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

An investigation of the basement complex aquifer system in Lofa county, Liberia, for the purpose of siting boreholes

Liberia is recovering from a 14 year civil war and only 51% of the rural population has access to safe drinking water. Little hydrogeological knowledge survives in Liberia, increasing the difficulty in successfully siting new boreholes. An understanding of the local hydrogeological environment is therefore needed to improve borehole site selection and increase success rates. This research provides a semi-quantitative characterization of the hydrogeological environment of the basement aquifer in Lofa county, Liberia. Based on literature review and analysis of borehole logs, the study has developed a conceptual hydrogeological model for the local conditions, which is further characterized using 2D geoelectrical sections. Groundwater is predominantly obtained from the saprolite and underlying fractured bedrock, but specific capacities (median 281 l h-1 m-1; 25th and 75th percentile of 179 and 490 l h-1 m-1, respectively) are constrained by the limited thickness of the saturated saprolite. This study has shown that the groundwater resources in the crystalline basement in this part of Liberia conform to the general conceptual model, allowing standard techniques used elsewhere for siting and developing groundwater to be used

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

Distribution of waiting times between electron cotunnelings

In the resonant tunneling regime sequential processes dominate single electron transport through quantum dots or molecules that are weakly coupled to macroscopic electrodes. In the Coulomb blockade regime, however, cotunneling processes dominate. Cotunneling is an inherently quantum phenomenon and thus gives rise to interesting observations, such as an increase in the current shot noise. Since cotunneling processes are inherently fast compared to the sequential processes, it is of interest to examine the short time behaviour of systems where cotunneling plays a role, and whether these systems display nonrenewal statistics. We consider three questions in this paper. Given that an electron has tunneled from the source to the drain via a cotunneling or sequential process, what is the waiting time until another electron cotunnels from the source to the drain? What are the statistical properties of these waiting time intervals? How does cotunneling affect the statistical properties of a system with strong inelastic electron-electron interactions? In answering these questions, we extend the existing formalism for waiting time distributions in single electron transport to include cotunneling processes via an $n$-resolved Markovian master equation. We demonstrate that for a single resonant level the analytic waiting time distribution including cotunneling processes yields information on individual tunneling amplitudes. For both a SRL and an Anderson impurity deep in the Coulomb blockade there is a nonzero probability for two electrons to cotunnel to the drain with zero waiting time inbetween. Furthermore, we show that at high voltages cotunneling processes slightly modify the nonrenewal behaviour of an Anderson impurity with a strong inelastic electron-electron interaction.Comment: 16 pages, 6 figure

Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions

The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterising transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which have historically been calculated in the long-time limit, waiting times are able to detect non-renewal behaviour in mesoscopic systems. They have failed, however, to correctly incorporate backtunneling events. Recently, a method has been developed that can describe unidirectional and bidirectional transport on an equal footing: the distribution of first-passage times. Rather than the time between successive electron tunnelings, the first-passage refers to the first time the number of extra electrons in the drain reaches $+1$. Here, we demonstrate the differences between first-passage time statistics and waiting time statistics in transport scenarios where the waiting time either cannot correctly reproduce the higher order current cumulants or cannot be calculated at all. To this end, we examine electron transport through a molecule coupled to two macroscopic metal electrodes. We model the molecule with strong electron-electron and electron-phonon interactions in three regimes: (i) sequential tunneling and cotunneling for a finite bias voltage through the Anderson model, (ii) sequential tunneling with no temperature gradient and a bias voltage through the Holstein model, and (iii) sequential tunneling at zero bias voltage and a temperature gradient through the Holstein model. We show that, for each transport scenario, backtunneling events play a significant role; consequently, the waiting time statistics do not correctly predict the renewal and non-renewal behaviour, whereas the first-passage time distribution does.Comment: 16 pages, 8 figures tota

Current-induced forces in nanosystems: A hierarchical equations of motion approach

A new approach to calculating current-induced forces in charge transport through nanosystems is introduced. Starting from the fully quantum mechanical hierarchical equations of motion formalism, a timescale separation between electronic and vibrational degrees of freedom is used to derive a classical Langevin equation of motion for the vibrational dynamics as influenced by current-induced forces, such as the electronic friction. The resulting form of the friction is shown to be equivalent to previously derived expressions. The numerical exactness of the hierarchical equations of motion approach, however, allows the investigation of transport scenarios with strong intrasystem and system-environment interactions. As a demonstration, the electronic friction of three example systems is calculated and analyzed: a single electronic level coupled to one classical vibrational mode, two electronic levels coupled to one classical vibrational mode, and a single electronic level coupled to both a classical and quantum vibrational mode

Volumetric Absorptive Microsampling (VAMS) for Targeted LC-MS/MS Determination of Tryptophan-Related Biomarkers

