14,420 research outputs found
General calculation of transition rates for rare-earth ions using many-body perturbation theory
The transition rates for rare-earth ions in crystals can be
calculated with an effective transition operator acting between model
and states calculated with effective Hamiltonian, such as
semi-empirical crystal Hamiltonian. The difference of the effective transition
operator from the original transition operator is the corrections due to mixing
in transition initial and final states of excited configurations from both the
center ion and the ligand ions. These corrections are calculated using
many-body perturbation theory. For free ions, there are important one-body and
two-body corrections. The one-body correction is proportional to the original
electric dipole operator with magnitude of approximately 40% of the uncorrected
electric dipole moment. Its effect is equivalent to scaling down the radial
integral \ME {5d} r {4f}, to about 60% of the uncorrected HF value. The
two-body correction has magnitude of approximately 25% relative to the
uncorrected electric dipole moment. For ions in crystals, there is an
additional one-body correction due to ligand polarization, whose magnitude is
shown to be about 10% of the uncorrected electric dipole moment.Comment: 10 pages, 1 figur
A QM/MM equation-of-motion coupled-cluster approach for predicting semiconductor color-center structure and emission frequencies
Valence excitation spectra are computed for all deep-center silicon-vacancy
defect types in 3C, 4H, and 6H silicon carbide (SiC) and comparisons are made
with literature photoluminescence measurements. Nuclear geometries surrounding
the defect centers are optimized within a Gaussian basis-set framework using
many-body perturbation theory or density functional theory (DFT) methods, with
computational expenses minimized by a QM/MM technique called SIMOMM. Vertical
excitation energies are subsequently obtained by applying excitation-energy,
electron-attached, and ionized equation-of-motion coupled-cluster (EOMCC)
methods, where appropriate, as well as time-dependent (TD) DFT, to small models
including only a few atoms adjacent to the defect center. We consider the
relative quality of various EOMCC and TD-DFT methods for (i) energy-ordering
potential ground states differing incrementally in charge and multiplicity,
(ii) accurately reproducing experimentally measured photoluminescence peaks,
and (iii) energy-ordering defects of different types occurring within a given
polytype. The extensibility of this approach to transition-metal defects is
also tested by applying it to silicon-substitutional chromium defects in SiC
and comparing with measurements. It is demonstrated that, when used in
conjunction with SIMOMM-optimized geometries, EOMCC-based methods can provide a
reliable prediction of the ground-state charge and multiplicity, while also
giving a quantitative description of the photoluminescence spectra, accurate to
within 0.1 eV of measurement in all cases considered.Comment: 13 pages, 4 figures, 6 tables, 5 equations, 100 reference
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Modeling Space-Time Data Using Stochastic Differential Equations
This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Business Administratio
Detecting Extra Dimension by Helium-like Ions
Considering that gravitational force might deviate from Newton's
inverse-square law and become much stronger in small scale, we present a method
to detect the possible existence of extra dimensions in the ADD model. By
making use of an effective variational wave function, we obtain the
nonrelativistic ground energy of a helium atom and its isoelectronic sequence.
Based on these results, we calculate gravity correction of the ADD model. Our
calculation may provide a rough estimation about the magnitude of the
corresponding frequencies which could be measured in later experiments.Comment: 8 pages, no figures, accepted by Mod. Phys. Lett.
Comment on "Quantum Phase Slips and Transport in Ultrathin Superconducting Wires"
In a recent Letter (Phys. Rev. Lett.78, 1552 (1997) ), Zaikin, Golubev, van
Otterlo, and Zimanyi criticized the phenomenological time-dependent
Ginzburg-Laudau model which I used to study the quantum phase-slippage rate for
superconducting wires. They claimed that they developed a "microscopic" model,
made qualitative improvement on my overestimate of the tunnelling barrier due
to electromagnetic field. In this comment, I want to point out that, i), ZGVZ's
result on EM barrier is expected in my paper; ii), their work is also
phenomenological; iii), their renormalization scheme is fundamentally flawed;
iv), they underestimated the barrier for ultrathin wires; v), their comparison
with experiments is incorrect.Comment: Substantial changes made. Zaikin et al's main result was expected
from my work. They underestimated tunneling barrier for ultrathin wires by
one order of magnitude in the exponen
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