67 research outputs found
Fluctuation theorem for counting-statistics in electron transport through quantum junctions
We demonstrate that the probability distribution of the net number of
electrons passing through a quantum system in a junction obeys a steady-state
fluctuation theorem (FT) which can be tested experimentally by the full
counting statistics (FCS) of electrons crossing the lead-system interface. The
FCS is calculated using a many-body quantum master equation (QME) combined with
a Liouville space generating function (GF) formalism. For a model of two
coupled quantum dots, we show that the FT becomes valid for long binning times
and provide an estimate for the finite-time deviations. We also demonstrate
that the Mandel (or Fano) parameter associated with the incoming or outgoing
electron transfers show subpoissonian (antibunching) statistics.Comment: 20 pages, 12 figures, accepted in Phy.Rev.
Exploring Foundations of Time-Independent Density Functional Theory for Excited-States
Based on the work of Gorling and that of Levy and Nagy, density-functional
formalism for many Fermionic excited-states is explored through a careful and
rigorous analysis of the excited-state density to external potential mapping.
It is shown that the knowledge of the ground-state density is a must to fix the
mapping from an excited-state density to the external potential. This is the
excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the
ground-state density the density of the excited-state gives the true many-body
wavefunctions of the system. Further, the excited-state Kohn-Sham system is
defined by comparing it's non-interacting kinetic energy with the true kinetic
energy. The theory is demonstrated by studying a large number of atomic
systems.Comment: submitted to J. Chem. Phy
Quantum master equation for electron transport through quantum dots and single molecules
A quantum master equation (QME) is derived for the many-body density matrix
of an open current-carrying system weakly coupled to two metal leads. The
dynamics and the steady-state properties of the system for arbitrary bias are
studied using projection operator techniques, which keep track of number of
electrons in the system. We show that coherences between system states with
different number of electrons, n, (Fock space coherences) do not contribute to
the transport to second order in system-lead coupling.
However, coherences between states with the same n may effect transport
properties when the damping rate is of the order or faster then the system Bohr
frequencies.
For large bias, when all the system many-body states lie between the chemical
potentials of the two leads, we recover previous results. In the rotating wave
approximation (when the damping is slow compared to the Bohr frequencies of the
system), the dynamics of populations and the coherences in the system
eigenbasis are decoupled. The QME then reduces to a birth and death master
equation for populations.Comment: 22 pages, 8 figures, paper accepted in Phys. Rev.
Multiple Core-Hole Coherence in X-Ray Four-Wave-Mixing Spectroscopies
Correlation-function expressions are derived for the coherent nonlinear
response of molecules to three resonant ultrafast pulses in the x-ray regime.
The ability to create two-core-hole states with controlled attosecond timing in
four-wave-mixing and pump probe techniques should open up new windows into the
response of valence electrons, which are not available from incoherent x-ray
Raman and fluorescence techniques. Closed expressions for the necessary
four-point correlation functions are derived for the electron-boson model by
using the second order cumulant expansion to describe the fluctuating
potentials. The information obtained from multidimensional nonlinear techniques
could be used to test and refine this model, and establish an anharmonic
oscillator picture for electronic excitations
Local-density approximation for exchange energy functional in excited-state density functional theory
An exchange energy functional is proposed and tested for obtaining a class of
excited-state energies using density functional formalism. The functional is
the excited-state counterpart of the local-density approximation functional for
the ground state. It takes care of the state dependence of the energy
functional and leads to highly accurate excitation energies
Positron and positronium affinities in the work-formalism Hartree-Fock approximation
Positron binding to anions is investigated within the work formalism proposed
by Harbola and Sahni for the halide anions and the systems Li^- through O^-
excluding Be^- and N^-. The toal ground-state energies of the anion-positron
bound systems are empirically found to be an upper bound to the Hartree-Fock
energies. The computed expectation values as well as positron and positronium
affinities are in good agreement with their restricted Hartree-Fock
counterparts. Binding of a positron to neutral species is also investigated
using an iterative method.Comment: 12 pages, to appear in Physical Review
A self-consistent quantum master equation approach to molecular transport
We propose a self-consistent generalized quantum master equation (GQME) to
describe electron transport through molecular junctions. In a previous study
[M.Esposito and M.Galperin. Phys. Rev. B 79, 205303 (2009)], we derived a
time-nonlocal GQME to cure the lack of broadening effects in Redfield theory.
To do so, the free evolution used in the Born-Markov approximation to close the
Redfield equation was replaced by a standard Redfield evolution. In the present
paper, we propose a backward Redfield evolution leading to a time-local GQME
which allows for a self-consistent procedure of the GQME generator. This
approach is approximate but properly reproduces the nonequilibrium steady state
density matrix and the currents of an exactly solvable model. The approach is
less accurate for higher moments such as the noise.Comment: 9 pages, 4 figure
Dynamic image potential at an Al(111) surface
We evaluate the electronic self-energy Sigma(E) at an Al(111) surface using the GW space-time method. This self-energy automatically includes the image potential V-im not present in any local-density approximation for exchange and correlation. We solve the energy-dependent quasiparticle equations and calculate the effective local potential experienced by electrons in the near-surface region. The relative contribution of exchange proves to be very different for states above the Fermi level. The image-plane position for interacting electrons is closer to the surface than for the purely electrostatic effects felt by test charges, and, like its classical counterpart, is drawn inwards by the effects of atomic structure
Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
The fluctuations in nonequilibrium systems are under intense theoretical and
experimental investigation. Topical ``fluctuation relations'' describe
symmetries of the statistical properties of certain observables, in a variety
of models and phenomena. They have been derived in deterministic and, later, in
stochastic frameworks. Other results first obtained for stochastic processes,
and later considered in deterministic dynamics, describe the temporal evolution
of fluctuations. The field has grown beyond expectation: research works and
different perspectives are proposed at an ever faster pace. Indeed,
understanding fluctuations is important for the emerging theory of
nonequilibrium phenomena, as well as for applications, such as those of
nanotechnological and biophysical interest. However, the links among the
different approaches and the limitations of these approaches are not fully
understood. We focus on these issues, providing: a) analysis of the theoretical
models; b) discussion of the rigorous mathematical results; c) identification
of the physical mechanisms underlying the validity of the theoretical
predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007
Work functions, ionization potentials, and in-between: Scaling relations based on the image charge model
We revisit a model in which the ionization energy of a metal particle is
associated with the work done by the image charge force in moving the electron
from infinity to a small cut-off distance just outside the surface. We show
that this model can be compactly, and productively, employed to study the size
dependence of electron removal energies over the range encompassing bulk
surfaces, finite clusters, and individual atoms. It accounts in a
straightforward manner for the empirically known correlation between the atomic
ionization potential (IP) and the metal work function (WF), IP/WF2. We
formulate simple expressions for the model parameters, requiring only a single
property (the atomic polarizability or the nearest neighbor distance) as input.
Without any additional adjustable parameters, the model yields both the IP and
the WF within 10% for all metallic elements, as well as matches the size
evolution of the ionization potentials of finite metal clusters for a large
fraction of the experimental data. The parametrization takes advantage of a
remarkably constant numerical correlation between the nearest-neighbor distance
in a crystal, the cube root of the atomic polarizability, and the image force
cutoff length. The paper also includes an analytical derivation of the relation
of the outer radius of a cluster of close-packed spheres to its geometric
structure.Comment: Original submission: 8 pages with 7 figures incorporated in the text.
Revised submission (added one more paragraph about alloy work functions): 18
double spaced pages + 8 separate figures. Accepted for publication in PR
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