A
bstract
In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these ...only provide a coarse probe of the full underlying operator growth structure. In this article we develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-all
q
-body interactions. We derive the full operator growth structure in the large
q
limit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.
A
bstract
Motivated by recent studies of the information paradox in (1+1)-D anti-de Sitter spacetime with a bath described by a (1+1)-D conformal field theory, we study the dynamics of second Ŕenyi ...entropy of the Sachdev-Ye-Kitaev (SYK) model (
χ
) coupled to a Majorana chain bath (
ψ
). The system is prepared in the thermofield double (TFD) state and then evolved by
H
L
+
H
R
. For small system-bath coupling, we find that the second Rényi entropy
S
χ
L
,
χ
R
2
of the SYK model undergoes a first order transition during the evolution. In the sense of holographic duality, the long-time solution corresponds to a “replica wormhole”. The transition time corresponds to the Page time of a black hole coupled to a thermal bath. We further study the information scrambling and retrieval by introducing a classical control bit, which controls whether or not we add a perturbation in the SYK system. The mutual information between the bath and the control bit shows a positive jump at the Page time, indicating that the entanglement wedge of the bath includes an island in the holographic bulk.
Highway bridges stand as paramount elements within transportation infrastructure systems. The ability to ensure swift recovery after extreme events, such as earthquakes, is a fundamental trait of ...resilient communities. Consequently, expediting the recovery process necessitates near real-time diagnosis of structural damage to provide dependable information. In this study, a data-driven approach for damage detection and assessment is investigated, focusing on bridge columns-the pivotal supporting elements of bridge systems-based on simulations derived from nonlinear time history analysis. This research introduces a set of cumulative intensity-based damage features, whose efficacy is demonstrated through unsupervised learning techniques. Leveraging the support vector machine, a prominent pattern recognition algorithm in supervised learning, alongside Bayesian optimization with a Gaussian process, seismic damage detection and assessment are explored. Encouragingly, the methodology yields high estimation accuracies for both binary outcomes (indicating the presence of damage or the occurrence of collapse) and multi-class classifications (indicating the severity of damage). This breakthrough opens avenues for the practical implementation of on-board sensor computing, enabling near real-time damage detection and assessment in bridge structures.
Recently, the graph convolutional network (GCN) has drawn increasing attention in the hyperspectral image (HSI) classification. Compared with the convolutional neural network (CNN) with fixed square ...kernels, GCN can explicitly utilize the correlation between adjacent land covers and conduct flexible convolution on arbitrarily irregular image regions; hence, the HSI spatial contextual structure can be better modeled. However, to reduce the computational complexity and promote the semantic structure learning of land covers, GCN usually works on superpixel-based nodes rather than pixel-based nodes; thus, the pixel-level spectral-spatial features cannot be captured. To fully leverage the advantages of the CNN and GCN, we propose a heterogeneous deep network called CNN-enhanced GCN (CEGCN), in which CNN and GCN branches perform feature learning on small-scale regular regions and large-scale irregular regions, and generate complementary spectral-spatial features at pixel and superpixel levels, respectively. To alleviate the structural incompatibility of the data representation between the Euclidean data-oriented CNN and non-Euclidean data-oriented GCN, we propose the graph encoder and decoder to propagate features between image pixels and graph nodes, thus enabling the CNN and GCN to collaborate in a single network. In contrast to other GCN-based methods that encode HSI into a graph during preprocessing, we integrate the graph encoding process into the network and learn edge weights from training data, which can promote the node feature learning and make the graph more adaptive to HSI content. Extensive experiments on three data sets demonstrate that the proposed CEGCN is both qualitatively and quantitatively competitive compared with other state-of-the-art methods.
The chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed ...in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.
There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic ...treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system's Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.
A
bstract
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.
With the popularity and growth of social networking, consumers often rely on the advice and recommendations from online friends when making purchase decisions. Social commerce in this regard ...represents a shift in consumers' thinking from inefficient individual-based consumption decisions to collaborative sharing and social shopping. In this study, we investigate social commerce from two different but interrelated angles (i.e., social shopping and social sharing). Built on the literature of social support, commitment-trust theory, and trust transfer theory, a research model was developed and empirically examined. The findings of this study demonstrated that both emotional and informational social support significantly affected consumers' trust and community commitment, which in turn exerted profound impacts on both social shopping and social sharing intention. Trust toward members also can be transferred into trust toward community, which further led to users' community commitment. Limitations and implications for both research and practice are discussed.
•Consumers' decisions in social commerce context are examined with insights from both social sharing and social shopping intentions.•Relational factors (i.e., community commitment, trust toward community and members) together explained 44.4% of the variance in social shopping intention, and 31.8% of the variance in social sharing intention.•The effect of trust toward members on social sharing intention is fully mediated by users' trust toward social commerce community.•Both emotional and informational social support significantly affected consumers' trust and the community commitment.
A
bstract
Sachdev-Ye-Kitaev (SYK) model, which describes
N
randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly ...AdS
2
dilaton gravity. Ref.
1
proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS
2
geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the
q
dependence of the spectral function.
A
bstract
Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a ...bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated
entanglement negativity
and its Rényi generalizations in holographic duality. We first review the definition of the Rényi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Rényi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Rényi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.
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