Biorthogonal dynamical quantum phase transitions in non-Hermitian systems

By using biorthogonal bases, we construct a complete framework for biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of associated state which is overlooked previously, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues, which naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a peculiar $1/2$ change in biorthogonal dynamical topological order parameter, which is beyond the traditional dynamical quantum phase transitions is observed. We also find the periodicity of biorthogonal dynamical quantum phase transitions depend on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.Comment: 8 pages, 5 figure

Aqua­bis(1H-imidazole-κN 3)bis­(4-methyl­benzoato-κ2 O,O′)cadmium(II)

In the title compound, [Cd(C8H7O2)2(C3H4N2)2(H2O)], the CdII atom is coordinated by four carboxyl­ate O atoms from two bidentate chelating 4-methyl­benzoate ligands, two N atoms from two imidazole ligands and one water mol­ecule in a distorted penta­gonal bipyramidal geometry. Inter­molecular O—H⋯O hydrogen bonds between the coordinated water mol­ecule and the carboxyl­ate O atoms of 4-methyl­benzoate lead to an infinite chain. These chains are further self-assembled into a two-dimensional layer through N—H⋯O hydrogen bonds between the imidazole ligands and carboxyl­ate groups. One of the imidazole ligands is disordered over two positions with site-occupancy factors of 0.737 (4) and 0.263 (4)

Bis(1H-benzimidazole-κN 3)bis­(4-methyl­benzoato-κ2 O,O′)copper(II)

In the title mononuclear complex, [Cu(C8H7O2)2(C7H6N2)2], the CuII atom lies on an inversion centre and is coordinated by two O atoms of two monodentate 4-methyl­benzoate ligands and two N atoms of two benzimidazole ligands in a square-planar geometry. The mol­ecules are linked into chains running parallel to the b axis by inter­molecular N—H⋯O hydrogen bonds and by π–π stacking inter­actions [centroid–centroid distance = 3.669 (2) Å] involving centrosymmetrically related imidazole rings

Diagnostic value of two dimensional shear wave elastography combined with texture analysis in early liver fibrosis.

BACKGROUND: Staging diagnosis of liver fibrosis is a prerequisite for timely diagnosis and therapy in patients with chronic hepatitis B. In recent years, ultrasound elastography has become an important method for clinical noninvasive assessment of liver fibrosis stage, but its diagnostic value for early liver fibrosis still needs to be further improved. In this study, the texture analysis was carried out on the basis of two dimensional shear wave elastography (2D-SWE), and the feasibility of 2D-SWE plus texture analysis in the diagnosis of early liver fibrosis was discussed. AIM: To assess the diagnostic value of 2D-SWE combined with textural analysis in liver fibrosis staging. METHODS: This study recruited 46 patients with chronic hepatitis B. Patients underwent 2D-SWE and texture analysis; Young\u27s modulus values and textural patterns were obtained, respectively. Textural pattern was analyzed with regard to contrast, correlation, angular second moment (ASM), and homogeneity. Pathological results of biopsy specimens were the gold standard; comparison and assessment of the diagnosis efficiency were conducted for 2D-SWE, texture analysis and their combination. RESULTS: 2D-SWE displayed diagnosis efficiency in early fibrosis, significant fibrosis, severe fibrosis, and early cirrhosis (AUC \u3e 0.7, P \u3c 0.05) with respective AUC values of 0.823 (0.678-0.921), 0.808 (0.662-0.911), 0.920 (0.798-0.980), and 0.855 (0.716-0.943). Contrast and homogeneity displayed independent diagnosis efficiency in liver fibrosis stage (AUC \u3e 0.7, P \u3c 0.05), whereas correlation and ASM showed limited values. AUC of contrast and homogeneity were respectively 0.906 (0.779-0.973), 0.835 (0.693-0.930), 0.807 (0.660-0.910) and 0.925 (0.805-0.983), 0.789 (0.639-0.897), 0.736 (0.582-0.858), 0.705 (0.549-0.883) and 0.798 (0.650-0.904) in four liver fibrosis stages, which exhibited equivalence to 2D-SWE in diagnostic efficiency (P \u3e 0.05). Combined diagnosis (PRE) displayed diagnostic efficiency (AUC \u3e 0.7, P \u3c 0.01) for all fibrosis stages with respective AUC of 0.952 (0.841-0.994), 0.896 (0.766-0.967), 0.978 (0.881-0.999), 0.947 (0.835-0.992). The combined diagnosis showed higher diagnosis efficiency over 2D-SWE in early liver fibrosis (P \u3c 0.05), whereas no significant differences were observed in other comparisons (P \u3e 0.05). CONCLUSION: Texture analysis was capable of diagnosing liver fibrosis stage, combined diagnosis had obvious advantages in early liver fibrosis, liver fibrosis stage might be related to the hepatic tissue hardness distribution