L-Tryptophan (TRP) metabolites and related biomarkers play crucial roles in physiological functions, and their imbalances are implicated in central nervous system pathologies and neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS), Alzheimer's disease, Parkinson's disease, schizophrenia and depression. The measurement of TRP metabolites and related biomarkers possesses great potential to elucidate the disease mechanisms, aid preclinical drug development, highlight potential therapeutic targets and evaluate the outcomes of therapeutic interventions. An effective, straightforward, sensitive and selective liquid chromatography-tandem mass spectrometry (LC-MS/MS) method was developed for the simultaneous determination of 24 TRP-related compounds in miniaturised murine whole blood samples. Sampling and sample pretreatment miniaturisation were achieved thanks to the development of a volumetric dried blood microsampling approach. Volumetric absorptive microsampling (VAMS) allows the accurate sampling of microvolumes of blood with advantages including, but not limited to, minimal sampling invasiveness, logistical improvements, method sustainability in terms of solvents and energy consumption, and improvement of animal studies in the framework of the 3Rs (Replacement, Reduction and Refinement) principles on animal welfare. The VAMS-LC-MS/MS method exhibited good selectivity, and correlation coefficient values for the calibration curves of each analyte were >0.9987. The limits of quantitation ranged from 0.1 to 25 ng/mL. The intra- and inter-day precisions in terms of RSD were <9.6%. All analytes were stable in whole blood VAMS samples stored at room temperature for at least 30 days with analyte losses < 14%. The developed method was successfully applied to the analysis of biological samples from mice, leading to the unambiguous determination of all the considered target analytes. This method can therefore be applied to analyse TRP metabolites and related biomarkers levels to monitor disease states, perform mechanistic studies and investigate the outcomes of therapeutic interventions

Operation of Faddeev-Kernel in Configuration Space

We present a practical method to solve Faddeev three-body equations at energies above three-body breakup threshold as integral equations in coordinate space. This is an extension of previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.Comment: 20 pages, 8 figures, to be published in Few-Body System

Evaluation of neonatally-induced mild diabetes in rats: Maternal and fetal repercussions

Many experimental studies have been performed to evaluate mild diabetes effects. However, results are divergent regarding glycemia and insulin measurement, fetal macrossomia, and placental weights. The aim was to investigate repercussions of neonatally-induced mild diabetes on the maternal organism and presence of congenital defects in their offspring in other mild diabetes model. On the day of birth, female offspring were distributed into two groups: Group streptozotocin (STZ): received 100 mg STZ/kg body weight, and Control Group: received vehicle in a similar time period. Maternal weights and glycemias were determined at days 0, 7, 14 and 21 of pregnancy. At day 21 of pregnancy, the rats were anesthetized and a laparotomy was performed to weigh and analyze living fetuses and placentas. The fetuses were classified as small (SPA), appropriate (APA) and large (LPA) for pregnancy age. Fetuses were also analyzed for the presence of external anomalies and processed for skeletal anomaly and ossification sites analysis. Statistical significance was considered as p < 0.05. In STZ group, there was increased glycemia at 0 and 14 days of pregnancy, lower weights throughout pregnancy, higher placental weight and index, an increased proportion of fetuses classified as SPA and LPA, and their fetuses presented with an increased frequency of abnormal sternebra, and absent cervical nuclei, which were not enough to cause the emergence of skeletal anomalies. Thus, this study shows that mild diabetes altered fetal development, characterized by intrauterine growth restriction. Further, the reached glycemia does not lead to any major congenital defects in the fetuses of streptozotocin-induced mild diabetic rats

Evolution of Diffusion-Weighted Magnetic Resonance Imaging Signal Abnormality in Sporadic Creutzfeldt-Jakob Disease, With Histopathological Correlation

IMPORTANCE: Prion diseases represent the archetype of brain diseases caused by protein misfolding, with the most common subtype being sporadic Creutzfeldt-Jakob disease (sCJD), a rapidly progressive dementia. Diffusion-weighted imaging (DWI) has emerged as the most sensitive magnetic resonance imaging (MRI) sequence for the diagnosis of sCJD, but few studies have assessed the evolution of MRI signal as the disease progresses. OBJECTIVES: To assess the natural history of the MRI signal abnormalities on DWI in sCJD to improve our understanding of the pathogenesis and to investigate the potential of DWI as a biomarker of disease progression, with histopathological correlation. DESIGN, SETTING, AND PARTICIPANTS: Gray matter involvement on DWI was assessed among 37 patients with sCJD in 26 cortical and 5 subcortical subdivisions per hemisphere using a semiquantitative scoring system of 0 to 2 at baseline and follow-up. A total brain score was calculated as the summed scores in the individual regions. In 7 patients, serial mean diffusivity measurements were obtained. Age at baseline MRI, disease duration, atrophy, codon 129 methionine valine polymorphism, Medical Research Council Rating Scale score, and histopathological findings were documented. The study setting was the National Prion Clinic, London, England. All participants had a probable or definite diagnosis of sCJD and had at least 2 MRI studies performed during the course of their illness. The study dates were October 1, 2008 to April 1, 2012. The dates of our analysis were January 19 to April 20, 2012. MAIN OUTCOMES AND MEASURES: Correlation of regional and total brain scores with disease duration. RESULTS: Among the 37 patients with sCJD in this study there was a significant increase in the number of regions demonstrating signal abnormality during the study period, with 59 of 62 regions showing increased signal intensity (SI) at follow-up, most substantially in the caudate and putamen (P < .001 for both). The increase in the mean (SD) total brain score from 30.2 (17.3) at baseline to 40.5 (20.6) at follow-up (P = .001) correlated with disease duration (r = 0.47, P = .003 at baseline and r = 0.35, P = .03 at follow-up), and the left frontal SI correlated with the degree of spongiosis (r = 0.64, P = .047). Decreased mean diffusivity in the left caudate at follow-up was seen (P < .001). Eight patients demonstrated decreased SI in cortical regions, including the left inferior temporal gyrus and the right lingual gyrus. CONCLUSIONS AND RELEVANCE: Magnetic resonance images in sCJD show increased extent and degree of SI on DWI that correlates with disease duration and the degree of spongiosis. Although cortical SI may fluctuate, increased basal ganglia SI is a consistent finding and is due to restricted diffusion. Diffusion-weighted imaging in the basal ganglia may provide a noninvasive biomarker in future therapeutic trials