Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath

The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with $N$ Majorana fermion modes coupled to another SYK model with $N^2$ Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from $2\pi/\beta$ ($\beta=1/(k_BT)$, $T$ is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a $\sqrt{T}$-dependence at relatively high temperature to a linear $T$-dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.Comment: 28 pages, 9 figures. References adde

Computation Sequences for Series and Polynomials

Approximation to the solutions of non-linear differential systems is very useful when the exact solutions are unattainable. Perturbation expansion replaces the system with a sequences of smaller problems, only the first of which is typically nonlinear. This works well by hand for the first few terms, but higher order computations are typically too demanding for all but the most persistent. Symbolic computation is thus attractive; however, symbolic computation of the expansions almost always encounters intermediate expression swell, by which we mean exponential growth in subexpression size or repetitions. A successful management of spatial complexity is vital to compute meaningful results. This thesis contains two parts. In the first part, we investigate a heat transfer problem where two-dimensional buoyancy-induced flow between two concentric cylinders is studied. Series expansion with respect to Rayleigh number is used to compute an approximation of a solution, using a symbolic- numerical algorithm. Computation sequences are used to help reduce the size of intermediate expressions. Up to 30th order solutions are computed. Accuracy, validity and stability of the computed series solution are studied. In the second part, Hilbert’s 16th problem is investigated to find the maximum number of limit cycles of certain systems. Focus values of the systems are computed using perturbation theory, which form multivariate polynomial sys- tems. The real roots of such systems leads to possible limit cycle conditions. A modular regular chains approach is used to triangularize the polynomial systems and help to compute the real roots. A system with 9 limit cycles is constructed using the computed real roots

Applications of artificial neural networks (ANNs) in several different materials research fields

PhDIn materials science, the traditional methodological framework is the identification of the composition-processing-structure-property causal pathways that link hierarchical structure to properties. However, all the properties of materials can be derived ultimately from structure and bonding, and so the properties of a material are interrelated to varying degrees. The work presented in this thesis, employed artificial neural networks (ANNs) to explore the correlations of different material properties with several examples in different fields. Those including 1) to verify and quantify known correlations between physical parameters and solid solubility of alloy systems, which were first discovered by Hume-Rothery in the 1930s. 2) To explore unknown crossproperty correlations without investigating complicated structure-property relationships, which is exemplified by i) predicting structural stability of perovskites from bond-valence based tolerance factors tBV, and predicting formability of perovskites by using A-O and B-O bond distances; ii) correlating polarizability with other properties, such as first ionization potential, melting point, heat of vaporization and specific heat capacity. 3) In the process of discovering unanticipated relationships between combination of properties of materials, ANNs were also found to be useful for highlighting unusual data points in handbooks, tables and databases that deserve to have their veracity inspected. By applying this method, massive errors in handbooks were found, and a systematic, intelligent and potentially automatic method to detect errors in handbooks is thus developed. Through presenting these four distinct examples from three aspects of ANN capability, different ways that ANNs can contribute to progress in materials science has been explored. These approaches are novel and deserve to be pursued as part of the newer methodologies that are beginning to underpin material research

Using Social Media to Combat Opioid Epidemic

Opioid addiction has become one of the largest and deadliest epidemics in the United States. To combat such deadly epidemic, there is an urgent need for novel tools and methodologies to gain new insights into the behavioral processes of opioid abuse and addiction. The role of social media in biomedical knowledge mining has turned into increasingly significant in recent years. The data from social media may contribute information beyond the knowledge of domain professionals (e.g., psychiatrists and epidemics researchers) and could potentially assist in sharpening our understanding toward the behavioral process of opioid addiction and treatment. In this thesis, we propose a novel framework to automate the analysis of social media (i.e., Twitter) for the detection of the opioid users. To model the Twitter users and posted tweets as well as their rich relationships, we constructed a structured heterogeneous information network (HIN) for representation. We then introduce a meta-path-based approach to characterize the semantic relatedness over users. As different meta-paths depict the relatedness over users at different views, we used Laplacian scores to aggregate different similarities formulated by different meta-paths and then a transductive classification model was built to make predictions. We conduct a comprehensive experimental study based on the real sample collections from Twitter to validate the effectiveness of our proposed approach. To improve the performance of automatic opioid user detection, we presented a meta-structure-based method to depict relatedness and integrate content-based similarity to formulate a similarity measure over users. We then aggregate different similarities using multi-kernel learning for opioid user detection. Comprehensive experimental results on real sample collections from Twitter demonstrate the effectiveness of our proposed learning models