Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models

The Sachdev-Ye-Kitaev model is a $(0+1)$-dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the Sachdev-Ye-Kitaev model, which is a lattice model with $N$ Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large $N$ limit, the higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev model such as local criticality in two-point functions, zero temperature entropy and chaos measured by the out-of-time-ordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a "butterfly velocity" describing the propagation of chaos in space. We mainly present results for a $(1+1)$-dimensional example, and discuss the general case near the end.Comment: 1+37 pages, published versio

Spread of entanglement in a Sachdev-Ye-Kitaev chain

We study the spread of R\'enyi entropy between two halves of a Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield double (TFD) state. The SYK chain model is a model of chaotic many-body systems, which describes a one-dimensional lattice of Majorana fermions, with spatially local random quartic interaction. We find that for integer R\'enyi index $n>1$, the R\'enyi entanglement entropy saturates at a parametrically smaller value than expected. This implies that the TFD state of the SYK chain does not rapidly thermalize, despite being maximally chaotic: instead, it rapidly approaches a prethermal state. We compare our results to the signatures of thermalization observed in other quenches in the SYK model, and to intuition from nearly-$\mathrm{AdS}_2$ gravity.Comment: 1+46 pages, 11 figure

Heat engine in the three-dimensional spacetime

We define a kind of heat engine via three-dimensional charged BTZ black holes. This case is quite subtle and needs to be more careful. The heat flow along the isochores does not equal to zero since the specific heat $C_V\neq0$ and this point completely differs from the cases discussed before whose isochores and adiabats are identical. So one cannot simply apply the paradigm in the former literatures. However, if one introduces a new thermodynamic parameter associated with the renormalization length scale, the above problem can be solved. We obtain the analytical efficiency expression of the three-dimensional charged BTZ black hole heat engine for two different schemes. Moreover, we double check with the exact formula. Our result presents the first specific example for the sound correctness of the exact efficiency formula. We argue that the three-dimensional charged BTZ black hole can be viewed as a toy model for further investigation of holographic heat engine. Furthermore, we compare our result with that of the Carnot cycle and extend the former result to three-dimensional spacetime. In this sense, the result in this paper would be complementary to those obtained in four-dimensional spacetime or ever higher. Last but not the least, the heat engine efficiency discussed in this paper may serve as a criterion to discriminate the two thermodynamic approaches introduced in Ref.[29] and our result seems to support the approach which introduces a new thermodynamic parameter $R=r_0$.Comment: Revised version. Discussions adde

Cholesteryl ester transfer protein (CETP) as a possible drug-resistance marker in breast cancer

A research dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in the fulfilment of the requirements for the Degree of Masters in Science, Signed on 24 May 2018 in JohannesburgHormone responsive breast cancer (BC) is the most common BC and relies on steroid hormones for cell proliferation and survival, therefore endocrine therapy; Tamoxifen (TAM), serves as the main therapeutic strategy in treating hormone receptor positive BC. Despite the use of TAM for over four decades, overcoming drug resistance remains challenging. Due to the fact that steroid hormones are derived from cholesterol and evidently, increased level of cholesterol is associated with cancer progression, in this research, we investigated the effect of reducing intracellular cholesterol as a possible alternative method to induce cell death in BC cells. An important protein involved in cholesterol homeostasis is the Cholesteryl Ester Transfer Protein (CETP). CETP maintains cholesterol homeostasis by storing cholesteryl esters (CEs) in lipid droplets. The intracellular accumulation of CEs leads to aggressive cancer development and drug resistance. Therefore, we aim to investigate whether CETP can possibly be used as a drug-resistance marker in BC. This study has shown that knocking-down CETP resulted in increase in apoptosis in MCF-7 cells when treated with TAM (by 10-40%) and various other drugs. Furthermore, CETP knock-down with the addition of a cholesterol-depleting agent increased apoptosis by 10 fold when compared to the non-transfected MCF-7 cells, possibly due to a decrease in CE content. Similar results were observed in MDA-MB-231 cells. Therefore, it was concluded that CETP could thus serve as a potential drug-resistance marker in cancer cells, more specifically BC. Furthermore, strategies targeting CETP could be used as a potential combination treatment for treating cancer.MT 201