54 research outputs found
Restoring the Pauli principle in the random phase approximation ground state
Random phase approximation ground state contains electronic configurations
where two (and more) identical electrons can occupy the same molecular
spin-orbital violating the Pauli exclusion principle. This overcounting of
electronic configurations happens due to quasiboson approximation in the
treatment of electron-hole pair operators. We describe the method to restore
the Pauli principle in the RPA wavefunction. The proposed theory is illustrated
by the calculations of molecular dipole moments and electronic kinetic
energies. The Hartree-Fock based RPA, which is corrected for the Pauli
principle, gives the results of comparable accuracy with M{\o}ller-Plesset
second order perturbation theory and coupled-cluster singles and doubles
method
Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport: inclusion of electron-electron interactions
Non-equilibrium Green's function theory for non-adiabatic effects in quantum
transport [Kershaw and Kosov, J.Chem. Phys. 2017, 147, 224109 and J. Chem.
Phys. 2018, 149, 044121] is extended to the case of interacting electrons. We
consider a general problem of quantum transport of interacting electrons
through a central region with dynamically changing geometry. The approach is
based on the separation of time scales in the non-equilibrium Green's functions
and the use of Wigner transformation to solve the Kadanoff-Baym equations. The
Green's functions and correlation self-energy are non-adiabatically expanded up
to the second order central time derivatives. We produced expressions for
Green's functions with non-adiabatic corrections and modified formula for
electric current; both depend not only on instantaneous molecular junction
geometry but also on nuclear velocities and accelerations. The theory is
illustrated by the study of electron transport through a model single-resonant
level molecular junction with local electron-electron repulsion and a
dynamically changing geometry
Nonadiabatic corrections to electric current in molecular junction due to nuclear motion at the molecule-electrode interfaces
We present quantum electron transport theory that incorporates dynamical
effects of motion of atoms on electrode-molecule interfaces in the calculations
of the electric current. The theory is based on non-equilibrium Green's
functions. We separate time scales in the Green's functions on fast relative
time and slow central time. The derivative with respect to the central time
serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym
equations for molecular Green's functions using Wigner representation and keep
terms up to the second order with respect to the central time derivatives.
Molecular Green's functions and consequently the electric current are expressed
as functions of molecular junction coordinates as well as velocities and
accelerations of molecule-electrode interface nuclei. We apply the theory to
model a molecular system and study the effects of non-adiabatic nuclear motion
on molecular junction conductivity
Counting quantum jumps: a summary and comparison of fixed-time and fluctuating-time statistics in electron transport
In quantum transport through nanoscale devices, fluctuations arise from
various sources: the discreteness of charge carriers, the statistical
non-equilibrium that is required for device operation, and unavoidable quantum
uncertainty. As experimental techniques have improved over the last decade,
measurements of these fluctuations have become available.} They have been
accompanied by a plethora of theoretical literature using many different
fluctuation statistics to describe the quantum transport. In this paper, we
overview three prominent fluctuation statistics: full counting, waiting time,
and first-passage time statistics. We discuss their weaknesses and strengths,
and explain connections between them in terms of renewal theory. In particular,
we discuss how different information can be encoded in different statistics
when the transport is non-renewal, and how this behavior manifests in the
measured physical quantities of open quantum systems. All theoretical results
are illustrated via a demonstrative transport scenario: a Markovian master
equation for a molecular electronic junction with electron-phonon interactions.
{{} We demonstrate that to obtain non-renewal behavior, and thus to have
temporal correlations between successive electron tunneling events, there must
be a strong coupling between tunneling electrons and out-of-equilibrium
quantized molecular vibrations.Comment: 24 pages, 8 figure
Coupled elastic membranes model for quantum heat transport in semiconductor nanowires
Presented here is a nanowire model, consisting of coupled elastic membranes
with the purpose of investigating thermal transport in quasi-one-dimensional
quantum systems. The vibrations of each elastic membrane are quantized and the
flow of the vibrational energy between adjacent membranes is allowed. The ends
of the nanowire are attached to thermal baths held at different temperatures.
We derived quantum master equation for energy flow across the nanowire and
obtained thermal currents and other key observables. We study the effects of a
disordered boundary on the thermal current by randomizing the membrane radii.
