Anatomy of Open-Boundary Bulk in Multiband Non-Hermitian Systems

Although the non-Bloch band theory is a milestone in elaborating bulk energy bands of non-Hermitian systems under open boundary condition (OBC), vital issues related to multivalued functions of non-Hermitian energy bands remain unsolved. In this paper, we anatomize the bulk properties of one-dimensional (1D) multiband non-Hermitian systems under OBC. We put forward the energy-band branches (EBBs) to settle the multivalued functions of non-Hermitian energy bands, which become gapped or gapless corresponding to disconnected or connected EBBs in the complex energy plane, where the branch points and branch cuts play a crucial role. We clarify the precise significance of the non-Hermitian skin effect (NHSE), which illustrates the asymptotic behavior of EBB-eigenstates (bulk eigenstates) in the deep bulk and compensates previous non-Bloch band theory. We also obtain a general expression of open-boundary Green's functions based on such EBBs and generalized Brillouin zones (GBZs), useful for studies on non-Hermitian dynamical evolution.Comment: 7+12 pages (main text + supplemental material), 3+5 figure

Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach

Surpassing the individual characteristics of the non-Hermitian skin effect (NHSE) and the scale-free (SF) effect observed recently, we systematically exploit the exponential decay behavior of bulk eigenstates via the transfer matrix approach in non-Hermitian systems. We concentrate on one-dimensional (1D) finite-size non-Hermitian systems with 2*2 transfer matrices in either the absence or presence of the boundary impurity. We analytically unveil that the unidirectional SF effect emerges with the singular transfer matrices, while the hybrid scale-free skin (SFS) effect appears with the nonsingular transfer matrices even when an open boundary condition (OBC) is imposed. The unidirectional SF effect exceeds the scope of the SF effect in previous works, while the hybrid SFS effect is an interesting interplay between the skin effect and the SF effect in finite-size systems. Our results reveal that the skin effect under the OBC prevails when it coexists with the SF effect as the system approaches the thermodynamic limit in the presence of the hybrid SFS effect. Our approach paves the way for rigorous and unified explorations of the skin and SF effects in both Hermitian and non-Hermitian systems with generic boundary conditions.Comment: 20 pages, 9 figure

Nontrivial worldline winding in non-Hermitian quantum systems

Amid the growing interest in non-Hermitian quantum systems, non-interacting models have received the most attention. Here, through the stochastic series expansion quantum Monte Carlo method, we investigate non-Hermitian physics in interacting quantum systems, e.g., various non-Hermitian quantum spin chains. While calculations yield consistent numerical results under open boundary conditions, non-Hermitian quantum systems under periodic boundary conditions observe an unusual concentration of imaginary-time worldlines over nontrivial winding and require enhanced ergodicity between winding-number sectors for proper convergences. Such nontrivial worldline winding is an emergent physical phenomenon that also exists in other non-Hermitian models and analytical approaches. Alongside the non-Hermitian skin effect and the point-gap spectroscopy, it largely extends the identification and analysis of non-Hermitian topological phenomena to quantum systems with interactions, finite temperatures, biorthogonal basis, and periodic boundary conditions in a novel and controlled fashion. Finally, we study the direct physical implications of such nontrivial worldline winding, which bring additional, potentially quasi-long-range contributions to the entanglement entropy

Complex semiclassical theory for non-Hermitian quantum systems

Non-Hermitian quantum systems exhibit fascinating characteristics such as non-Hermitian topological phenomena and skin effect, yet their studies are limited by the intrinsic difficulties associated with their eigenvalue problems, especially in larger systems and higher dimensions. In Hermitian systems, the semiclassical theory has played an active role in analyzing spectrum, eigenstate, phase, transport properties, etc. Here, we establish a complex semiclassical theory applicable to non-Hermitian quantum systems by an analytical continuation of the physical variables such as momentum, position, time, and energy in the equations of motion and quantization condition to the complex domain. Further, we propose a closed-orbit scheme and physical meaning under such complex variables. We demonstrate that such a framework straightforwardly yields complex energy spectra and quantum states, topological phases and transitions, and even the skin effect in non-Hermitian quantum systems, presenting an unprecedented perspective toward nontrivial non-Hermitian physics, even with larger systems and higher dimensions.Comment: 16 pages, 10 figure

