389 research outputs found
Why is the ground state electron configuration for Lithium ?
The electronic ground state for Lithium is , and not . The
traditional argument for why this is so is based on a screening argument that
claims that the electron is better shielded by the electrons, and
therefore higher in energy then the configuration that includes the
electron. We show that this argument is flawed, and in fact the actual reason
for the ordering is because the electron-electron interaction energy is higher
for the repulsion than it is for the repulsion.Comment: 4 page
How many electrons are needed to flip a local spin?
Considering the spin of a local magnetic atom as a quantum mechanical
operator, we illustrate the dynamics of a local spin interacting with a
ballistic electron represented by a wave packet. This approach improves the
semi-classical approximation and provides a complete quantum mechanical
understanding for spin transfer phenomena. Sending spin-polarized electrons
towards a local magnetic atom one after another, we estimate the minimum number
of electrons needed to flip a local spin.Comment: 3 figure
Temperature Dependence of the Conductivity Sum Rule in the Normal State due to Inelastic Scattering
We examine the temperature dependence of the optical sum rule in the normal
state due to interactions. To be concrete we adopt a weak coupling approach
which uses an electron-boson exchange model to describe inelastic scattering of
the electrons with a boson, in the Migdal approximation. While a number of
recent works attribute the temperature dependence in the normal state to that
which arises in a Sommerfeld expansion, we show that in a wide parameter regime
this contribution can be quite small. Instead, most of the temperature
dependence arises from the zeroth order term in the `expansion', through the
temperature dependence of the spectral function, and the interaction parameters
contained therein. For low boson frequencies this circumstance causes a linear
T-dependence in the sum rule. We develop some analytical expressions and
understanding of the temperature dependence.Comment: 11 pages, 9 figure
Dynamical properties of the single--hole -- model on a 32--site square lattice
We present results of an exact diagonalization calculation of the spectral
function for a single hole described by the -- model
propagating on a 32--site square cluster. The minimum energy state is found at
a crystal momentum , consistent with
theory, and our measured dispersion relation agrees well with that determined
using the self--consistent Born approximation. In contrast to smaller cluster
studies, our spectra show no evidence of string resonances. We also make a
qualitative comparison of the variation of the spectral weight in various
regions of the first Brillouin zone with recent ARPES data.Comment: 10 pages, 5 postscript figures include
Intraband Optical Spectral Weight in the presence of a van Hove singularity: application to BiSrCaCuO
The Kubo single band sum rule is used to determine the optical spectral
weight of a tight binding band with further than nearest neighbour hopping. We
find for a wide range of parameters and doping concentrations that the change
due to superconductivity at low temperature can be either negative or positive.
In contrast, the kinetic energy change is always negative. We use an ARPES
determined tight binding parametrization of BiSrCaCuO
to investigate whether this can account for recent observations of a positive
change in the spectral weight due to the onset of superconductivity. With this
band structure we find that in the relevant doping regime a straightforward BCS
calculation of the optical spectral weight cannot account for the experimental
observations.Comment: 10 page 9 figure
Welfare and Convergence Speed in the Ramsey Model under two Classes of Gorman Preferences
Using a one-sector, discrete-time Ramsey model, we analyze and compare the implications for welfare, capital accumulation, and speed of convergence to the steady state of two classes of utility functions that represent Gorman preferences, namely homothetic and Stone\u2013Geary preferences. For identical economies, we show that the preference structure does not affect only the capital dynamics and social welfare but also the speed of convergence to the steady-state equilibrium
Optical sum rule violation, superfluid weight and condensation energy in the cuprates
The model of hole superconductivity predicts that the superfluid weight in
the zero-frequency -function in the optical conductivity has an
anomalous contribution from high frequencies, due to lowering of the system's
kinetic energy upon entering the superconducting state. The lowering of kinetic
energy, mainly in-plane in origin, accounts for both the condensation energy of
the superconductor as well as an increased potential energy due to larger
Coulomb repulsion in the paired state. It leads to an apparent violation of the
conductivity sum rule, which in the clean limit we predict to be substantially
larger for in-plane than for c-axis conductivity. However, because cuprates are
in the dirty limit for c-axis transport, the sum rule violation is found to be
greatly enhanced in the c-direction. The model predicts the sum rule violation
to be largest in the underdoped regime and to decrease with doping, more
rapidly in the c-direction that in the plane. So far, experiments have detected
sum rule violation in c-axis transport in several cuprates, as well as a
decrease and disappearance of this violation for increasing doping, but no
violation in-plane. We explore the predictions of the model for a wide range of
parameters, both in the absence and in the presence of disorder, and the
relation with current experimental knowledge.Comment: submitted to Phys.Rev.
The double well potential in quantum mechanics: a simple, numerically exact formulation
The double well potential is arguably one of the most important potentials in
quantum mechanics, because the solution contains the notion of a state as a
linear superposition of `classical' states, a concept which has become very
important in quantum information theory. It is therefore desirable to have
solutions to simple double well potentials that are accessible to the
undergraduate student. We describe a method for obtaining the numerically exact
eigenenergies and eigenstates for such a model, along with the energies
obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact
solution is accessible with elementary mathematics, though numerical solutions
are required. We also find that the WKB approximation is remarkably accurate,
not just for the ground state, but for the excited states as well.Comment: 10 pages, 4 figures; suitable for undergraduate courses in quantum
mechanic
Properties of the superconducting state in a two-band model
Eliashberg theory is used to investigate the range of thermodynamic
properties possible within a two-band model for s-wave superconductivity and to
identify signatures of its two-band nature. We emphasize dimensionless BCS
ratios (those for the energy gaps, the specific heat jump and the negative of
its slope near Tc, the thermodynamic critical field Hc(0), and the normalized
slopes of the critical field and the penetration depth near Tc), which are no
longer universal even in weak coupling. We also give results for
temperature-dependent quantities, such as the penetration depth and the energy
gap. Results are presented both for microscopic parameters appropriate to MgB2
and for variations away from these. Strong coupling corrections are identified
and found to be significant. Analytic formulas are provided which show the role
played by the anisotropy in coupling in some special limits. Particular
emphasis is placed on small interband coupling and on the opposite limit of no
diagonal coupling. The effect of impurity scattering is considered,
particularly for the interband case.Comment: 20 pages, 14 figures, final version accepted in PR
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