Electron Correlations in a Quantum Dot with Bychkov-Rashba Coupling

We report on a theoretical approach developed to investigate the influence of Bychkov-Rashba interaction on a few interacting electrons confined in a quantum dot. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Inter-electron interaction causes level crossings in the ground state and a jump in magnetization. As the coupling strength is increased, that jump is shifted to lower magnetic fields. Low-field magnetization will therefore provide a direct probe of the spin-orbit coupling strength in a quantum dot

Temperature dependence of spin polarizations at higher Landau Levels

We report our results on temperature dependence of spin polarizations at $\nu=1$ in the lowest as well as in the next higher Landau level that compare well with recent experimental results. At $\nu=3$, except having a much smaller magnitude the behavior of spin polarization is not much influenced by higher Landau levels. In sharp contrast, for filling factor $\nu=\frac83$ we predict that unlike the case of $\nu=\frac23$ the system remains fully spin polarized even at vanishingly small Zeeman energies.Comment: 4 pages, REVTEX, and 3 .ps files, To be published in Physical Review Letter

Exact mean field inference in asymmetric kinetic Ising systems

We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local magnetizations and the exact relation between equal-time and time-delayed correlations. It can also be used to solve efficiently the inverse problem, i.e. determine the couplings and local fields from a set of patterns, also in cases where the fields and couplings are time-dependent. This approach generalizes some recent attempts to solve this dynamical inference problem, which were valid in the limit of weak coupling. It provides the exact solution to the problem also in strongly coupled problems. This mean field inference can also be used as an efficient approximate method to infer the couplings and fields in problems which are not infinite range, for instance in diluted asymmetric spin glasses.Comment: 10 pages, 7 figure

A multi-domain hybrid method for head-on collision of black holes in particle limit

A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method. The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-domain method composed of the spectral domains only does not yield the proper power-law decay unless the range of the computational domain is large. The finite-difference domain helps reduce boundary effects due to the truncation of the computational domain. The multi-domain approach with the finite-difference boundary domain method reduces the computational costs significantly and also yields the proper power-law decay. Stable and accurate interface conditions between the finite-difference and spectral domains and the spectral and spectral domains are derived. For the singular source term, we use both the Gaussian model with various values of full width at half maximum and a localized discrete $\delta$-function. The discrete $\delta$-function was generalized to adopt the Gauss-Lobatto collocation points of the spectral domain. The gravitational waveforms are measured. Numerical results show that the developed hybrid method accurately yields the quasi-normal modes and the power-law decay profile. The numerical results also show that the power-law decay profile is less sensitive to the shape of the regularized $\delta$-function for the Gaussian model than expected. The Gaussian model also yields better results than the localized discrete $\delta$-function.Comment: 25 pages; published version (IJMPC

Stress and large-scale spatial structures in dense, driven granular flows

We study the appearance of large-scale dynamical heterogeneities in a simplified model of a driven, dissipative granular system. Simulations of steady-state gravity-driven flows of inelastically colliding hard disks show the formation of large-scale linear structures of particles with a high collision frequency. These chains can be shown to carry much of the collisional stress in the system due to a dynamical correlation that develops between the momentum transfer and time between collisions in these "frequently-colliding" particles. The lifetime of these dynamical stress heterogeneities is seen to grow as the flow velocity decreases towards jamming, leading to slowly decaying stress correlations reminiscent of the slow dynamics observed in supercooled liquids.Comment: 8 pages, 6 figure

The orientation of elliptical galaxies

We determine the orientations of the light distribution of individual elliptical galaxies by combining the profiles of photometric data from the literature with triaxial models. The orientation is given by a Bayesian probability distribution. The likelihood of obtaining the data from a model is a function of the parameters describing the intrinsic shape and the orientation. Integrating the likelihood over the shape parameters, we obtain the estimates of the orientation. We find that the position angle difference between the two suitably chosen points from the profiles of the photometric data plays a key role in constraining the orientation of the galaxy. We apply the methodology to a sample of ten galaxies. The alignment of the intrinsic principle axes of the NGC 3379, 4486 and NGC 5638 are studied.Comment: accepted in Astrophysics and Space Scienc

Correspondence between Electro-Magnetic Field and other Dark Energies in Non-linear Electrodynamics

In this work, we have considered the flat FRW model of the universe filled with electro-magnetic field. First, the Maxwell's electro-magnetic field in linear form has been discussed and after that the modified Lagrangian in non-linear form for accelerated universe has been considered. The corresponding energy density and pressure for non-linear electro-magnetic field have been calculated. We have found the condition such that the electro-magnetic field generates dark energy. The correspondence between the electro-magnetic field and the other dark energy candidates namely tachyonic field, DBI-essence, Chaplygin gas, hessence dark energy, k-essenece and dilaton dark energy have been investigated. We have also reconstructed the potential functions and the scalar fields in this scenario.Comment: 11 pages, 7 figure

Charged anisotropic matter with linear or nonlinear equation of state

Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplification achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or non-linear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the electric force acting on these fluid elements is finite, although the acting electric field is zero. Net charges can be huge ($10^{19}\,C$) and maximum electric field intensities are very large ($10^{23}-10^{24}\,statvolt/cm$) even in the case of zero net charge. Inward-directed fluid forces caused by pressure anisotropy may allow equilibrium configurations with larger net charges and electric field intensities than those found in studies of charged isotropic fluids. Links of these results with charged strange quark stars as well as models of dark matter including massive charged particles are highlighted. The van der Waals equation of state leading to matter densities constrained by cubic polynomial equations is briefly considered. The fundamental question of stability is left open.Comment: 22 Latex pages, 17 figures, Inclusion of new paragraph at the end of Conclusion & some of the old captions of the Figures are replaced with new caption