Screening in coupled low-dimensional systems: an effective polarizability picture

The screening of an individual low-dimensional object can be strongly influenced by the objects nearby. We propose that such environment's influence can be absorbed into an effective polarizability, instead of its intrinsic polarizability. Using a toy system consists of two spatially separated 2DEG layers gas an example, this picture is analytically deduced via a multi-component RPA theoretical method. We show that the resultant effective polarizability of backside layer is just the dielectric function describing the system's collective plasmon excitations. Furthermore, several interesting topics are discussed, e.g. the mutual modulation of Friedel oscillation, the ultimate screening limit imposed by metal layer, smoothing potential inhomogeneity in back screening configuration.Comment: 6 pages, 4 figure

Non-neutral charged two-dimension system and its quasihole structure

Most of our current knowledge on condensed matters contains a default assumption: the matters are neutral charged. On the other hand, the two-dimension(2D) vortex-Coulomb gas charge analogy is a very successful theoretical tool in explaining superfluid, type-II superconductor and fractional quantum Hall effect(FQHE), because the interaction among vortices show similarity with 2D Coulomb potential. Here, by breaking the 'neutral charged' assumption, we suggest the positively charged 2D semiconductor system can possess non-trivial particle-like charge centers(called 'quasihole'), which is the charge version of 'vortex'. Using the hypernetted-chain (HNC) approximation, the structure of quasihole is elucidated. Numerical calculations show that the quasihole can be projected onto another 2D layer, producing an electric field configuration characterized by 3/2 topological charge.Comment: 6 pages, 3 figure

An artificial charge-density-wave conductor realized by double quantum wells

Charge-density-wave (CDW) is a modulation of the conduction electron density in a conductor. Under low temperature, it can spontaneously happen in some compounds that consist of anisotropic one-dimensional crystal structures, via a strong electron-lattice interaction mechanism. Many celebrated phenomena, e.g. non-linear transport, narrow-band noise, mode-locking5 and chaos under AC voltage, etc., have been reported in CDW. However, evaluating the application potential of CDW conductors has been hampered by the inconvenient shapes and sizes of CDW single crystals. Although modern fabrication technology can partly resolve those troubles, (for example, cleaved film and nanowire NbSe3 device), the imperfections induced by fabrication that corrupt measured properties are not easy to control and estimate. Here we demonstrate a convenient CDW conductor fabricated by semiconductor double quantum wells (DQW) in a field-effect transistor (FET) configuration: a modulated electron density in one QW resulted from the charged QW nearby. The electric field dependent depinning transport characteristic of CDW is clearly present. This "artificial" CDW, capable of integrating with semiconductor industry, may give fresh impetus to revive the interests in CDW

Empirical Study of the GARCH model with Rational Errors

We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the model. The Bayesian inference is implemented by the Metropolis-Hastings algorithm with an adaptive multi-dimensional Student's t-proposal density. In order to compare the model with the GARCH model with the standard normal errors we calculate information criterions: AIC and DIC, and find that both criterions favor the GARCH model with a rational error distribution. We also calculate the accuracy of the volatility by using the realized volatility and find that a good accuracy is obtained for the GARCH model with a rational error distribution. Thus we conclude that the GARCH model with a rational error distribution is superior to the GARCH model with the normal errors and it can be used as an alternative GARCH model to those with other fat-tailed distributions.Comment: 10 page

Box-Cox transformation of firm size data in statistical analysis

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions.Comment: 4 pages, 9 figure

