On thermalization in the SYK and supersymmetric SYK models

The eigenstate thermalization hypothesis is a compelling conjecture which strives to explain the apparent thermal behavior of generic observables in closed quantum systems. Although we are far from a complete analytic understanding, quantum chaos is often seen as a strong indication that the ansatz holds true. In this paper, we address the thermalization of energy eigenstates in the Sachdev-Ye-Kitaev model, a maximally chaotic model of strongly-interacting Majorana fermions. We numerically investigate eigenstate thermalization for specific few-body operators in the original SYK model as well as its $\mathcal{N}=1$ supersymmetric extension and find evidence that these models satisfy ETH. We discuss the implications of ETH for a gravitational dual and the quantum information-theoretic properties of SYK it suggests.Comment: Published versio

Note on the Green's function formalism and topological invariants

It has been discovered previously that the topological order parameter could be identified from the topological data of the Green's function, namely the (generalized) TKNN invariant in general dimensions, for both non-interacting and interacting systems. In this note, we show that this phenomenon has a clear geometric derivation. This proposal could be regarded as an alternative proof for the identification of the corresponding topological invariant and the topological order parameter

Note on global symmetry and SYK model

The goal of this note is to explore the behavior of effective action in the SYK model with general continuous global symmetries. A global symmetry will decompose the whole Hamiltonian of a many-body system to several single charge sectors. For the SYK model, the effective action near the saddle point is given as the free product of the Schwarzian action part and the free action of the group element moving in the group manifold. With a detailed analysis in the free sigma model, we prove a modified version of Peter-Weyl theorem that works for generic spin structure. As a conclusion, we could make a comparison between the thermodynamics and the spectral form factors between the whole theory and the single charge sector, to make predictions on the SYK model and see how symmetry affects the chaotic behavior in certain timescales.Comment: 44 page

Shot clustering technique for story browsing for large video databases

Automatic video segmentation is the first and necessary step for organizing a long video file into several smaller units for subsequent browsing and retrieval. The smallest basic unit is shot--a contiguous sequence of frames recorded from a single camera operation. Since users of a video database management system are more likely to recall important events or stories rather than a particular frame or shot, relevant shots are typically grouped into a high-level unit called scene that is more meaningful to viewers. This thesis presents ShotWeave, a novel technique for clustering relevant shots into a scene for narrative films. Each scene is part of a story. Browsing through these scenes unfolds the entire story of the film, allowing the users to locate their desire video segments quickly and efficiently. The crux of ShotWeave is the use of similarity measures of carefully selected regions of representative frames of shots in the clustering process. These regions capture essential information needed to maintain viewers' thought in presence of shot breaks as intended by common continuity-editing techniques used in film literature. The experimental results show that ShotWeave performs well, and is more robust than two recent shot clustering techniques on full-length films consisting of a wide range of camera motions and a complex composition of related shots

The νR\nu_{R}-philic scalar dark matter

Right-handed neutrinos ($\nu_{R}$) offer an intriguing portal to new physics in hidden sectors where dark matter (DM) may reside. In this work, we delve into the simplest hidden sector involving only a real scalar exclusively coupled to $\nu_{R}$, referred to as the $\nu_{R}$-philic scalar. We investigate the viability of the $\nu_{R}$-philic scalar to serve as a DM candidate, under the constraint that the coupling of $\nu_{R}$ to the standard model is determined by the seesaw relation and is responsible for the observed DM abundance. By analyzing the DM decay channels and solving Boltzmann equations, we identify the viable parameter space. In particular, our study reveals a lower bound ($\sim10^{4}$ GeV) on the mass of $\nu_{R}$ for the $\nu_{R}$-philic scalar to be DM. The DM mass may vary from sub-keV to sub-GeV. Within the viable parameter space, monochromatic neutrino lines from DM decay can be an important signal for DM indirect detection.Comment: 21 pages, 5 figure

Supersymmetric SYK model and random matrix theory

In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N = 1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry

Transforming individual ambidexterity to organisational ambidexterity: a configurational perspective on leadership factors as an aggregating process

Organisational ambidexterity (i.e. the ability to balance exploration and exploitation) is crucial to organisations’ survival and development. It can be achieved at multiple levels, but the connection between different levels, especially from the individual to the firm level, has received scant attention in the literature. Utilising micro-foundations theory, this paper aims to study how leadership factors (i.e. top team management [TMT] behavioural integration, a chief executive officer’s [CEO] characteristics and ambidextrous behaviours, and senior managers’ ambidextrous behaviours) complete a mechanism to transform individual ambidexterity (IA) to organisational ambidexterity (OA), filling the gap in the IA–OA process. Our study provides a configurational perspective on finding the sufficient combined effort among different leadership factors to complete the IA–OA process