The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional (2-D) dielectric mixture is calculated by FDTD simulations of such a sample in a TEM waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits. Calculated permittivity distribution is also compared with theoretical mixture models. No model seems to be able to predict the simulated behavior over the whole range of volume fraction.
The rotational properties of a mixture of two distinguishable Bose gases that are confined in a ring potential provide novel physical effects that we demonstrate in this study. Persistent currents are shown to be stable for a range of the population imbalance between the two components at low angular momentum. At higher values of the angular momentum, even small admixtures of a second species of atoms make the persistent currents highly fragile.PACS numbers: 05.30. Jp, 03.75.Lm, 67.60.Bc Introduction. One of the most fascinating phenomena associated with superfluidity [1] is the stability of persistent currents. In some remarkable experiments that have been performed recently, Bose-Einstein condensed atoms were confined in annular traps [2,3], in which persistent currents could be created and observed [4]. In an earlier experiment, the resistant-free motion of an object through a Bose-Einstein condensate below some critical velocity, was also observed [5].Motivated by these recent advances, in the present study we consider a mixture of two (distinguishable) Bose gases at zero temperature [6,7], that are confined to one dimension with periodic boundary conditions, i.e. in a ring potential, deriving a series of exact and analytic results.The main issue of our study concerns the rotational properties of this system and the stability of persistent currents. In higher dimensions it has been argued that mixtures of Bose gases do not support persistent currents, because there is no energy cost for the system to get rid of its circulation (i.e., the line integral of the velocity field around a closed loop that encircles the ring), as long as angular momentum can be transferred between the two species [8]. Here, we demonstrate that when the total angular momentum per atom varies between zero and unity, currents are stable for a certain range of the ratio of the populations of the two species. We calculate the critical strength of the coupling for a given value of this ratio, which we determine analytically and exactly. On the other hand, for higher values of the angular momentum per atom, persistent currents in one-component systems are very fragile, as even small admixtures of a second species of atoms destabilize the currents.Model. Assuming a ring potential (which corresponds to a very tight annular trap along the transverse direction [9]), the Hamiltonian of the system that we study for the two components that we label as A and B is H = H AA + H BB +Ũ AB
The present paper reports the results of a numerical analysis of electric fields in random dielectric materials. The effective permittivity of a three-dimensional (3-D) dielectric mixture is calculated by the finite difference method. The results show the distribution of the effective permittivity of a mixture with different random inclusion positionings. New empirical mixing models are created as least squares approximations to fit the collection of numerical results. The calculated permittivity distribution is also compared with theoretical mixture models, showing that in case of clustered inclusions, the Bruggeman model is quite reasonable. On the other hand, if the inclusions in the mixture are separate, the results are closer to the Maxwell-Garnett model.
We investigate universal properties of strongly confined particles that turn out to be dramatically different from what is observed for electrons in atoms and molecules. For a large class of harmonically confined systems, such as small quantum dots and optically trapped atoms, many-body particle addition and removal energies, and energy gaps, are accurately obtained from single-particle eigenvalues. Transport blockade phenomena are related to the derivative discontinuity of the exchange-correlation functional. This implies that they occur very generally, with Coulomb blockade being a particular realization of a more general phenomenon. In particular, we predict a van der Waals blockade in cold atom gases in traps. DOI: 10.1103/PhysRevLett.99.010402 PACS numbers: 31.15.Ew, 32.80.Pj, 71.10.ÿw, 73.21.ÿb Many-body effects in confined systems of interacting quantum particles are a recurring theme, ranging from nuclei over molecules to nanostructured semiconductors [1]. With an initial focus on Bose-Einstein condensation [2], today also the properties of confined fermionic atoms [3] are of concern, and the ability to manipulate trapped atoms recently led to the suggestion of atomtronics [4]. Confinement is often modeled by harmonic-oscillator potentials, but in spite of decades of research the many-body physics in the microscopic as well as the mesoscopic regime is still not fully understood. Even quantities as fundamental as particle-addition and removal energies and energy gaps are hard to calculate if effects of confinement and of particle-particle interactions are of comparable magnitude.In electronic-structure calculations, addition and removal energies, and gaps are often calculated from density-functional theory (DFT) [5]. A large body of knowledge has been accumulated on how such calculations should be done and when their results are reliable. This knowledge, however, is largely based on the behavior of electrons in atoms, molecules, and solids. Extrapolation to other systems is fraught with dangers and may lead astray in many ways.In this work, we reassess the calculation of these quantities in confined systems. A key ingredient of our analysis are near-exact ground-state energies, obtained from diagonalizing the many-body Hamiltonian, which allow an unbiased assessment of approximate schemes. As concrete examples, we consider electrons in small quantum dots [1] and fermionic atoms in optical traps [3]. Surprisingly, we find that accurate particle addition and removal energies can be obtained from local-density single-particle potentials, which is not at all what one would expect from experience with atoms, molecules, and bulk semiconductors. From addition and removal energies, we calculate energy gaps and estimate the effect of the derivative discontinuity in confined systems. We relate this discontinuity to Coulomb blockade [6], which allows us to adopt a more general view on blockade phenomena than the usual one, leading, in particular, to the prediction of van der Waals blockade in systems of trapped ...
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