350 research outputs found
Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics
We use renormalization group to calculate the reunion and survival exponents
of a set of random walkers interacting with a long range and a short
range interaction. These exponents are used to study the binding-unbinding
transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version
(PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902
(2001) (E
Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory
Thermodynamics provides a transparent definition of the free energy of
density functional theory (DFT), and of its derivatives - the potentials, at
finite temperatures T. By taking the T to 0 limit, it is shown here that both
DFT and spin-dependent DFT (for ground states) suffer from precisely the same
benign ambiguities: (a) charge and spin quantization lead to "up to a constant"
indeterminacies in the potential and the magnetic field respectively, and (b)
the potential in empty subspaces is undetermined but irrelevant. Surprisingly,
these simple facts were inaccessible within the standard formulation, leading
to recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.
Improved tensor-product expansions for the two-particle density matrix
We present a new density-matrix functional within the recently introduced
framework for tensor-product expansions of the two-particle density matrix. It
performs well both for the homogeneous electron gas as well as atoms. For the
homogeneous electron gas, it performs significantly better than all previous
density-matrix functionals, becoming very accurate for high densities and
outperforming Hartree-Fock at metallic valence electron densities. For isolated
atoms and ions, it is on a par with previous density-matrix functionals and
generalized gradient approximations to density-functional theory. We also
present analytic results for the correlation energy in the low density limit of
the free electron gas for a broad class of such functionals.Comment: 4 pages, 2 figure
Kohn Anomalies in Superconductors
I present the detailed behavior of phonon dispersion curves near momenta
which span the electronic Fermi sea in a superconductor. I demonstrate that an
anomaly, similar to the metallic Kohn anomaly, exists in a superconductor's
dispersion curves when the frequency of the phonon spanning the Fermi sea
exceeds twice the superconducting energy gap. This anomaly occurs at
approximately the same momentum but is {\it stronger} than the normal-state
Kohn anomaly. It also survives at finite temperature, unlike the metallic
anomaly. Determination of Fermi surface diameters from the location of these
anomalies, therefore, may be more successful in the superconducting phase than
in the normal state. However, the superconductor's anomaly fades rapidly with
increased phonon frequency and becomes unobservable when the phonon frequency
greatly exceeds the gap. This constraint makes these anomalies useful only in
high-temperature superconductors such as .Comment: 18 pages (revtex) + 11 figures (upon request), NSF-ITP-93-7
Electron spin relaxation by nuclei in semiconductor quantum dots
We have studied theoretically the electron spin relaxation in semiconductor
quantum dots via interaction with nuclear spins. The relaxation is shown to be
determined by three processes: (i) -- the precession of the electron spin in
the hyperfine field of the frozen fluctuation of the nuclear spins; (ii) -- the
precession of the nuclear spins in the hyperfine field of the electron; and
(iii) -- the precession of the nuclear spin in the dipole field of its nuclear
neighbors. In external magnetic fields the relaxation of electron spins
directed along the magnetic field is suppressed. Electron spins directed
transverse to the magnetic field relax completely in a time on the order of the
precession period of its spin in the field of the frozen fluctuation of the
nuclear spins. Comparison with experiment shows that the hyperfine interaction
with nuclei may be the dominant mechanism of electron spin relaxation in
quantum dots
Electronic structure of rectangular quantum dots
We study the ground state properties of rectangular quantum dots by using the
spin-density-functional theory and quantum Monte Carlo methods. The dot
geometry is determined by an infinite hard-wall potential to enable comparison
to manufactured, rectangular-shaped quantum dots. We show that the electronic
structure is very sensitive to the deformation, and at realistic sizes the
non-interacting picture determines the general behavior. However, close to the
degenerate points where Hund's rule applies, we find spin-density-wave-like
solutions bracketing the partially polarized states. In the
quasi-one-dimensional limit we find permanent charge-density waves, and at a
sufficiently large deformation or low density, there are strongly localized
stable states with a broken spin-symmetry.Comment: 8 pages, 9 figures, submitted to PR
Density-functional calculation of ionization energies of current-carrying atomic states
Current-density-functional theory is used to calculate ionization energies of
current-carrying atomic states. A perturbative approximation to full
current-density-functional theory is implemented for the first time, and found
to be numerically feasible. Different parametrizations for the
current-dependence of the density functional are critically compared. Orbital
currents in open-shell atoms turn out to produce a small shift in the
ionization energies. We find that modern density functionals have reached an
accuracy at which small current-related terms appearing in open-shell
configurations are not negligible anymore compared to the remaining difference
to experiment.Comment: 7 pages, 2 tables, accepted by Phys. Rev.
Hamiltonian Theory of the Composite Fermion Wigner Crystal
Experimental results indicating the existence of the high magnetic field
Wigner Crystal have been available for a number of years. While variational
wavefunctions have demonstrated the instability of the Laughlin liquid to a
Wigner Crystal at sufficiently small filling, calculations of the excitation
gaps have been hampered by the strong correlations. Recently a new Hamiltonian
formulation of the fractional quantum Hall problem has been developed. In this
work we extend the Hamiltonian approach to include states of nonuniform
density, and use it to compute the excitation gaps of the Wigner Crystal
states. We find that the Wigner Crystal states near are
quantitatively well described as crystals of Composite Fermions with four
vortices attached. Predictions for gaps and the shear modulus of the crystal
are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table
Probing the Shape of Quantum Dots with Magnetic Fields
A tool for the identification of the shape of quantum dots is developed. By
preparing a two-electron quantum dot, the response of the low-lying excited
states to a homogeneous magnetic field, i.e. their spin and parity
oscillations, is studied for a large variety of dot shapes. For any geometric
configuration of the confinement we encounter characteristic spin singlet -
triplet crossovers. The magnetization is shown to be a complementary tool for
probing the shape of the dot.Comment: 11 pages, 4 figure
Exchange-correlation vector potentials and vorticity-dependent exchange-correlation energy densities in two-dimensional systems
We present a new approach how to calculate the scalar exchange-correlation
potentials and the vector exchange-correlation potentials from current-carrying
ground states of two-dimensional quantum dots. From these exchange-correlation
potentials we derive exchange-correlation energy densities and examine their
vorticity (or current) dependence. Compared with parameterizations of
current-induced effects in literature we find an increased significance of
corrections due to paramagnetic current densities.Comment: 5 figures, submitted to PR
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