Density matrix of chaotic quantum systems

The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal form of the observable matrix elements in the eigenbasis of Hamiltonian. It was recently proposed that the density matrix elements have also a universal form, which can be used to understand the nonequilibrium dynamics at the whole time scale, from the transient regime to the long-time steady limit. In this paper, we numerically test these assumptions for density matrix in the models of spins.Comment: 6 pages, 5 figure

Characterisation and modelling of graphene FET detectors for flexible terahertz electronics

Low-cost electronics for future high-speed wireless communication and non-invasive inspection at terahertz frequencies require new materials with advanced mechanical and electronic properties. Graphene, with its unique combination of flexibility and high carrier velocity, can provide new opportunities for terahertz electronics. In particular, several types of power sensors based on graphene have been demonstrated and found suitable as fast and sensitive detectors over a wide part of the electromagnetic spectrum. Nevertheless, the underlying physics for signal detection are not well understood due to the lack of accurate characterisation methods, which hampers further improvement and optimisation of graphene-based power sensors. In this thesis, progress on modelling, design, fabrication and characterisation of terahertz graphene field-effect transistor (GFET) detectors is presented. Amajor part is devoted to the first steps towards flexible terahertz electronics.The characterisation and modelling of terahertz GFET detectors from 1 GHz to 1.1 THz are presented. The bias dependence, the scattering parameters and the detector voltage response were simultaneously accessed. It is shown that the voltage responsivity can be accurately described using a combination of a quasi-static equivalent circuit model, and the second-order series expansion terms of the nonlinear dc I-V characteristic. The videobandwidth, or IF bandwidth, of GFET detectors is estimated from heterodyne measurements. Moreover, the low-frequency noise of GFET detectors between 1 Hz and 1 MHz is investigated. From this, the room-temperature Hooge parameter of fabricated GFETs is extracted to be around 2*10^{-3}. It is found that the thermal noise dominates above 100 Hz, which sets the necessary switching time to reduce the effect of 1/f noise.A state-of-the-art GFET detector at 400 GHz, with a maximum measured optical responsivity of 74 V/W, and a minimum noise-equivalent power of 130 pW/Hz^{0.5} is demonstrated. It is shown that the detector performance is affected by the quality of the graphene film and adjacent layers, hence indicating the need to improve the fabrication process of GFETs.As a proof of concept, a bendable GFET terahertz detector on a plastic substrate is demonstrated. The effects of bending strain on dc I-V characteristics, responsivity and sensitivity are investigated. The detector exhibits a robust performance for tensile strain of more than 1% corresponding to a bending radius of 7 mm. Finally, a linear array of terahertz GFET detectors on a flexible substrate for imaging applications is fabricated and tested. The results show the possibility of realising bendable and curved focal plane arrays.In summary, in this work, the combination of improved device models and more accurate characterisation techniques of terahertz GFET detectors will allow for further optimisation. It is shown that graphene can open up for flexible terahertz electronics for future niche applications, such as wearable smart electronics and curved focal plane imaging

Robust Multiple Testing under High-dimensional Dynamic Factor Model

Large-scale multiple testing under static factor models is commonly used to select skilled funds in financial market. However, static factor models are arguably too stringent as it ignores the serial correlation, which severely distorts error rate control in large-scale inference. In this manuscript, we propose a new multiple testing procedure under dynamic factor models that is robust against both heavy-tailed distributions and the serial dependence. The idea is to integrate a new sample-splitting strategy based on chronological order and a two-pass Fama-Macbeth regression to form a series of statistics with marginal symmetry properties and then to utilize the symmetry properties to obtain a data-driven threshold. We show that our procedure is able to control the false discovery rate (FDR) asymptotically under high-dimensional dynamic factor models. As a byproduct that is of independent interest, we establish a new exponential-type deviation inequality for the sum of random variables on a variety of functionals of linear and non-linear processes. Numerical results including a case study on hedge fund selection demonstrate the advantage of the proposed method over several state-of-the-art methods.Comment: 29 pages, 4 table

Computer-aided diagnosis of low grade endometrial stromal sarcoma (LGESS)

Low grade endometrial stromal sarcoma (LGESS) accounts for about 0.2% of all uterine cancer cases. Approximately 75% of LGESS patients are initially misdiagnosed with leiomyoma, which is a type of benign tumor, also known as fibroids. In this research, uterine tissue biopsy images of potential LGESS patients are preprocessed using segmentation and stain normalization algorithms. We then apply a variety of classic machine learning and advanced deep learning models to classify tissue images as either benign or cancerous. For the classic techniques considered, the highest classification accuracy we attain is about 0.85, while our best deep learning model achieves an accuracy of approximately 0.87. These results clearly indicate that properly trained learning algorithms can aid in the diagnosis of LGESS