44 research outputs found
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
Two-band second moment model and an interatomic potential for caesium
A semi-empirical formalism is presented for deriving interatomic potentials
for materials such as caesium or cerium which exhibit volume collapse phase
transitions. It is based on the Finnis-Sinclair second moment tight binding
approach, but incorporates two independent bands on each atom. The potential is
cast in a form suitable for large-scale molecular dynamics, the computational
cost being the evaluation of short ranged pair potentials. Parameters for a
model potential for caesium are derived and tested
The role of occupied d states in the relaxation of hot electrons in Au
We present first-principles calculations of electron-electron scattering
rates of low-energy electrons in Au. Our full band-structure calculations
indicate that a major contribution from occupied d states participating in the
screening of electron-electron interactions yields lifetimes of electrons in Au
with energies of above the Fermi level that are larger than
those of electrons in a free-electron gas by a factor of . This
prediction is in agreement with a recent experimental study of ultrafast
electron dynamics in Au(111) films (J. Cao {\it et al}, Phys. Rev. B {\bf 58},
10948 (1998)), where electron transport has been shown to play a minor role in
the measured lifetimes of hot electrons in this material.Comment: 4 pages, 2 figures, to appear in Phys. Rev.
Mixing time of critical Ising model on trees is polynomial in the height
In the heat-bath Glauber dynamics for the Ising model on the lattice,
physicists believe that the spectral gap of the continuous-time chain exhibits
the following behavior. For some critical inverse-temperature , the
inverse-gap is bounded for , polynomial in the surface area
for and exponential in it for . This has
been proved for except at criticality. So far, the only underlying
geometry where the critical behavior has been confirmed is the complete graph.
Recently, the dynamics for the Ising model on a regular tree, also known as the
Bethe lattice, has been intensively studied. The facts that the inverse-gap is
bounded for were
established, where is the critical spin-glass parameter, and the
tree-height plays the role of the surface area.
In this work, we complete the picture for the inverse-gap of the Ising model
on the -ary tree, by showing that it is indeed polynomial in at
criticality. The degree of our polynomial bound does not depend on , and
furthermore, this result holds under any boundary condition. We also obtain
analogous bounds for the mixing-time of the chain. In addition, we study the
near critical behavior, and show that for , the inverse-gap
and mixing-time are both .Comment: 53 pages; 3 figure
Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach
We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian
with a competing long-range repulsive term in the presence of an external
magnetic field. The model is analytically solved within the self consistent
Hartree approximation for two different initial conditions: disordered or zero
field cooled (ZFC), and fully magnetized or field cooled (FC). To test the
predictions of the approximation we develop a suitable numerical scheme to
ensure the isotropic nature of the interactions. Both the analytical approach
and the numerical simulations of two-dimensional finite systems confirm a
simple aging scenario at zero temperature and zero field. At zero temperature a
critical field is found below which the initial conditions are relevant
for the long time dynamics of the system. For a logarithmic growth of
modulated domains is found in the numerical simulations but this behavior is
not captured by the analytical approach which predicts a growth law at
Basis Functions for Linear-Scaling First-Principles Calculations
In the framework of a recently reported linear-scaling method for
density-functional-pseudopotential calculations, we investigate the use of
localized basis functions for such work. We propose a basis set in which each
local orbital is represented in terms of an array of `blip functions'' on the
points of a grid. We analyze the relation between blip-function basis sets and
the plane-wave basis used in standard pseudopotential methods, derive criteria
for the approximate equivalence of the two, and describe practical tests of
these criteria. Techniques are presented for using blip-function basis sets in
linear-scaling calculations, and numerical tests of these techniques are
reported for Si crystal using both local and non-local pseudopotentials. We
find rapid convergence of the total energy to the values given by standard
plane-wave calculations as the radius of the linear-scaling localized orbitals
is increased.Comment: revtex file, with two encapsulated postscript figures, uses epsf.sty,
submitted to Phys. Rev.
Correlation Entropy of an Interacting Quantum Field and H-theorem for the O(N) Model
Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy
(of the nth order) for an interacting quantum field, obtained by `slaving'
(truncation with causal factorization) of the higher (n+1 th) order correlation
functions in the Schwinger-Dyson system of equations. This renders an otherwise
closed system effectively open where dissipation arises. The concept of
correlation entropy is useful for addressing issues related to thermalization.
As a small yet important step in that direction we prove an H-theorem for the
correlation entropy of a quantum mechanical O(N) model with a Closed Time Path
Two Particle Irreducible Effective Action at the level of Next-to-Leading-Order
large N approximation. This model may be regarded as a field theory in
space dimensions.Comment: 22 page
Theory of inelastic lifetimes of low-energy electrons in metals
Electron dynamics in the bulk and at the surface of solid materials are well
known to play a key role in a variety of physical and chemical phenomena. In
this article we describe the main aspects of the interaction of low-energy
electrons with solids, and report extensive calculations of inelastic lifetimes
of both low-energy electrons in bulk materials and image-potential states at
metal surfaces. New calculations of inelastic lifetimes in a homogeneous
electron gas are presented, by using various well-known representations of the
electronic response of the medium. Band-structure calculations, which have been
recently carried out by the authors and collaborators, are reviewed, and future
work is addressed.Comment: 28 pages, 18 figures, to appear in Chem. Phy
Far-from-equilibrium quantum many-body dynamics
The theory of real-time quantum many-body dynamics as put forward in Ref.
[arXiv:0710.4627] is evaluated in detail. The formulation is based on a
generating functional of correlation functions where the Keldysh contour is
closed at a given time. Extending the Keldysh contour from this time to a later
time leads to a dynamic flow of the generating functional. This flow describes
the dynamics of the system and has an explicit causal structure. In the present
work it is evaluated within a vertex expansion of the effective action leading
to time evolution equations for Green functions. These equations are applicable
for strongly interacting systems as well as for studying the late-time
behaviour of nonequilibrium time evolution. For the specific case of a bosonic
N-component phi^4 theory with contact interactions an s-channel truncation is
identified to yield equations identical to those derived from the 2PI effective
action in next-to-leading order of a 1/N expansion. The presented approach
allows to directly obtain non-perturbative dynamic equations beyond the widely
used 2PI approximations.Comment: 20 pp., 6 figs; submitted version with added references and typos
corrected