Dynamical singularity of the rate function for quench dynamics in finite size quantum systems

The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of Loschmidt echo in the thermodynamical limit. In general, exact zeros of Loschmidt echo are not accessible in a finite size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of dynamical singularity of the rate function for finite size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite size system is divergent at a series of critical times. We demonstrate our scheme by considering the Su-Schrieffer-Heeger model and the Creutz model as concrete examples. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.Comment: 8 pages, 6 figure

Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions

The fidelity is widely used to detect quantum phase transition, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zero of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity $\mathcal{F}(\gamma,\tilde{\gamma})$ always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states ($\gamma$ and $\tilde{\gamma}$) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zero of fidelity can be always accessed by tuning the magnetic flux when $\gamma$ and $\tilde{\gamma}$ belong to different phases. On the other hand, no exact zero of fidelity can be observed if $\gamma$ and $\tilde{\gamma}$ are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model and Haldane model. Our work provides a practicable way to detect quantum phase transition via the calculation of fidelity of finite-size systems.Comment: 9 pages, 8 figure

Prediction of Preoperative Scale Score of Dystonia Based on Few-Shot Learning

As a neurological disease, dystonia mainly has symptoms including muscle stiffness, dyskinesia, tremor, muscle spasm, etc. Dystonia score plays an important role in targeted auxiliary diagnosis, treatment plan design, and follow-up evaluation of patients. In this paper, the feature information of brain lateralization is extracted from electroencephalography (EEG) signals by clustering method, while information on time domain, frequency domain, and time sequence are extracted from EEG signals and electromyography (EMG) signals. Various deep-learning models are used to predict dystonia scores. Experiments show that this method can effectively predict dystonia based on the quantitative indicators extracted from few-shot neural signals. The methodology in this paper can help doctors judge the disease more accurately, make personalized treatment plans, and assist in monitoring the treatment effect

Comparison of dimensionally-split and multi-dimensional atmospheric transport schemes for long time-steps

Dimensionally split advection schemes are attractive for atmospheric modelling due to their efficiency and accuracy in each spatial dimension. Accurate long time steps can be achieved without significant cost using the flux-form semi-Lagrangian technique. The dimensionally split scheme used in this paper is constructed from the one-dimensional Piecewise Parabolic Method and extended to two dimensions using COSMIC splitting. The dimensionally split scheme is compared with a genuinely multi-dimensional, method of lines scheme which, with implicit time-stepping, is stable for Courant numbers significantly larger than one. Two-dimensional advection test cases on Cartesian planes are proposed that avoid the complexities of a spherical domain or multi-panel meshes. These are solid body rotation, horizontal advection over orography and deformational flow. The test cases use distorted non-orthogonal meshes either to represent sloping terrain or to mimic the distortions near cubed-sphere edges. Mesh distortions are expected to accentuate the errors associated with dimension splitting, however, the accuracy of the dimensionally split scheme decreases only a little in the presence of mesh distortions. The dimensionally split scheme also loses some accuracy when long time-steps are used. The multi-dimensional scheme is almost entirely insensitive to mesh distortions and asymptotes to second-order accuracy at high resolution. As is expected for implicit time-stepping, phase errors occur when using long time-steps but the spatially well-resolved features are advected at the correct speed and the multi-dimensional scheme is always stable. A naive estimate of computational cost (number of multiplies) reveals that the implicit scheme is the most expensive, particularly for large Courant numbers. If the multi-dimensional scheme is used instead with explicit time-stepping, the Courant number is restricted to less than one, the accuracy is maintained and the cost becomes similar to the dimensionally split scheme

Variable-Based Fault Localization via Enhanced Decision Tree

Fault localization, aiming at localizing the root cause of the bug under repair, has been a longstanding research topic. Although many approaches have been proposed in the last decades, most of the existing studies work at coarse-grained statement or method levels with very limited insights about how to repair the bug (granularity problem), but few studies target the finer-grained fault localization. In this paper, we target the granularity problem and propose a novel finer-grained variable-level fault localization technique. Specifically, we design a program-dependency-enhanced decision tree model to boost the identification of fault-relevant variables via discriminating failed and passed test cases based on the variable values. To evaluate the effectiveness of our approach, we have implemented it in a tool called VARDT and conducted an extensive study over the Defects4J benchmark. The results show that VARDT outperforms the state-of-the-art fault localization approaches with at least 247.8% improvements in terms of bugs located at Top-1, and the average improvements are 330.5%. Besides, to investigate whether our finer-grained fault localization result can further improve the effectiveness of downstream APR techniques, we have adapted VARDT to the application of patch filtering, where VARDT outperforms the state-of-the-art PATCH-SIM by filtering 26.0% more incorrect patches. The results demonstrate the effectiveness of our approach and it also provides a new way of thinking for improving automatic program repair techniques