Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity

In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of \emph{gapped quantum liquid} as a special kind of gapped quantum states that can "dissolve" any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids, but with unstable ground-state degeneracy. (2) We point out that the universality classes of generalized local unitary (gLU) transformations (without any symmetry) contain both topologically ordered states and symmetry-breaking states. This allows us to use a gLU invariant -- topological entanglement entropy -- to probe the symmetry-breaking properties hidden in the exact ground state of a finite system, which does not break any symmetry. This method can probe symmetry- breaking orders even without knowing the symmetry and the associated order parameters. (3) The universality classes of topological orders and symmetry-breaking orders can be distinguished by \emph{stochastic local (SL) transformations} (i.e.\ \emph{local invertible transformations}): small SL transformations can convert the symmetry-breaking classes to the trivial class of product states with finite probability of success, while the topological-order classes are stable against any small SL transformations, demonstrating a phenomenon of emergence of unitarity. This allows us to give a new definition of long-range entanglement based on SL transformations, under which only topologically ordered states are long-range entangled.Comment: Revised version. Figures and references adde

Gene Expression Order Attributed to Genome Reduction and the Steady Cellular State in Escherichia coli

Transcriptomes not only reflect the growth status but also link to the genome in bacteria. To investigate if and how genome or cellular state changes contribute to the gene expression order, the growth profile-associated transcriptomes of an assortment of genetically differentiated Escherichia coli either exponentially growing under varied conditions or in response to environmental disturbance were analyzed. A total of 168 microarray data sets representing 56 transcriptome variations, were categorized by genome size (full length or reduced) and cellular state (steady or unsteady). At the genome-wide level, the power-law distribution of gene expression was found to be significantly disturbed by the genome size but not the cellular state. At the regulatory network level, more networks with improved coordination of growth rates were observed in genome reduction than at the steady state. At the single-gene level, both genome reduction and steady state increased the correlation of gene expression to growth rate, but the enriched gene categories with improved correlations were different. These findings not only illustrate the order of gene expression attributed to genome reduction and steady cellular state but also indicate that the accessory sequences acquired during genome evolution largely participated in the coordination of transcriptomes to growth fitness

Effects of Coronal Density and Magnetic Field Distributions on a Global Solar EUV Wave

We investigate a global extreme-ultraviolet (EUV) wave associated with a coronal mass ejection (CME)-driven shock on 2017 September 10. The EUV wave is transmitted by north- and south-polar coronal holes (CHs), which is observed by the Solar Dynamics Observatory (SDO) and Solar Terrestrial Relations Observatory A (STEREO-A) from opposite sides of the Sun. We obtain key findings on how the EUV wave interacts with multiple coronal structures, and on its connection with the CME-driven shock: (1) the transmitted EUV wave is still connected with the shock that is incurvated to the Sun, after the shock has reached the opposite side of the eruption; (2) the south CH transmitted EUV wave is accelerated inside an on-disk, low-density region with closed magnetic fields, which implies that an EUV wave can be accelerated in both open and closed magnetic field regions; (3) part of the primary EUV wavefront turns around a bright point (BP) with a bipolar magnetic structure when it approaches a dim, low-density filament channel near the BP; (4) the primary EUV wave is diffused and apparently halted near the boundaries of remote active regions (ARs) that are far from the eruption, and no obvious AR related secondary waves are detected; (5) the EUV wave extends to an unprecedented scale of ~360{\deg} in latitudes, which is attributed to the polar CH transmission. These results provide insights into the effects of coronal density and magnetic field distributions on the evolution of an EUV wave, and into the connection between the EUV wave and the associated CME-driven shock.Comment: 16 pages, 8 figures, and 3 animations available at http://doi.org/10.13140/RG.2.2.12408.29442 , http://doi.org/10.13140/RG.2.2.25830.06723 , and http://doi.org/10.13140/RG.2.2.19119.18088 ; published in Ap

Temperature-insensitive detection of low-concentration nanoparticles using a functionalized high-Q microcavity

The ability to detect nanoparticles in extremely dilute solutions in the presence of environmental noise is crucial for biosensing applications. In this paper we propose a scheme for detecting target nanoparticles through their scattering effects in a high-Q whispering gallery microcavity. The detection signal, defined as the total linewidth broadening of the two new split modes that appear upon nanoparticle adsorption, is highly sensitive and proportional to the nanoparticle concentration. Furthermore, this new method of detection eliminates the requirement for strict temperature control and is capable of distinguishing the signal from the biorecognitions (e.g., antibodies) initially attached to the resonator and that from the target nanoparticles (e.g., antigens)