Quantum shot noise in mesoscopic superconductor-semiconductor heterostructures

Shot noise in a mesoscopic electrical conductor have become one of the most attentiondrawing subject over the last decade. This is because the shot-noise measurements provide a powerful tool to study charge transport in mesoscopic systems [1]. While conventional resistance measurements yield information on the average probability for the transmission of electrons from source to drain, shot-noise provides additional information on the electron transfer process, which can not be obtained from resistance measurements. For example, one can determine the charge ‘q’ of the current carrying quasi-particles in different systems from the Poisson shot noise SI = 2q�I� [2] where �I� is the mean current of the system. For instance, the quasi-particle charge is a fraction of the electron charge ‘e’ in the fractional quantum Hall regime [3, 4, 5]. The multiple charge quanta were observed in an atomic point contact between two superconducting electrodes [6]. Shot-noise also provides information on the statistics of the electron transfer. Shot noise in general is suppressed from its classical value SI = 2e�I�, due to the correlations. In mesoscopic conductors, due to the Pauli principle in fermion statistics, electrons are highly correlated. As a results, the noise is fully suppressed in the limit of a perfect open channel T = 1. For the opposite limit of low transmission T � 1, transmission of electron follows a Poisson process and recovers the Schottky result SI = 2e�I� [2]. For many channel systems, shot-noise is suppressed to 1/2 × 2e�I� for a symmetric double barrier junction [7, 8], to 1/3 in a disordered wire [9, 10, 11, 12, 13, 14] and to 1/4 in an open chaotic cavity [15, 16, 17]. When a superconductor is involved, the shot-noise can be enhanced by virtue of the Andreev reflection process taking place at the interface between a normal metal and a superconductor. In some limiting cases, e.g. in the tunneling and disordered limit, the shot-noise can be doubled with respect to its normal state value [18, 19, 20, 21]. One of the main results of this thesis is an extensive comparison of our experimental data on conductance and shot noise measurements in a S-N junction with various theoretical models. In addition to measure shot-noise in a two-terminal geometry, one can also perform the fluctuation measurements on multi-terminal conductors. Whereas shotnoise corresponds to the autocorrelation of fluctuations from the same leads, crosscorrelation measurements of fluctuations between different leads provide a wealth of new experiments. For example, the exchange-correlations can be measured directly from these geometry [22]. Experimental attempt in mesoscopic electronic device was the correlation measurements [14, 23] on electron beam-splitter geometry [24] which is the analogue to the Hanbury-Brown Twiss (HBT) experiment in optics. In their experiment, Hanbury-Brown and Twiss demonstrated the intensity-intensity correlations of the light of a star in order to determine its diameter [25]. They measured a positive correlations between two different output photon beams as predicted to the particles obeying Bose-Einstein statistics. This behavior is often called ‘bunching’. On the other hand, a stream of the particles obeying Fermi-Dirac statistics is expected to show a anti-bunching behavior, resulting in a negative correlation of the intensity fluctuations. Latter one was confirmed by a Fermionic version of HBT experiments in single-mode, high-mobility semiconductor 2DEG systems [14, 23]. Whereas in a single electron picture, correlations between Fermions are always negative1 (anti-bunching), the correlation signal is expected to become positive if two electrons are injected simultaneously to two arms and leave the device through different leads for the coincident detection in both outputs2. One simple example is the splitting of the cooper pair in a Y-junction geometry in front of the superconductor. Fig.1.1 shows the possible experimental scheme of the correlation measurement as described here and the sample realized in an high-mobility semiconductor heterostructures. Since all three experiments were done3, only one left unfolded, ‘The positive correlations from the Fermionic system’. The main motivation of this thesis work was to find a positive correlations in the device shown in Fig.1.1. In a well defined single channel collision experiment on an electron beam splitter, it has theoretically been shown that the measured correlations are sensitive to the spin entanglement [29, 30]. This is another even more exciting issue and we would like to mention that the experimental quest for positive correlations is important for the new field of quantum computation and communication in the solid state, [31, 32] in which entangled electrons play a crucial role. A natural source of entanglement is found in superconductors in which electrons are paired in a spin-singlet state. A source of entangled electrons may therefore be based on a superconducting injector.[33, 34, 27, 35, 36, 37, 38, 38, 39, 40, 41] Even more so, an electronic beamsplitter is capable of distinguishing entangled electrons from single electrons.[29, 42] However, the positive correlations have not been observed in solid-state mesoscopic devices until today. This thesis is organized as follows. Chapter 2 is devoted to the theoretical background of the electrical transport and the current fluctuations. We introduce the basic concept of electrical transport and the shot noise in normal state and superconductor-normal metal (S-N) junction. We also briefly review the theoretical proposals and arguments about the current-current cross-correlations in threeterminal systems. In Chapter 3, we describe the sample fabrication techniques which have been done in our laboratory such as e-beam lithography, metallization and etching. We present also the characterization of our particular system, niobium (Nb) / InAs-based 2DEG junction. Chapter 4 describes the reliable low-temperature measurement technique for detecting the noise. We characterize our measurement setup using a simple RC-circuit model. In Chapter 5, our main results about the shot noise of S-N junction are presented in detail

