Topological phases of non-Hermitian systems

Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi-)edge modes. We then apply the K-theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify a Z2 topological index for arbitrary quantum channels. Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.Comment: 31 pages, 18 figures, 2 tables, to appear in Physical Review

Platelet Activation in Patients After Splenectomy with Total Gastrectomy for Gastric Cancer

We investigated change in platelet activation using flow cytometry in patients before and after splenectomy with total gastrectomy for gastric cancer. Methods: Six patients who underwent splenectomy for lymphadenectomy with total gastrectomy for gastric cancer were the subjects in this study. In the patients, platelet count and platelet activation were evaluated before the operation, 1 week after the operation, and 1 month after the operation. Expression of CD62P (P-selectin) was analysed as a marker of platelet activation using flow cytometry. Results: Although platelet count significantly increased 1 week after the operation, the platelet count 1 month after the operation did not increase significantly. Expression of CD62P (P-selectin) significantly decreased at 1 week and 1 month after the operation, compared with the level before the operation. No postoperative complications occurred in any patient. Conclusion: In the present study, platelet activation did not progress after the operation. The results mean that the risk of thrombosis after splenectomy does not increase

Collagenolytic Serine-Carboxyl Proteinase from Alicyclobacillus sendaiensis Strain NTAP-1: Purification, Characterization, Gene Cloning, and Heterologous Expression

Enzymatic degradation of collagen produces peptides, the collagen peptides, which show a variety of bioactivities of industrial interest. Alicyclobacillus sendaiensis strain NTAP-1, a slightly thermophilic, acidophilic bacterium, extracellularly produces a novel thermostable collagenolytic activity, which exhibits its optimum at the acidic region (pH 3.9) and is potentially applicable to the efficient production of such peptides. Here, we describe the purification to homogeneity, characterization, gene cloning, and heterologous expression of this enzyme, which we call ScpA. Purified ScpA is a monomeric, pepstatin-insensitive carboxyl proteinase with a molecular mass of 37 kDa which exhibited the highest reactivity toward collagen (type I, from a bovine Achilles tendon) among the macromolecular substrates examined. On the basis of the sequences of the peptides obtained by digestion of collagen with ScpA, the following synthetic peptides were designed as substrates for ScpA and kinetically analyzed: Phe-Gly-Pro-Ala(*)Gly-Pro-Ile-Gly (k(cat), 5.41 s(−1); K(m), 32 μM) and Met-Gly-Pro-Arg(*)Gly-Phe-Pro-Gly-Ser (k(cat), 351 s(−1); K(m), 214 μM), where the asterisks denote the scissile bonds. The cloned scpA gene encoded a protein of 553 amino acids with a calculated molecular mass of 57,167 Da. Heterologous expression of the scpA gene in the Escherichia coli cells yielded a mature 37-kDa species after a two-step proteolytic cleavage of the precursor protein. Sequencing of the scpA gene revealed that ScpA was a collagenolytic member of the serine-carboxyl proteinase family (the S53 family according to the MEROPS database), which is a recently identified proteinase family on the basis of crystallography results. Unexpectedly, ScpA was highly similar to a member of this family, kumamolysin, whose specificity toward macromolecular substrates has not been defined