Dimension dependence of correlation energies in two‐electron atoms

Correlation energies (CEs) for two‐electron atom ground states have been computed as a function of the dimensionality of space D. The classical limit D→∞ and hyperquantum limit D→1 are qualitatively different and especially easy to solve. In hydrogenic units, the CE for any two‐electron atom is found to be roughly 35% smaller than the real‐world value in the D→∞ limit, and about 70% larger in the D→1 limit. Between the limits the CE varies almost linearly in 1/D. Accurate approximations to real CEs may therefore be obtained by linear interpolation or extrapolation from the much more easily evaluated dimensional limits. We give two explicit procedures, each of which yields CEs accurate to about 1%; this is comparable to the best available configuration interaction calculations. Steps toward the generalization of these procedures to larger atoms are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70213/2/JCPSA6-86-6-3512-1.pd

Dimensional expansions for two‐electron atoms

Approximate expansions in inverse powers of the dimensionality of space D are obtained for the ground‐state energies of two‐electron atoms. The method involves fitting polynomials in δ=1/D to accurate eigenvalues of the generalized D‐dimensional Schrödinger equation. To the maximum order obtainable from the data, about δ7, the power series for nuclear charges Z=2, 3, and 6 all diverge at D=3. Asymptotic summation yields an energy for the Z=2 atom 1% in excess of the true value at D=3. However, expansions with a shifted origin, i.e., expansions in (δ−δ0), show improved convergence. Of particular interest is the case δ0=1, because the expansion coefficients can in principle be calculated by perturbation theory applied to the one‐dimensional atom. Series in powers of (δ−1) appear to converge rapidly. Also the series in (δ−1) can be evaluated even for the hydride ion, with Z=1. For helium, this series is quite comparable to the more familiar expansion in powers of λ=1/Z, with errors in the partial sums decreasing by roughly an order of magnitude per term. Thus, for Z=2 the first four terms of the expansion in (δ−1) yield an energy within 0.02% of the true value at D=3. Similar results are found in an analogous treatment of accurate eigenvalues for the Hartree–Fock approximation. This provides a rapidly convergent dimensional expansion for the correlation energy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70931/2/JCPSA6-86-4-2114-1.pd

Photoemission Evidence for a Remnant Fermi Surface and d-Wave-Like Dispersion in Insulating Ca2CuO2Cl2

An angle resolved photoemission study on Ca2CuO2Cl2, a parent compound of high Tc superconductors is reported. Analysis of the electron occupation probability, n(k) from the spectra shows a steep drop in spectral intensity across a contour that is close to the Fermi surface predicted by the band calculation. This analysis reveals a Fermi surface remnant even though Ca2CuO2Cl2 is a Mott insulator. The lowest energy peak exhibits a dispersion with approximately the |cos(kxa)-cos(kya)| form along this remnant Fermi surface. Together with the data from Dy doped Bi2Sr2CaCu2O(8 + delta) these results suggest that this d-wave like dispersion of the insulator is the underlying reason for the pseudo gap in the underdoped regime.Comment: 9 pages, including 7 figures. Published in Science, one figure correcte

A Theory of the Pseudogap State of the Cuprates

The phase diagram for a general model for Cuprates is derived in a mean-field approximation. A phase violating time-reversal without breaking translational symmetry is possible when both the ionic interactions and the local repulsions are large compared to the energy difference between the Cu and O single-particle levels. It ends at a quantum critical point as the hole or electron doping is increased. Such a phase is necessarily accompanied by singular forward scattering such that, in the stable phase, the density of states at the chemical potential, projected to a particular point group symmetry of the lattice is zero producing thereby an anisotropic gap in the single-particle spectrum. It is suggested that this phase occupies the "pseudogap" region of the phase diagram of the cuprates. The temperature dependence of the single-particle spectra, the density of states, the specific heat and the magnetic susceptibility are calculated with rather remarkable correspondence with the experimental results. The importance of further direct experimental verification of such a phase in resolving the principal issues in the theory of the Cuprate phenomena is pointed out. To this end, some predictions are provided.Comment: 41 pages, 8 figure

The Temperature Evolution of the Spectral Peak in High Temperature Superconductors

Recent photoemission data in the high temperature cuprate superconductor Bi2212 have been interpreted in terms of a sharp spectral peak with a temperature independent lifetime, whose weight strongly decreases upon heating. By a detailed analysis of the data, we are able to extract the temperature dependence of the electron self-energy, and demonstrate that this intepretation is misleading. Rather, the spectral peak loses its integrity above Tc due to a large reduction in the electron lifetime.Comment: 5 pages, revtex, 4 encapsulated postscript figure

Probing superconducting phase fluctuations from the current noise spectrum of pseudogaped metal-superconductor tunnel junctions

We study the current noise spectra of a tunnel junction of a metal with strong pairing phase fluctuation and a superconductor. It is shown that there is a characteristic peak in the noise spectrum at the intrinsic Josephson frequency $\omega_J=2eV$ when $\omega_J$ is smaller than the pairing gap but larger than the pairing scattering rate. In the presence of an AC voltage, the tunnelling current noise shows a series of characteristic peaks with increasing DC voltage. Experimental observation of these peaks will give direct evidence of the pair fluctuation in the normal state of high-$T_c$ superconductors and from the half width of the peaks the pair decay rate can be estimated.Comment: 4 pages, 3 figure

Relationship of Objectively-Measured Habitual Physical Activity to Chronic Inflammation and Fatigue in Middle-Aged and Older Adults

Habitual (non-exercise) physical activity (PA) declines with age, and aging-related increases in inflammation and fatigue may be important contributors to variability in PA

The Unusual Superconducting State of Underdoped Cuprates

There is increasing experimental evidence that the superconducting energy gap $\Delta_0$ in the underdoped cuprates is independent of doping concentration $x$ while the superfluid density is linear in $x$. We show that under these conditions, thermal excitation of the quasiparticles is very effective in destroying the superconducting state, so that $T_c$ is proportional to $x\Delta_0$ and part of the gap structure remains in the normal state. We then estimate $H_{c2}$ and predict it to be proportional to $x^2$. We also discuss to what extent the assumptions that go into the quasiparticle description can be derived in the U(1) and SU(2) formulations of the t-J model.Comment: 4 pages RevTe