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

The ionization of hydrogen and of hydrogenic positive ions by electron impact

Ionization of hydrogen and hydrogenic positive ions by electron impac

CJD mimics and chameleons

Rapidly progressive dementia mimicking Creutzfeldt-Jakob disease (CJD) is a relatively rare presentation but a rewarding one to become familiar with, as the potential diagnoses range from the universally fatal to the completely reversible. Patients require urgent decisions about assessment and investigation and have quickly evolving needs for treatments and support, through symptom management and end-of-life care in most cases. We have based this pragmatic review on the experiences of a specialist prion referral centre in the UK, which, unsurprisingly, is strongly biased towards seeing patients with CJD. Cases eventually proven not to have prion disease might be described as 'CJD-mimics'; being referred from UK neurologists, these are the most challenging cases. CJD in its classical presentation is very rarely mimicked; however, it is highly heterogeneous, and atypical forms can mimic virtually all common neurodegenerative syndromes. Warning features of a mimic include generalised seizures, hyponatraemia, fever, a facial movement disorder, a normal neurological examination and a modestly rapid presentation. Contrast-enhancing lesions or MRI signal hyperintensity outside the striatum, thalamus or cortex and a cerebrospinal fluid pleocytosis are key investigation pointers to a CJD mimic

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

21st Century Teenagers and Young Adults who are Deaf or Hard of Hearing: Outcomes and Possibilities

The purpose of this study was to document demographics, characteristics, and long-term outcomes of teenagers and young adults who are deaf or hard of hearing (DHH) and who all attended the Moog Center for Deaf Education for preschool and/or a portion of elementary school. Data were obtained via an online survey that was designed to assess educational, personal, and professional outcomes of individuals who were currently in high school and beyond. Survey questions were about the lives of these individuals after leaving the Moog Center. Participants included 108 individuals who were DHH, ranging from 15 to 32 years of age. Results indicate this group of individuals obtained high levels of achievement in terms of educational attainment, employment experience, social involvement, and communication competence, which demonstrates what is possible for individuals who are DHH

Factors Affecting Treatment Outcome in a Naturalistic Study of Psychological Therapy for Personality Disorder

This three-part thesis focuses on psychological therapy for personality disorders (PDs) and factors that influence both treatment completion and outcome. Part one is a literature review investigating documented mechanisms of change in the cognitive behavioural therapy (CBT) and dialectical behavioural therapy (DBT) treatment for borderline personality disorder (BPD) in current research. Although much research has focussed on improving treatment outcomes for BPD, there is very little research investigating the proposed changes by which these outcomes might occur. Three distinct categories of mechanism of change were found to be consistent across the literature examined. These categories are discussed in detail along with implications for future research and clinical practice. Part two presents a longitudinal empirical study of factors which affect treatment completion and treatment outcome in the CBT or DBT treatment of PD. Data spanning a six year period was collected and analysed for 231 patients. Results showed that therapist expertise was the only variable examined associated with treatment completion: more experienced therapists retained their patients in treatment for longer than less experienced therapists. Therapeutic dose (number of sessions attended), therapist expertise and substance misuse all predicted changes in risk outcome (deliberate self-harm, suicide attempts) and in number of PD diagnoses following treatment. Only therapeutic dose predicted change in other clinical diagnoses following treatment. Implications and strength of these findings are discussed in relation to problems with incomplete data, statistical analyses and non-representative sampling issues. Part three is a critical appraisal of the entire research process reflecting upon its challenges and successes. This section also includes a commentary on the field of PD research in general, and considers issues pertinent to future research

The global melt inclusion C/Ba array: Mantle variability, melting process, or degassing?

The Earth’s mantle holds more carbon than its oceans, atmosphere and con- tinents combined, yet the distribution of carbon within the mantle remains uncertain. Our best constraints on the distribution of carbon within the up- per mantle are derived from the carbon-trace element systematics of ultra- depleted glasses and melt inclusions from mid-ocean ridge basalts. How- ever, carbon-trace element systematics are susceptible to modification by crustal processes, including concurrent degassing and mixing, and melt in- clusion decrepitation. In this study we explore how the influence of these processes varies systematically with both the mantle source and melting pro- cess, thereby modulating both global and local carbon-trace element trends. We supplement the existing melt inclusion data from Iceland with four new datasets, significantly enhancing the spatial and geochemical coverage of melt inclusion datasets from the island. Within the combined Iceland dataset there is significant variation in melt inclusion C/Ba ratio, which is tightly correlated with trace element enrichment. The trends in C/Ba- Ba space displayed by our new data coincide with the same trends in data compiled from global ocean islands and mid-ocean ridges, forming a global array. The overall structure of the global C/Ba-Ba array is not a property of the source, instead it is controlled by CO2 vapour loss pre- and post-melt inclusion entrapment; i.e., the array is a consequence of degassing creating near-constant maximum melt-inclusion carbon contents over many orders of magnitude of Ba concentration. On Iceland, extremely high C/Ba (>100) and C/Nb (>1000) ratios are found in melt inclusions from the most depleted eruptions. The high C/Ba and C/Nb ratios are unlikely to be either analytical artefacts, or to be the product of extreme fractionation of the most incompatible elements during silicate melting. Whilst high C/Ba and C/Nb ratios could be generated by regassing of melt inclusions by CO2 vapour, or by mantle melting occurring in the presence of residual graphite, we suggest the high values most likely derive from an intrinsically high C/Ba and C/Nb mantle component that makes up a small fraction of the Icelandic mantle