Fredholm determinants and the statistics of charge transport

Using operator algebraic methods we show that the moment generating function of charge transport in a system with infinitely many non-interacting Fermions is given by a determinant of a certain operator in the one-particle Hilbert space. The formula is equivalent to a formula of Levitov and Lesovik in the finite dimensional case and may be viewed as its regularized form in general. Our result embodies two tenets often realized in mesoscopic physics, namely, that the transport properties are essentially independent of the length of the leads and of the depth of the Fermi sea.Comment: 30 pages, 2 figures, reference added, credit amende

Laboratory study of magnetic reconnection in lunar-relevant mini-magnetospheres

Mini-magnetospheres are small ion-scale structures that are well-suited to studying kinetic-scale physics of collisionless space plasmas. Such ion-scale magnetospheres can be found on local regions of the Moon, associated with the lunar crustal magnetic field. In this paper, we report on the laboratory experimental study of magnetic reconnection in laser-driven, lunar-like ion-scale magnetospheres on the Large Plasma Device (LAPD) at the University of California - Los Angeles. In the experiment, a high-repetition rate (1 Hz), nanosecond laser is used to drive a fast moving, collisionless plasma that expands into the field generated by a pulsed magnetic dipole embedded into a background plasma and magnetic field. The high-repetition rate enables the acquisition of time-resolved volumetric data of the magnetic and electric fields to characterize magnetic reconnection and calculate the reconnection rate. We notably observe the formation of Hall fields associated with reconnection. Particle-in-cell simulations reproducing the experimental results were performed to study the micro-physics of the interaction. By analyzing the generalized Ohm's law terms, we find that the electron-only reconnection is driven by kinetic effects, through the electron pressure anisotropy. These results are compared to recent satellite measurements that found evidence of magnetic reconnection near the lunar surface

Dephasing and Measurement Efficiency via a Quantum Dot Detector

We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.Comment: 7 pages, 3 figure

Quantum Disorder and Quantum Chaos in Andreev Billiards

We investigate the crossover from the semiclassical to the quantum description of electron energy states in a chaotic metal grain connected to a superconductor. We consider the influence of scattering off point impurities (quantum disorder) and of quantum diffraction (quantum chaos) on the electron density of states. We show that both the quantum disorder and the quantum chaos open a gap near the Fermi energy. The size of the gap is determined by the mean free time in disordered systems and by the Ehrenfest time in clean chaotic systems. Particularly, if both times become infinitely large, the density of states is gapless, and if either of these times becomes shorter than the electron escape time, the density of states is described by random matrix theory. Using the Usadel equation, we also study the density of states in a grain connected to a superconductor by a diffusive contact.Comment: 20 pages, 10 figure

Proximity effects at ferromagnet-superconductor interfaces

We study proximity effects at ferromagnet superconductor interfaces by self-consistent numerical solution of the Bogoliubov-de Gennes equations for the continuum, without any approximations. Our procedures allow us to study systems with long superconducting coherence lengths. We obtain results for the pair potential, the pair amplitude, and the local density of states. We use these results to extract the relevant proximity lengths. We find that the superconducting correlations in the ferromagnet exhibit a damped oscillatory behavior that is reflected in both the pair amplitude and the local density of states. The characteristic length scale of these oscillations is approximately inversely proportional to the exchange field, and is independent of the superconducting coherence length in the range studied. We find the superconducting coherence length to be nearly independent of the ferromagnetic polarization.Comment: 13 Pages total. Compressed .eps figs might display poorly, but will print fin

Proximity effects and characteristic lengths in ferromagnet-superconductor structures

We present an extensive theoretical investigation of the proximity effects that occur in Ferromagnet/Superconductor ($F/S$) systems. We use a numerical method to solve self consistently the Bogoliubov-de Gennes equations in the continuum. We obtain the pair amplitude and the local density of states (DOS), and use these results to extract the relevant lengths characterizing the leakage of superconductivity into the magnet and to study spin splitting into the superconductor. These phenomena are investigated as a function of parameters such as temperature, magnet polarization, interfacial scattering, sample size and Fermi wavevector mismatch, all of which turn out to have important influence on the results. These comprehensive results should help characterize and analyze future data and are shown to be in agreement with existing experiments.Comment: 24 pages, including 26 figure

Measurement of finite-frequency current statistics in a single-electron transistor

Electron transport in nano-scale structures is strongly influenced by the Coulomb interaction which gives rise to correlations in the stream of charges and leaves clear fingerprints in the fluctuations of the electrical current. A complete understanding of the underlying physical processes requires measurements of the electrical fluctuations on all time and frequency scales, but experiments have so far been restricted to fixed frequency ranges as broadband detection of current fluctuations is an inherently difficult experimental procedure. Here we demonstrate that the electrical fluctuations in a single electron transistor (SET) can be accurately measured on all relevant frequencies using a nearby quantum point contact for on-chip real-time detection of the current pulses in the SET. We have directly measured the frequency-dependent current statistics and hereby fully characterized the fundamental tunneling processes in the SET. Our experiment paves the way for future investigations of interaction and coherence induced correlation effects in quantum transport.Comment: 7 pages, 3 figures, published in Nature Communications (open access

Charge densities and charge noise in mesoscopic conductors

We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. The partial density of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial density of states determine the degree of dephasing generated by a weakly coupled voltage probe. In addition the partial density of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. The partial density of states permit the formulation of a Friedel sum rule which can be applied locally. We introduce the off-diagonal elements of the partial density of states matrix to describe charge fluctuation processes. This generalization leads to a local Wigner-Smith life-time matrix.Comment: 10 pages, 2 figure

Nonlinear complexity analysis of brain fMRI signals in schizophrenia

Peer reviewedPublisher PD

Association between age of cannabis initiation and gray matter covariance networks in recent onset psychosis

Cannabis use during adolescence is associated with an increased risk of developing psychosis. According to a current hypothesis, this results from detrimental effects of early cannabis use on brain maturation during this vulnerable period. However, studies investigating the interaction between early cannabis use and brain structural alterations hitherto reported inconclusive findings. We investigated effects of age of cannabis initiation on psychosis using data from the multicentric Personalized Prognostic Tools for Early Psychosis Management (PRONIA) and the Cannabis Induced Psychosis (CIP) studies, yielding a total sample of 102 clinically-relevant cannabis users with recent onset psychosis. GM covariance underlies shared maturational processes. Therefore, we performed source-based morphometry analysis with spatial constraints on structural brain networks showing significant alterations in schizophrenia in a previous multisite study, thus testing associations of these networks with the age of cannabis initiation and with confounding factors. Earlier cannabis initiation was associated with more severe positive symptoms in our cohort. Greater gray matter volume (GMV) in the previously identified cerebellar schizophrenia-related network had a significant association with early cannabis use, independent of several possibly confounding factors. Moreover, GMV in the cerebellar network was associated with lower volume in another network previously associated with schizophrenia, comprising the insula, superior temporal, and inferior frontal gyrus. These findings are in line with previous investigations in healthy cannabis users, and suggest that early initiation of cannabis perturbs the developmental trajectory of certain structural brain networks in a manner imparting risk for psychosis later in life