776 research outputs found
Thomas Slater to General Jacob Morris, October 3, 1828
Thomas Slater wrote from Lebanon, NY to Jacob Morris, addressed to Butternutts, Ostego County, NY to inform him of the death of Peter Kean, his son-in-law, the day before. Attached to this letter is another one dated May 25, 1931 it is addressed to Christine Griffin Kean Roosevelt, Peter\u27s granddaughter, from J.C. Pearson. Pearson had sent her the previous letter and offered to sell it to her for $2.
People Included: Peter Philip James Kean, Sarah Sabina Kean, Mr. Dayton, Mr. Palmerhttps://digitalcommons.kean.edu/lhc_1820s/1011/thumbnail.jp
Majorana solutions to the two-electron problem
A review of the known different methods and results devised to study the
two-electron atom problem, appeared in the early years of quantum mechanics, is
given, with particular reference to the calculations of the ground state energy
of helium. This is supplemented by several, unpublished results obtained around
the same years by Ettore Majorana, which results did not convey in his
published papers on the argument, and thus remained unknown until now.
Particularly interesting, even for current research in atomic and nuclear
physics, is a general variant of the variational method, developed by Majorana
in order to take directly into account, already in the trial wavefunction, the
action of the full Hamiltonian operator of a given quantum system. Moreover,
notable calculations specialized to the study of the two-electron problem show
the introduction of the remarkable concept of an effective nuclear charge
different for the two electrons (thus generalizing previous known results), and
an application of the perturbative method, where the atomic number Z was
treated effectively as a continuous variable, contributions to the ground state
energy of an atom with given Z coming also from any other Z. Instead,
contributions relevant mainly for pedagogical reasons count simple broad range
estimates of the helium ionization potential, obtained by suitable choices for
the wavefunction, as well as a simple alternative to Hylleraas' method, which
led Majorana to first order calculations comparable in accuracy with well-known
order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure
Curvature, hybridization, and STM images of carbon nanotubes
The curvature effects in carbon nanotubes are studied analytically as a
function of chirality. The pi-orbitals are found to be significantly
rehybridized in all tubes, so that they are never normal to the tubes' surface.
This results in a curvature induced gap in the electronic band-structure, which
turns out to be larger than previous estimates. The tilting of the pi-orbitals
should be observable by atomic resolution scanning tunneling microscopy
measurements.Comment: Four pages in revtex format including four epsfig-embedded figures.
The latest version in PDF format is available from
http://fy.chalmers.se/~eggert/papers/hybrid.pd
The coupling constant averaged exchange–correlation energy density
The exchange–correlation energy, central to density-functional theory, may be represented in terms of the coupling constant averaged (CCA) exchange–correlation energy density. We present an approach to calculate the CCA energy density using accurate ab initio methods and its application to simple atomic systems. This function provides a link between intrinsically non-local, many-body electronic structure methods and simple local and semi-local density-functional approximations (DFAs). The CCA energy density is resolved into separate exchange and correlation terms and the features of each compared with those of quantities commonly used to construct DFAs. In particular, the more complex structure of the correlation energy density is found to exhibit features that align well with those present in the Laplacian of the density, suggesting its role as a key variable to be used in the construction of improved semi-local correlation functionals. The accurate results presented in this work are also compared with those provided by the Laplacian-dependent Becke–Roussel model for the exchange energy
Parity (and time-reversal) anomaly in a semiconductor
The physics of a parity anomaly, potentially observable in a narrow-gap
semiconductor, is revisited. Fradkin, Dagotto, and Boyanovsky have suggested
that a Hall current of anomalous parity can be induced by a Peierls distortion
on a domain wall. I argue that a perturbation inducing the parity anomaly must
break the time reversal symmetry, which rules out the Peierls distortion as a
potential cause. I list all possible perturbations that can generate the
anomaly.Comment: 11 pages, 1 figure. Sign errors fixe
Broken Symmetry in Density-Functional Theory: Analysis and Cure
We present a detailed analysis of the broken-symmetry mean-field solutions
using a four-electron rectangular quantum dot as a model system. Comparisons of
the density-functional theory predictions with the exact ones show that the
symmetry breaking results from the single-configuration wave function used in
the mean-field approach. As a general cure we present a scheme that
systematically incorporates several configurations into the density-functional
theory and restores the symmetry. This cure is easily applicable to any
density-functional approach.Comment: 4 pages, 4 figures, submitted to PR
The Origin of Magnetic Interactions in Ca3Co2O6
We investigate the microscopic origin of the ferromagnetic and
antiferromagnetic spin exchange couplings in the quasi one-dimensional cobalt
compound Ca3Co2O6. In particular, we establish a local model which stabilizes a
ferromagnetic alignment of the S=2 spins on the cobalt sites with trigonal
prismatic symmetry, for a sufficiently strong Hund's rule coupling on the
cobalt ions. The exchange is mediated through a S=0 cobalt ion at the
octahedral sites of the chain structure. We present a strong coupling
evaluation of the Heisenberg coupling between the S=2 Co spins on a separate
chain. The chains are coupled antiferromagnetically through super-superexchange
via short O-O bonds.Comment: 5 Pages, 3 Figures; added anisotropy term in eq. 9; extended
discussion of phase transitio
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
Coupled-mode systems are used in physical literature to simplify the
nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic
potential and to approximate localized solutions called gap solitons by
analytical expressions involving hyperbolic functions. We justify the use of
the one-dimensional stationary coupled-mode system for a relevant elliptic
problem by employing the method of Lyapunov--Schmidt reductions in Fourier
space. In particular, existence of periodic/anti-periodic and decaying
solutions is proved and the error terms are controlled in suitable norms. The
use of multi-dimensional stationary coupled-mode systems is justified for
analysis of bifurcations of periodic/anti-periodic solutions in a small
multi-dimensional periodic potential.Comment: 18 pages, no figure
Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory
The density of an atom in a state of well-defined angular momentum has a
specific finite spherical harmonic content, without and with interactions.
Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and
Local Density Approximations, generally violate this feature. We analyze, by
means of perturbation theory, the degree of this violation and show that it is
small. The correct symmetry of the density can be assured by a
constrained-search formulation without significantly altering the calculated
energies. We compare our procedure to the (different) common practice of
spherically averaging the self-consistent potential. Kohn-Sham density
functional theory with the exact exchange-correlation potential has the correct
finite spherical harmonic content in its density; but the corresponding exact
single particle potential and wavefunctions contain an infinite number of
spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic
expansion of Hartree density. Some typos corrected, references adde
On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)
In October 1924, the Physical Review, a relatively minor journal at the time,
published a remarkable two-part paper by John H. Van Vleck, working in virtual
isolation at the University of Minnesota. Van Vleck combined advanced
techniques of classical mechanics with Bohr's correspondence principle and
Einstein's quantum theory of radiation to find quantum analogues of classical
expressions for the emission, absorption, and dispersion of radiation. For
modern readers Van Vleck's paper is much easier to follow than the famous paper
by Kramers and Heisenberg on dispersion theory, which covers similar terrain
and is widely credited to have led directly to Heisenberg's "Umdeutung" paper.
This makes Van Vleck's paper extremely valuable for the reconstruction of the
genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did
not take the next step and develop matrix mechanics himself.Comment: 82 page
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