Treatments of the exchange energy in density-functional theory

Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree-Fock equations, the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn-Sham equations, the Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn-Sham formulation of the Hartree-Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N=1,2,...), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.Comment: 19 pages; original manuscript from 2001 (v1) revised for publication, with presentation substantially improved, some errors corrected, plus an additional summarizing figure (Appendix B) include

Joint effect of lattice interaction and potential fluctuation in colossal magnetoresistive manganites

Taking into account both the Jahn-Teller lattice distortion and the on-site electronic potential fluctuations in the orbital-degenerated double-exchange model, in which both the core-spin and the lattice distortion are treated classically, we investigate theoretically the metal-insulator transition (MIT) in manganites by considering the electronic localization effect. An inverse matrix method is developed for calculation in which we use the inverse of the transfer matrix to obtain the localization length. We find that within reasonable range of parameters, both the lattice effect and the potential fluctuation are responsible to the occurrence of the MIT. The role of the orbital configuration is also discussed.Comment: 4 figure

Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems

We seek to derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PT's) of the associated 4 x 4 density matrices). But the full implementation of the test--requiring that the determinant of the PT be nonnegative for separability to hold--appears to be, at least presently, computationally intractable. So, we have previously implemented--using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/{135 pi^2} =0.76854$. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a still further improved upper bound of 1129/2100 = 0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESF's that comes close to reproducing our numerical estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the end are correcte

Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence

The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional and 15-dimensional in nature, respectively. The total volumes of the spaces they occupy with respect to the Hilbert-Schmidt and Bures metrics are obtainable as special cases of formulas of Zyczkowski and Sommers. We claim that if one could determine certain metric-independent 3-dimensional "eigenvalue-parameterized separability functions" (EPSFs), then these formulas could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes occupied by only the separable two-qubit states (and hence associated separability probabilities). Motivated by analogous earlier analyses of "diagonal-entry-parameterized separability functions", we further explore the possibility that such 3-dimensional EPSFs might, in turn, be expressible as univariate functions of some special relevant variable--which we hypothesize to be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical results we obtain are rather closely supportive of this hypothesis. Both the real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude roughly 50% at C=1/2, as well as a number of additional matching discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.

Structure and Response in the World Trade Network

We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40 years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive to evolutionary shocks and recovers more slowly from them now than it did 40 years ago, due to structural changes in the world trade network induced by globalization. We also show that recession-induced change to the world trade network leads to an \emph{increased} hierarchical structure of the global trade network for a few years after the recession.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

d1005+68: A New Faint Dwarf Galaxy in the M81 Group

We present the discovery of d1005+68, a new faint dwarf galaxy in the M81 Group, using observations taken with the Subaru Hyper Suprime-Cam. d1005+68's color-magnitude diagram is consistent with a distance of $3.98_{-0.43}^{+0.39}$ Mpc, establishing group membership. We derive an absolute $V$-band magnitude, from stellar isochrone fitting, of $M_{V} = -7.94_{-0.50}^{+0.38}$, with a half-light radius of $r_{h} = 188_{-41}^{+39}$ pc. These place d1005+68 within the radius-luminosity locus of Local Group and M81 satellites and among the faintest confirmed satellites outside the Local Group. Assuming an age of 12 Gyr, d1005+68's red giant branch is best fit by an isochrone of [Fe/H] $= -1.90 \pm 0.24$. It has a projected separation from nearby M81 satellite BK5N of only 5 kpc. As this is well within BK5N's virial radius, we speculate that d1005+68 may be a satellite of BK5N. If confirmed, this would make d1005+68 one of the first detected satellites-of-a-satellite.Comment: 7 pages, 4 figures, 1 table, additional affiliations include

Spin swap vs. double occupancy in quantum gates

We propose an approach to realize quantum gates with electron spins localized in a semiconductor that uses double occupancy to advantage. With a fast (non-adiabatic) time control of the tunnelling, the probability of double occupancy is first increased and then brought back exactly to zero. The quantum phase built in this process can be exploited to realize fast quantum operations. We illustrate the idea focusing on the half-swap operation, which is the key two-qubit operation needed to build a CNOT gate.Comment: 5 pages, 2 figure

On the structure of the body of states with positive partial transpose

We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An analogous property holds for the set of positive-partial-transpose states for an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma