Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT

We investigate a weak version of subsystem eigenstate thermalization hypothesis (ETH) for a two-dimensional large central charge conformal field theory by comparing the local equivalence of high energy state and thermal state of canonical ensemble. We evaluate the single-interval R\'enyi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of R\'enyi entropy by two different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central charge expansion. We then evaluate the relative entropy of the reduced density matrices to measure the difference between the heavy primary state and thermal state of canonical ensemble, and find that the aforementioned nontrivial eighth order results make the relative entropy unsuppressed in the large central charge limit. By using Pinsker's and Fannes-Audenaert inequalities, we can exploit the results of relative entropy to yield the lower and upper bounds on trace distance of the excited-state and thermal-state reduced density matrices. Our results are consistent with subsystem weak ETH, which requires the above trace distance is of power-law suppression by the large central charge. However, we are unable to pin down the exponent of power-law suppression. As a byproduct we also calculate the relative entropy to measure the difference between the reduced density matrices of two different heavy primary states.Comment: 28 pages, 4 figures;v2 change author list;v3 related subtleties about weak ETH clarified; v4 minor correction to match JHEP versio

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length $\ell$ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the R\'enyi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of $\ell^9$ for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.Comment: V1, 34 pages, 5 figures, see collection of complete results in the attached Mathematica notebook; V2, 38 pages, 5 figures, published versio

A novel fault-tolerant control strategy for near space hypersonic vehicles via least squares support vector machine and backstepping method

Near Space Hypersonic Vehicle (NSHV) could play significant roles in both military and civilian applications. It may cause huge losses of both personnel and property when a fatal fault occurs. It is therefore paramount to conduct fault-tolerant research for NSHV and avoid some catastrophic events. Toward this end, this paper presents a novel fault-tolerant control strategy by using the LSSVM (Least Squares Support Vector Machine)-based inverse system and Backstepping method. The control system takes advantage of the superiority of the LSSVM in solving the problems with small samples, high dimensions and local minima. The inverse system is built with an improved LSSVM. The adaptive controller is designed via the Backstepping which has the unique capability in dealing with nonlinear control systems. Finally, the experiment results demonstrate that the proposed method performs well

Antecedents of User Stickiness and Loyalty and Their Effects on Users’ Group-Buying Repurchase Intention

Intense competition among a vast number of group-buying websites leads to higher product homogeneity, which allows customers to switch to alternative websites easily and reduce their website stickiness and loyalty. This study explores the antecedents of user stickiness and loyalty and their effects on consumers’ group-buying repurchase intention. Results indicate that systems quality, information quality, service quality, and alternative system quality each has a positive relationship with user loyalty through user stickiness. Meanwhile, information quality directly impacts user loyalty. Thereafter, user stickiness and loyalty each has a positive relationship with consumers’ repurchase intention. Theoretical and managerial implications are also discussed

How Authoritarian Leadership and Renqing Orientation Improve Tacit Knowledge Sharing

Following an indigenous approach and fairness theory, we develop a theoretical model to investigate when and how authoritarian leadership will improve tacit knowledge sharing (KS). Drawing on survey data from 309 Chinese employees, we examine whether authoritarian leadership will affect procedural fairness (PF) perception and interactional fairness (IF) perception, which in turn, will affect tacit KS; and examine whether leader renqing orientation (LRO) will moderate these mediation processes. Our data demonstrate that authoritarian leadership is negatively related to IF perception, which is positively related to tacit KS. Moreover, authoritarian leadership significantly increases tacit KS intention through PF perception only when LRO is high. Authoritarian leadership significantly decreases tacit KS intention through PF perception and IF perception only when LRO is low. Theoretical and practical implications are discussed