaction with the external field into account is illustrated in connection with the THG spectrum and dcKerr effect. The dependence of the TPA and THG spectra on the Coulomb interaction indicate a scaling relation. We apply this relation to the quantitative evaluation and obtain results comparable to those of experiments.Comment: 14 pages, 12 figure

Relaxation Dynamics of Photocarriers in One-Dimensional Mott Insulators Coupled to Phonons

We examine recombination processes of photocarriers in one-dimensional Mott insulators coupled to phonons. Performing density matrix renormalization group calculations, we find that, even for small electron-phonon coupling, many phonons are generated dynamically, which cause initial relaxation process after the irradiation. At the same time, spin-charge coupling coming from mixing of high- and low-energy states by the irradiation is suppressed. We discuss differences between Mott and band insulators in terms of relaxation dynamics.Comment: 5 pages, 3 figure

Bioengineering the ameloblastoma tumour to study its effect on bone nodule formation

Ameloblastoma is a benign, epithelial cancer of the jawbone, which causes bone resorption and disfigurement to patients affected. The interaction of ameloblastoma with its tumour stroma drives invasion and progression. We used stiff collagen matrices to engineer active bone forming stroma, to probe the interaction of ameloblastoma with its native tumour bone microenvironment. This bone-stroma was assessed by nano-CT, transmission electron microscopy (TEM), Raman spectroscopy and gene analysis. Furthermore, we investigated gene correlation between bone forming 3D bone stroma and ameloblastoma introduced 3D bone stroma. Ameloblastoma cells increased expression of MMP-2 and -9 and RANK temporally in 3D compared to 2D. Our 3D biomimetic model formed bone nodules of an average surface area of 0.1 mm2 and average height of 92.37 ± 7.96 μm over 21 days. We demonstrate a woven bone phenotype with distinct mineral and matrix components and increased expression of bone formation genes in our engineered bone. Introducing ameloblastoma to the bone stroma, completely inhibited bone formation, in a spatially specific manner. Multivariate gene analysis showed that ameloblastoma cells downregulate bone formation genes such as RUNX2. Through the development of a comprehensive bone stroma, we show that an ameloblastoma tumour mass prevents osteoblasts from forming new bone nodules and severely restricted the growth of existing bone nodules. We have identified potential pathways for this inhibition. More critically, we present novel findings on the interaction of stromal osteoblasts with ameloblastoma

Angle-resolved photoemission study of MX-chain compound [Ni(chxn)2_2Br]Br2_2

We report on the results of angle-resolved photoemission experiments on a quasi-one-dimensional $MX$-chain compound [Ni(chxn)$_2$Br]Br$_2$ (chxn = 1$R$,2$R$-cyclohexanediamine), a one-dimensional Heisenberg system with $S=1/2$ and $J \sim 3600$ K, which shows a gigantic non-linear optical effect. A "band" having about 500 meV energy dispersion is found in the first half of the Brillouin zone $(0\le kb/\pi <1/2)$, but disappears at $kb / \pi \sim 1/2$. Two dispersive features, expected from the spin-charge separation, as have been observed in other quasi-one-dimensional systems like Sr$_2$CuO$_3$, are not detected. These characteristic features are well reproduced by the $d$-$p$ chain model calculations with a small charge-transfer energy $\Delta$ compared with that of one-dimensional Cu-O based compounds. We propose that this smaller $\Delta$ is the origin of the absence of clear spin- and charge-separation in the photoemission spectra and strong non-linear optical effect in [Ni(chxn)$_2$Br]Br$_2$.Comment: 4 pages, 3 figure

Squeezing Kappa (κ) out of the transportable array: A strategy for using bandlimited data in regions of sparse seismicity

The κ parameter (Anderson and Hough, 1984), and namely its site-specific component (κ0), is important for predicting and simulating high-frequency ground motion. We develop a framework for estimating κ0 and addressing uncertainties under the challenging conditions often imposed in practice: 1. Low seismicity (limited, poor-quality, distant records); 2. Limited-bandwidth data from the Transportable Array (maximum usable frequency 16 Hz); 3. Low magnitudes (ML1.2-3.4) and large uncertainty in stress drop (corner frequency). We cannot resolve stress drop within the bandwidth, so we propose an approach that only requires upper and lower bounds on its regional values to estimate κ0. To address uncertainties, we combine three measurement approaches (acceleration spectrum slope, AS; displacement spectrum slope, DS; broadband spectral fit, BB). We also examine the effect of crustal amplification, and find that neglecting it can affect κ0 by up to 35%. DS estimates greatly exceed AS estimates. We propose a reason behind this bias, related to the residual effect of the corner frequency on κAS and κDS. For our region, we estimate a frequency-independent mean S-wave Q of 900±300 at 9-16 Hz, and an ensemble mean κ0 over all sites of 0.033±0.014 s. This value is similar to the native κ0 of the NGA-West2 ground motion prediction equations, indicating that these do not need to be adjusted for κ0 for use in Southern Arizona. We find that stress drop values in this region may be higher compared to estimates of previous studies, possibly due to trade-offs between stress drop and κ0. For this dataset, the within-approach uncertainty is much larger than the between-approach uncertainty, and it cannot be reduced if the data quality is not improved. The challenges discussed here will be relevant in studies of κ for other regions with band-limited data, e.g., any region where data come primarily from the TA