Petri net approaches for modeling, controlling, and validating flexible manufacturing systems

In this dissertation, we introduce the fundamental ideas and constructs of Petri net models such as ordinary, timed, colored, stochastic, control, and neural, and present some studies that emphasize Petri nets theories and applications as extended research fields that provide suitable platforms in modeling, controlling, validating, and evaluating concurrent systems, information systems, and a versatile dynamic system and manufacturing systems;We then suggest some of extensions that help make Petri nets useful for modeling and analyzing discrete event systems and manufacturing systems models based on the context of a versatile manufacturing system, and applies extended Petri nets models to several manufacturing systems such as an assembly cell, an Automated Palletized Conveyor System, and a tooling machine to show increased modeling power and efficient analysis methods;Finally, Validation methods are presented for these models and results of a performance analysis from a deterministic and stochastic model are used to reorganize and re-evaluate a manufacturing system in order to increase its flexibility

The Mx/G/1 queue with queue length dependent service times

We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.Bong Dae Choi, Yeong Cheol Kim, Yang Woo Shin, and Charles E. M. Pearc

In-situ wear behaviors of various rubbers in low-pressure hydrogen environment

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Estimation of the Characteristic Wavelength Parameter in 1D Leray-Burgers Equation with PINN

In this paper, we employ the Physics-Informed Neural Network (PINN) to estimate the practical range of the characteristic wavelength parameter(referred to as the smoothing parameter) $\alpha$ in the Leray-Burgers equation. The Leray-Burgers equation, a regularization of the inviscid Burgers equation, incorporates a Helmholtz filter with a characteristic wavelength $\alpha$ to replace the usual convective velocity, inducing a regularized convective velocity. The filter bends the equation's characteristics slightly and makes them not intersect each other, leading to a global solution in time. By conducting computational experiments with various initial conditions, we determine the practical range of $\alpha >0$ that closely approximates the solutions of the inviscid Burgers equation. Our findings indicate that the value of $\alpha$ depends on the initial data, with the practical range of $\alpha$ being between 0.01 and 0.05 for continuous initial profiles and between 0.01 and 0.03 for discontinuous initial profiles. The Leray-Burgers equation captures shock and rarefaction waves within the temporal domain for which training data exists. However, as the temporal domain extends beyond the training interval, data-driven forward computation demonstrates that the predictions generated by the PINN start to deviate from the exact solutions. This study also highlights the effectiveness and efficiency of the Leray-Burgers equation in real practical problems, specifically Traffic State Estimation

Circuit Structure and Control Method to Reduce Size and Harmonic Distortion of Interleaved Dual Buck Inverter

A new circuit structure and control method for a high power interleaved dual-buck inverter are proposed. The proposed inverter consists of six switches, four diodes and two inductors, uses a dual-buck structure to eliminate zero-cross distortion, and operates in an interleaved mode to reduce the current stress of switch. To reduce the total harmonic distortion at low output power, the inverter is controlled using discontinuous-current-mode control combined with continuous-current-mode control. The experimental inverter had a power-conversion efficiency of 98.5% at output power = 1300 W and 98.3% at output power = 2 kW, when the inverter was operated at an input voltage of 400 V-DC, output voltage of 220 V-AC/60 Hz, and switching frequency of 20 kHz. The total harmonic distortion was < 0.66%, which demonstrates that the inverter is suitable for high-power dc-ac power conversion.11Ysciescopu