Inexact Shift-and-Invert Arnoldi for Toeplitz Matrix Exponential

We revisit the shift-and-invert Arnoldi method proposed in [S. Lee, H. Pang, and H. Sun. {\it Shift-invert Arnoldi approximation to the Toeplitz matrix exponential}, SIAM J. Sci. Comput., 32: 774--792, 2010] for numerical approximation to the product of Toeplitz matrix exponential with a vector. In this approach, one has to solve two large scale Toeplitz linear systems in advance. However, if the desired accuracy is high, the cost will be prohibitive. Therefore, it is interesting to investigate how to solve the Toeplitz systems inexactly in this method. The contribution of this paper is in three regards. First, we give a new stability analysis on the Gohberg-Semencul formula (GSF) and define the GSF condition number of a Toeplitz matrix. It is shown that, when the size of the Toeplitz matrix is large, our result is sharper than the one given in [M. Gutknecht and M. Hochbruck. {\it The stability of inversion formulas for Toeplitz matrices}, Linear Algebra Appl., 223/224: 307--324, 1995]. Second, we establish a relation between the error of Toeplitz systems and the residual of Toeplitz matrix exponential. We show that if the GSF condition number of the Toeplitz matrix is medium sized, then the Toeplitz systems can be solved in a low accuracy. Third, based on this relationship, we present a practical stopping criterion for relaxing the accuracy of the Toeplitz systems, and propose an inexact shift-and-invert Arnoldi algorithm for the Toeplitz matrix exponential problem. Numerical experiments illustrate the numerical behavior of the new algorithm, and show the effectiveness of our theoretical results.Comment: 17 page

Study for (anti)hypertriton and light (anti)nuclei production in high energy collisions at sNN\sqrt{s_{\rm{NN}}} = 200 GeV

We used the parton and hadron cascade (PACIAE) model and the dynamically constrained phase-space coalescence (DCPC) model to investigate the production of (anti)hypertriton and light (anti)nuclei generated by 0-10% centrality 12C+12C, 24Mg+24Mg, 40Ca+40Ca and 64Cu+64Cu collisions at $\sqrt{s_{\rm{NN}}}$ = 200 GeV with |y| < 1.5 and pT < 5. We studied the yield ratios of antiparticle to particle and the rapidity distributions of the different (anti)nuclei, and found that the amount of antimatter produced is significantly lower than that of the corresponding particles, the results of theoretical model are well consistent with PHOBOS data. The yield ratios of the particle to antiparticle in different transverse momentum region is also given, and we found the ratios is increased with the increase of the transverse momentum.Comment: 7pages, 3figures. arXiv admin note: text overlap with arXiv:1209.418

Green's function relativistic mean field theory for Λ\Lambda hypernuclei

The relativistic mean-field theory with Green's function method is extended to study $\Lambda$ hypernuclei. Taking hypernucleus $^{61}_{\Lambda}$Ca as an example, the single-particle resonant states for $\Lambda$ hyperons are investigated by analyzing density of states and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow $1f_{5/2}$ and $1f_{7/2}$ states are very similar as bound states while that of the wide $1g_{7/2}$ and $1g_{9/2}$ states are like scattering states. Besides, the impurity effect of $\Lambda$ hyperons on the single-neutron resonant states are investigated. For most of the resonant states, both the energies and widths decrease with adding more $\Lambda$ hyperons due to the attractive $\Lambda N$ interaction. Finally, the energy level structure of $\Lambda$ hyperons in the Ca hypernucleus isotopes with mass number $A=53-73$ are studied, obvious shell structure and small spin-orbit splitting are found for the single-$\Lambda$ spectrum.Comment: 10pages, 6 figures,2 table

Combinatorics of the Springer correspondence for classical Lie algebras and their duals in characteristic 2

We give a combinatorial description of the Springer correspondence for classical Lie algebras $\mathfrak{g}$ of type $B,C$ or $D$ and their duals $\mathfrak{g}^*$ in characteristic 2. The combinatorics used here is of the same kind as those appearing in the description of (generalized) Springer correspondence for unipotent case of classical groups $G$ by Lusztig in odd characteristic and by Lusztig and Spaltentstein in characteristic 2. It is very nice that this combinatorics gives a unified description for (generalized) Springer correspondences of classical groups in all cases, namely, in $G$, $\mathfrak{g}$ and $\mathfrak{g}^*$ in all characteristics. Moreover, it gives rise to close formulas for computing the correspondences.Comment: 30 page

A Probit Network Model with Arbitrary Dependence

In this paper, we adopt a latent variable method to formulate a network model with arbitrarily dependent structure. We assume that the latent variables follow a multivariate normal distribution and a link between two nodes forms if the sum of the corresponding node parameters exceeds the latent variable. The dependent structure among edges is induced by the covariance matrix of the latent variables. The marginal distribution of an edge is a probit function. We refer this model to as the \emph{Probit Network Model}. We show that the moment estimator of the node parameter is consistent. To the best of our knowledge, this is the first time to derive consistency result in a single observed network with globally dependent structures. We extend the model to allow node covariate information.Comment: 16 page