We evaluate the model as a nanowire analogue as well as study the effects of a
disordered boundary on thermal conductivity. The calculations show that the
membrane lattice model demonstrates diameter phonon confinement and a severe
reduction in thermal conductivity due to surface roughness which is
characteristic of semiconductor nanowires. The surface roughness also produces
a length dependence of the thermal conductivity of the form , with dependent on disorder characteristics, in the
otherwise ballistic regime. Finally, the parameters of the model are fitted to
available experimental data for silicon nanowires and the results of the
calculations are assessed against the experimental data.Comment: 12 Pages, 10 Figure
Telegraph noise in Markovian master equation for electron transport through molecular junctions
We present a theoretical approach to solve the Markovian master equation for quantum transport with stochastic telegraph noise. Considering probabilities as functionals of a random telegraph process, we use Novikov’s functional method to convert the stochastic master equation to a set of deterministic differential equations. The equations are then solved in the Laplace space, and the expression for the probability vector averaged over the ensemble of realisations of the stochastic process is obtained. We apply the theory to study the manifestations of telegraph noise in the transport properties of molecular junctions. We consider the quantum electron transport in a resonant-level molecule as well as polaronic regime transport in a molecular junction with electron-vibration interaction
Waiting time between charging and discharging processes in molecular junctions
When electric current flows through a molecular junction, the molecule constantly charges and discharges by tunneling electrons. These charging and discharging events occur at specific but random times and are separated by stochastic time intervals. These time intervals can be associated with the dwelling time for a charge (electron or hole) to reside on the molecule. In this paper, the statistical properties of these time intervals are studied and a general formula for their distribution is derived. The theory is based on the Markovian master equation which takes into account transitions between the vibrational states of charged and neutral molecules in the junction. Two quantum jump operators are identified from the Liouvillian of the master equation—one corresponds to charging of the molecule and the other discharges the molecule back to the neutral state. The quantum jump operators define the conditional probability that given that the molecule was charged by a tunneling electron at time t, the molecule becomes neutral at a later time t + τ discharging the electron to the drain electrode. Statistical properties of these time intervals τ are studied with the use of this distribution
Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport
We develop nonequilibribrium Green's function based transport theory, which
includes effects of nonadiabatic nuclear motion in the calculation of the
electric current in molecular junctions. Our approach is based on the
separation of slow and fast timescales in the equations of motion for the
Green's functions by means of the Wigner representation. Time derivatives with
respect to central time serves as a small parameter in the perturbative
expansion enabling the computation of nonadiabatic corrections to molecular
Green's functions. Consequently, we produce series of analytic expressions for
non-adiabatic electronic Green's functions (up to the second order in the
central time derivatives); which depend not solely on instantaneous molecular
geometry but likewise on nuclear velocities and accelerations. Extended formula
for electric current is derived which accounts for the non-adiabatic
corrections. This theory is concisely illustrated by the calculations on a
model molecular junction
Coherent time-dependent oscillations and temporal correlations in triangular triple quantum dots
The fluctuation behavior of triple quantum dots (TQDs) has, so far, largely
focused on current cumulants in the long-time limit via full counting
statistics. Given that (TQDs) are non-trivial open quantum systems with many
interesting features, such as Aharonov-Bohm interference and coherent
population blocking, new fluctuating-time statistics, such as the waiting time
distribution (WTD), may provide more information than just the current
cumulants alone. In this paper, we use a Born-Markov master equation to
calculate the standard and higher-order WTDs for coherentlycoupled TQDs arrayed
in triangular ring geometries for several transport regimes. In all cases we
find that the WTD displays coherent oscillations that correspond directly to
individual time-dependent dot occupation probabilities, a result also reported
recently in Ref.[1]. Our analysis, however, goes beyond the single-occupancy
and single waiting time regimes, investigating waiting time behavior for TQDs
occupied by multiple electrons and with finite electron-electron interactions.
We demonstrate that, in these regimes of higher occupancy, quantum coherent
effects introduce correlations between successive waiting times, which we can
tune via an applied magnetic field. We also show that correlations can be used
to distinguish between TQD configurations that have identical FCS and that dark
states can be tuned with Aharonov-Bohm interference for more complicated
regimes than single-occupancy
- …