803 research outputs found
Dimension dependence of correlation energies in twoâelectron atoms
Correlation energies (CEs) for twoâelectron atom ground states have been computed as a function of the dimensionality of space D. The classical limit Dââ and hyperquantum limit Dâ1 are qualitatively different and especially easy to solve. In hydrogenic units, the CE for any twoâelectron atom is found to be roughly 35% smaller than the realâworld value in the Dââ limit, and about 70% larger in the Dâ1 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 twoâelectron atoms
Approximate expansions in inverse powers of the dimensionality of space D are obtained for the groundâstate energies of twoâelectron atoms. The method involves fitting polynomials in δ=1/D to accurate eigenvalues of the generalized Dâdimensional SchrĂśdinger 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 (δâδ0), 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 oneâdimensional atom. Series in powers of (δâ1) appear to converge rapidly. Also the series in (δâ1) 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 Îť=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 (δâ1) 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 HartreeâFock 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
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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
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
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 when 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- superconductors and
from the half width of the peaks the pair decay rate can be estimated.Comment: 4 pages, 3 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
The Unusual Superconducting State of Underdoped Cuprates
There is increasing experimental evidence that the superconducting energy gap
in the underdoped cuprates is independent of doping concentration
while the superfluid density is linear in . We show that under these
conditions, thermal excitation of the quasiparticles is very effective in
destroying the superconducting state, so that is proportional to
and part of the gap structure remains in the normal state. We then
estimate and predict it to be proportional to . 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
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