New insights into the use of Neolithic pottery in Guangxi of South China: organic residue analysis of experimental and archaeological pottery

Abstract As one of the world’s earliest pottery origins in Eurasia, the role of pottery during Neolithic period in South China remains unclear. Here, we present a new understanding on the utilization pattern of early pottery from the Neolithic sites of Dayan, Dingsishan and Zengpiyan in Guangxi province, China. Compound-specific stable isotope analysis of pottery and bone lipids show that a persistent use of terrestrial C3 and C4 resources throughout the pottery utilization history highlight the culinary practice and terrestrial exploitation during Neolithic period. Contrary to the traditional view that the primary use of these pottery was closely linked with aquatic resource processing, no aquatic biomarkers were found in the potsherds, yet these compounds were detected in the cooking experiments in this study, indicating that aquatic resources in these sites were probably processed or consumed in other ways. Moreover, a remarkable diachronic change from extensive use of C3 and C4 resources to the intensive use of certain kinds of C3 resources in different Neolithic stages, further indicating that an ecological tradition rooted in the subtropical and tropical environments as well as the Neolithic social evolution exerted great influence upon the initial production and the subsequent utilization of early pottery in prehistoric South China

Genome-Wide Gene Expression Profile Analyses Identify CTTN as a Potential Prognostic Marker in Esophageal Cancer

<div><p>Aim</p><p>Esophageal squamous cell carcinoma (ESCC) is one of the most common fatal malignances of the digestive tract. Its prognosis is poor mainly due to the lack of reliable markers for early detection and prognostic prediction. Here we aim to identify the molecules involved in ESCC carcinogenesis and those as potential markers for prognosis and as new molecular therapeutic targets.</p><p>Methods</p><p>We performed genome-wide gene expression profile analyses of 10 primary ESCCs and their adjacent normal tissues by cDNA microarrays representing 47,000 transcripts and variants. Candidate genes were then validated by semi quantitative reverse transcription-PCR (RT-PCR), tissue microarrays (TMAs) and immunohistochemistry (IHC) staining.</p><p>Results</p><p>Using an arbitrary cutoff line of signal log ratio of ≥1.5 or ≤−1.5, we observed 549 up-regulated genes and 766 down-regulated genes in ESCCs compared with normal esophageal tissues. The functions of 302 differentially expressed genes were associated with cell metabolism, cell adhesion and immune response. Several candidate deregulated genes including four overexpressed (CTTN, DMRT2, MCM10 and SCYA26) and two underexpressed (HMGCS2 and SORBS2) were subsequently verified, which can be served as biomarkers for ESCC. Moreover, overexpression of cortactin (CTTN) was observed in 126/198 (63.6%) of ESCC cases and was significantly associated with lymph node metastasis (P = 0.000), pathologic stage (P = 0.000) and poor survival (P<0.001) of ESCC patients. Furthermore, a significant correlation between CTTN overexpression and shorter disease-specific survival rate was found in different subgroups of ESCC patient stratified by the pathologic stage (P<0.05).</p><p>Conclusion</p><p>Our data provide valuable information for establishing molecules as candidates for prognostic and/or as therapeutic targets.</p></div

Expression of CTTN in ESCC and normal esophageal tissues.

<p>Note:*<i>P</i><0.005.</p

Association between CTTN over-expression and clinicopathologic characteristics of patients with ESCC (n = 198).

<p>*<i>P</i><0.05.</p

Kaplan-Meier plots for the Disease-specific survival rate of ESCC patients.

<p>(A) Kaplan-Meier plots for the Disease-specific survival (DSS) rate of ESCC patients with (n = 126, green line) or without (n = 72, blue line) CTNN overexpression. (B) Kaplan-Meier plots for the DSS rate of ESCC patients with pathologic stage I+IIA (n = 113, blue line) or IIB+III (n = 85, green line).</p