Scaling behavior of quantum critical relaxation dynamics in a heat bath

We study the scaling behavior of the relaxation dynamics to thermal equilibrium when a quantum system is near the quantum critical point. In particular, we investigate systems whose relaxation dynamics is described by a Lindblad master equation. We find that the universal scaling behavior not only exhibits in the equilibrium stage at the long-time limit, but also manifests itself in the non-equilibrium relaxation process. While the critical behavior is dictated by the low-lying energy levels of the Hamiltonian, the dissipative part in the Lindblad equation also plays important roles in two aspects: First, the dissipative part makes the high energy levels decay fast after which the universal behavior controlled by the low-lying modes emerges. Second, the dissipation rate gives rise to a time scale that affects the scaling behavior. We confirm our theory by solving the Lindblad equation for the one-dimensional transverse-field Ising model.Comment: 5 pages, 4 figure

Scaling in driven dynamics starting in the vicinity of a quantum critical point

We study the driven critical dynamics with an equilibrium initial state near a quantum critical point. In contrast to the original Kibble-Zurek mechanism, which describes the driven dynamics starting from an adiabatic stage that is far from the critical point, the initial adiabacity is broken in this scenario. As a result, the scaling behavior cannot be described by the original Kibble-Zurek scaling. In this work we propose a scaling theory, which includes the initial parameters as additional scaling variables, to characterize the scaling behavior. In particular, this scaling theory can be used to describe the driven scaling behavior starting from a finite-temperature equilibrium state near a quantum critical point. We numerically confirm the scaling theory by simulating the real-time dynamics of the one-dimensional quantum Ising model at both zero and finite temperatures.Comment: 6 pages, 5 figure

Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques

We propose a novel unsupervised approach for sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools. Specifically, we apply diffusion-based algorithms, diffusion map (DM) and alternating diffusion (AD) algorithms, to reconstruct the intrinsic geometry of sleep dynamics by reorganizing the spectral information of an electroencephalogram (EEG) extracted from a nonlinear-type time frequency analysis tool, the synchrosqueezing transform (SST). The visualization is achieved by the nonlinear dimension reduction properties of DM and AD. Moreover, the reconstructed nonlinear geometric structure of the sleep dynamics allows us to achieve the automatic annotation purpose. The hidden Markov model is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC* and ST*, with the leave-one-subject-out cross validation. The overall accuracy and macro F1 achieve 82:57% and 76% in Sleep-EDF SC* and 77.01% and 71:53% in Sleep-EDF ST*, which is compatible with the state-of-the-art results by supervised learning-based algorithms. The results suggest the potential of the proposed algorithm for clinical applications.Comment: 41 pages, 21 figures. arXiv admin note: text overlap with arXiv:1803.0171

Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid

An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of correlation functions over different length scales has been difficult. We develop a powerful numerical method based on infinite DMRG utilizing a finite system with infinite boundary conditions, which can be applied to correlation functions near an impurity. For the $S=1/2$ chain, we demonstrate that the full crossover can be precisely obtained, and that their limiting behaviors show a good agreement with field-theory predictions

Diffuse to fuse EEG spectra -- intrinsic geometry of sleep dynamics for classification

We propose a novel algorithm for sleep dynamics visualization and automatic annotation by applying diffusion geometry based sensor fusion algorithm to fuse spectral information from two electroencephalograms (EEG). The diffusion geometry approach helps organize the nonlinear dynamical structure hidden in the EEG signal. The visualization is achieved by the nonlinear dimension reduction capability of the chosen diffusion geometry algorithms. For the automatic annotation purpose, the {support vector machine} is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC$^*$ {(SC = Sleep Cassette)} and ST$^*$ {(ST = Sleep Telemetry)}, with the leave-one-subject-out cross validation. When we have a single EEG channel (Fpz-Cz), the overall accuracy, macro F1 and Cohen's kappa achieve $82.72\%$,$75.91\%$ and $76.1\%$ respectively in Sleep-EDF SC$^*$ and $78.63\%$, $73.58\%$ and $69.48\%$ in Sleep-EDF ST$^*$. This performance is compatible {with} the state-of-the-art results. When we have two EEG channels (Fpz-Cz and Pz-Oz), the overall accuracy, macro F1 and Cohen's kappa achieve $84.44\%$,$78.25\%$ and $78.36\%$ respectively in Sleep-EDF SC$^*$ and $79.05\%$, $74.73\%$ and $70.31\%$ in Sleep-EDF ST$^*$. The results suggest the potential of the proposed algorithm in practical applications

