Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a modified local density approximation calculation. A parametrization for the FS exchange-correlation functional is obtained. The method is simple and gives post-processing corrections that can be applied to any MB results. Applications to a model insulator (P2 in a supercell), to semiconducting Si, and to metallic Na show that the method delivers greatly improved FS corrections.PACS numbers: 02.70. Ss, 71.15.Nc, Realistic many-body (MB) calculations for extended systems are needed to accurately treat systems where the otherwise successful density functional theory (DFT) approach fails. Examples range from strongly correlated materials, such as high-temperature superconductors, to systems with moderate correlation, for instance where accurate treatments of bond-stretching or bond-breaking are required. DFT or Hartree Fock (HF), which are effectively independent-particle methods, routinely exploit Bloch's theorem in calculations for extended systems. In crystalline materials, the cost of the calculations depends only on the number of atoms in the periodic cell, and the macroscopic limit is achieved by a quadrature in the Brillouin zone, using a finite number of k-points. MB methods, by contrast, cannot avail themselves of this simplification. Instead calculations must be performed using increasingly larger simulation cells (supercells). Because the Coulomb interactions are long-ranged, finite-size (FS) effects tend to persist to large system sizes, making reliable extrapolations impractical. The resulting FS errors in state-of-the-art MB quantum simulations often can be more significant than statistical and other systematic errors. Reducing FS errors is thus a key to broader applications of MB methods in real materials, and the subject has drawn considerable attention [1,2].In this paper, we introduce an external correction method, which is designed to approximately include FS corrections in modified DFT calculations with finite-size functionals. The method is simple, and provides postprocessing corrections applicable to any previously obtained MB results. Conceptually, it gives a consistent framework for relating FS effects in MB and DFT calculations, which is important if the two methods are to be seamlessly interfaced to bridge length scales. The correction method is applied to a model insulator (P 2 in a supercell), to semiconducting bulk Si, and to Na metal. We find that it consistently removes most of the FS errors, leading to rapid convergence of the MB results to the infinite system.We write the N -electron MB Hamiltonian in a supercell as (Rydberg atomic units are used throughout):where the ionic potential on i can be local or non-local, and r i is an electron position. The Coulomb interaction V FS between electrons depends on the supercell size and shape, due to modificatio...

We report a detailed theoretical model of recently-demonstrated magnetic trap system based on a pair of magnetic tips. The model takes into account key parameters such as tip diameter, facet angle and gap separation. It yields quantitative descriptions consistent with experiments such as the vertical and radial frequency, equilibrium position and the optimum facet angle that produces the strongest confinement. We arrive at striking conclusions that a maximum confinement enhancement can be achieved at an optimum facet angle θmax = arccos 2/3 and a critical gap exists beyond which this enhancement effect no longer applies. This magnetic trap and its theoretical model serves as a new and interesting example of a simple and elementary magnetic trap in physics. PACS numbers: 04.60.BcVarious electromagnetic trap systems play important role in physics for their ability to trap and isolate particles or matter that have produced many applications and discoveries. Examples are Penning trap [1, 2], optical dipole trap or optical tweezer [3][4][5], magneto optic trap [6,7] and various diamagnetic traps [8][9][10][11][12]. For diamagnetic trap systems, high field-gradient product (B ∇B) is necessary to achieve trapping or levitation [13]. A new approach is to use magnetic tip geometry as recently demonstrated by O'Brien et al. [14]. The tip geometry maximizes B ∇B at the trapped object that leads to stronger field confinement, thus high frequency and high quality factor (Q). This characteristics is of high interest for research that explores macroscopic limits of classical mechanics and quantum mechanics. Such magnetic trap also offers interesting alternative to optical trap as the latter can lead to excessive heating and encounters instabilities in vacuum [15]. The ability to achieve high magnetic field gradients in a localized position using magnetic tip is also useful for other applications such as for nuclear magnetic resonant imaging [16] and magnetic force microscopy [17].Currently, there is strong interest in magnetic trap system for various applications such as precision gravimetry [18], study of displacement and velocity of Brownian particle [19], gas temperature measurement [20], and research that explores the boundaries of the classical and quantum systems. For example, trapped nanodiamond can be used to investigate the quantum mechanical properties such as superposition of states [21,22], control of electron spin of nanodiamond nitrogen-vacancy centers and to observe the electron spin resonance properties [23]. Such a trap could also serve an important role to test quantum mechanical properties of gravity [24,25].In the recent demonstration of a magnetic tip trap O'Brien et al. uses two cylindrical magnets with sharpened tips and a microdiamond as the trapped object [14]. The tips are separated by a gap d = 2a as shown in Fig. 1(a). The trapping occurs due to diamagnetic repulsion that balances the gravity of the diamond and the cylindrical symmetry that produces a stable potential confinement in three dimension. ...

A brief report on the final round of the first World Physics Olympiad (WoPhO) held in Lombok, West Nusa Tenggara, Indonesia is presented. The theoretical and experimental problems are presented and the mark distribution is discussed.

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