66,937 research outputs found
A combined R-matrix eigenstate basis set and finite-differences propagation method for the time-dependent Schr\"{od}dinger equation: the one-electron case
In this work we present the theoretical framework for the solution of the
time-dependent Schr\"{o}dinger equation (TDSE) of atomic and molecular systems
under strong electromagnetic fields with the configuration space of the
electron's coordinates separated over two regions, that is regions and
. In region the solution of the TDSE is obtained by an R-matrix basis
set representation of the time-dependent wavefunction. In region a grid
representation of the wavefunction is considered and propagation in space and
time is obtained through the finite-differences method. It appears this is the
first time a combination of basis set and grid methods has been put forward for
tackling multi-region time-dependent problems. In both regions, a high-order
explicit scheme is employed for the time propagation. While, in a purely
hydrogenic system no approximation is involved due to this separation, in
multi-electron systems the validity and the usefulness of the present method
relies on the basic assumption of R-matrix theory, namely that beyond a certain
distance (encompassing region ) a single ejected electron is distinguishable
from the other electrons of the multi-electron system and evolves there (region
II) effectively as a one-electron system. The method is developed in detail for
single active electron systems and applied to the exemplar case of the hydrogen
atom in an intense laser field.Comment: 13 pages, 6 figures, submitte
Optical Generation and Quantitative Characterizations of Electron-hole Entanglement
Using a method of characterizing entanglement in the framework of quantum
field theory, we investigate the optical generation and quantitative
characterizations of quantum entanglement in an electron-hole system, in
presence of spin-orbit coupling, and especially make a theoretical analysis of
a recent experimental result. Basically, such entanglement should be considered
as between occupation numbers of single particle basis states, and is
essentially generated by coupling between different single particle basis
states in the second quantized Hamiltonian. Interaction with two resonant light
modes of different circular polarizations generically leads to a superposition
of ground state and two heavy-hole excitonic states. When and only when the
state is a superposition of only the two excitonic eigenstates, the
entanglement reduces to that between two distinguishable particles, each with
two degrees of freedom, namely, band index, as characterized by angular
momentum, and orbit, as characterized by position or momentum. The band-index
state, obtained by tracing over the orbital degree of freedom, is found to be a
pure state, hence the band-index and orbital degrees of freedom are separated
in this state. We propose some basic ideas on spatially separating the electron
and the hole, so that the entanglement of band-indices, or angular momenta, is
between spatially separated electron and hole.Comment: 8 pages. Journal versio
Singlet-triplet splitting, correlation and entanglement of two electrons in quantum dot molecules
Starting with an accurate pseudopotential description of the single-particle
states, and following by configuration-interaction treatment of correlated
electrons in vertically coupled, self-assembled InAs/GaAs quantum
dot-molecules, we show how simpler, popularly-practiced approximations, depict
the basic physical characteristics including the singlet-triplet splitting,
degree of entanglement (DOE) and correlation. The mean-field-like
single-configuration approaches such as Hartree-Fock and local spin density,
lacking correlation, incorrectly identify the ground state symmetry and give
inaccurate values for the singlet-triplet splitting and the DOE. The Hubbard
model gives qualitatively correct results for the ground state symmetry and
singlet-triplet splitting, but produces significant errors in the DOE because
it ignores the fact that the strain is asymmetric even if the dots within a
molecule are identical. Finally, the Heisenberg model gives qualitatively
correct ground state symmetry and singlet-triplet splitting only for rather
large inter-dot separations, but it greatly overestimates the DOE as a
consequence of ignoring the electron double occupancy effect.Comment: 13 pages, 9 figures. To appear in Phys. Rev.
Restricted and unrestricted Hartree-Fock calculations of conductance for a quantum point contact
Very short quantum wires (quantum contacts) exhibit a conductance structure
at a value of conductance close to . It is believed that the
structure arises due to the electron-electron interaction, and it is also
related to electron spin. However details of the mechanism of the structure are
not quite clear. Previously we approached the problem within the restricted
Hartree-Fock approximation. This calculation demonstrated a structure similar
to that observed experimentally. In the present work we perform restricted and
unrestricted Hartree-Fock calculations to analyze the validity of the
approximations. We also consider dependence of the effect on the electron
density in leads. The unrestricted Hartree-Fock method allows us to analyze
trapping of the single electron within the contact. Such trapping would result
in the Kondo model for the ``0.7 structure''. The present calculation confirms
the spin-dependent bound state picture and does not confirm the Kondo model
scenario.Comment: 6 pages, 9 figure
Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems
We perform the quantitative evaluation of the entanglement dynamics in
scattering events between two insistinguishable electrons interacting via
Coulomb potential in 1D and 2D semiconductor nanostructures. We apply a
criterion based on the von Neumann entropy and the Schmidt decomposition of the
global state vector suitable for systems of identical particles. From the
timedependent numerical solution of the two-particle wavefunction of the
scattering carriers we compute their entanglement evolution for different spin
configurations: two electrons with the same spin, with different spin, singlet,
and triplet spin state. The procedure allows to evaluate the mechanisms that
govern entanglement creation and their connection with the characteristic
physical parameters and initial conditions of the system. The cases in which
the evolution of entanglement is similar to the one obtained for
distinguishable particles are discussed.Comment: 22 pages, 7 figures, submitted to Physical Review
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