1,759 research outputs found
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 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
, and respectively in Sleep-EDF SC and
, and 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
, and respectively in Sleep-EDF SC and
, and 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 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 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 -FeSe Nanowires
We studied the electrical transport on -FeSe
single-crystal nanowires, exhibiting Fe-vacancy order
and mixed valence of Fe. We observed a first-order metal-insulator transition
of the transition temperature at 28~K at zero magnetic field. The
dielectric relaxation reveals that the transition is related to an energy gap
expansion of 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 -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 -FeSe 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
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