Few-Photon All-Optical {\pi} Phase modulation Based on a Double-{\Lambda} System

We propose an efficient all-optical phase modulation based on a double-{\Lambda} system and demonstrate a {\pi} phase shift of a few-photon pulse induced by another few-photon pulse in cold rubidium atoms with this scheme. By changing the phases of the applied laser fields, one can control the property of the double-{\Lambda} medium. This phase-dependent mechanism makes the double-{\Lambda} system different form the conventional cross-Kerr-based system which only depends on the applied laser intensities. The proposed scheme provides a new route to generate strong nonlinear interactions between photons, and may have potential for applications in quantum information technologies.Comment: 5 pages, 4 figure

A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification

Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general pipeline to apply PH to study time series; particularly the instantaneous heart rate time series for the heart rate variability (HRV) analysis. The first step is capturing the shapes of time series from two different aspects -- {the PH's and hence persistence diagrams of its} sub-level set and Taken's lag map. Second, we propose a systematic {and computationally efficient} approach to summarize persistence diagrams, which we coined {\em persistence statistics}. To demonstrate our proposed method, we apply these tools to the HRV analysis and the sleep-wake, REM-NREM (rapid eyeball movement and non rapid eyeball movement) and sleep-REM-NREM classification problems. The proposed algorithm is evaluated on three different datasets via the cross-database validation scheme. The performance of our approach is better than the state-of-the-art algorithms, and the result is consistent throughout different datasets

Kibble-Zurek mechanism in quantum link model

We study the driven critical dynamics of the quantum link model, whose Hamiltonian describes the one-dimensional $U(1)$ lattice gauge theory. We find that combined topological defects emerge after the quench and they consist of both gauge field and matter field excitations. Furthermore, the ratio of gauge field and matter field excitation is $1/2$ due to the constraint of the Gauss' law. We show that the scaling of these combined topological defects satisfies the usual Kibble-Zurek mechanism. We verify that both the electric flux and the entanglement entropy satisfy the finite-time scaling theory in the whole driven process. Possible experimental realizations are discussed.Comment: 8.1 pages, 7 figure

Possible Topological Phase Transition in Fe-Vacancy-Ordered β\beta-Fe4+δ_{4+\delta}Se5_{5} Nanowires

We studied the electrical transport on $\beta$-Fe$_{4+\delta}$Se$_{5}$ single-crystal nanowires, exhibiting $\sqrt{5}\times\sqrt{5}$ Fe-vacancy order and mixed valence of Fe. We observed a first-order metal-insulator transition of the transition temperature at $\sim$28~K at zero magnetic field. The dielectric relaxation reveals that the transition is related to an energy gap expansion of $\sim$12~meV, involving the charge-orbital ordering. At nearly 28~K, colossal positive magnetoresistance emerges, resulting from the magnetic-field dependent shift of the transition temperature. Through the transition, the magnetotransport behavior transits from two-dimension-like to one-dimension-like conduction. The transition temperature demonstrates anisotropy with the $c$-axis as the preferred orientation in magnetic fields, suggesting the spin-orbital coupling. Our findings demonstrate the novel magnetoresistive transition intimating a topological transition in the Fe-vacancy-ordered $\beta$-Fe$_{4+\delta}$Se$_{5}$ nanowires. The results provide valuable information to better understand the orbital nature and the emergence of superconductivity in FeSe-based materials

Direct Measurement of Spatial Distortions of Charge Density Waves in K0.3MoO3

Using X-ray scattering and the technique of multiple diffreactions, we revisit the dynamical transition of charge density waves (CDWs) in K0.3MoO3 under applied voltages. In addition to the usual transport and half width (of Bragg peaks) measurements, we also measure the triplet phase by three-wave diffraction, which provides, for the first time, the {\em direct} evidence for the spatial distortions of CDWs. This novel and sensitive technique developed here can be applied to general periodic media, including stripes in high temperature superconductors, and provide a new perspective into interesting phenomena in these materials.Comment: minor changes, 4 pages, 4 figure