Explicit definition of PT\mathcal{PT} symmetry for non-unitary quantum walks with gain and loss

$\mathcal{PT}$ symmetry, that is, a combined parity and time-reversal symmetry is a key milestone for non-Hermite systems exhibiting entirely real eigenenergy. In the present work, motivated by a recent experiment, we study $\mathcal{PT}$ symmetry of the time-evolution operator of non-unitary quantum walks. We present the explicit definition of $\mathcal{PT}$ symmetry by employing a concept of symmetry time frames. We provide a necessary and sufficient condition so that the time-evolution operator of the non-unitary quantum walk retains $\mathcal{PT}$ symmetry even when parameters of the model depend on position. It is also shown that there exist extra symmetries embedded in the time-evolution operator. Applying these results, we clarify that the non-unitary quantum walk in the experiment does have $\mathcal{PT}$ symmetry.Comment: 14 pages, 8 figure

Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems

Recently, effects of nonlinearity on topologically nontrivial systems have attracted attention and the stability of topologically protected edge states has been studied for a quantum walk with nonlinear effects, which is akin to time-periodically driven systems (Floquet systems). In the previous work, it has been found that the edge states can be stable attractors or unstable repellers depending on their intrinsic topological property, while the stability is not affected by the strength of nonlinearity. In the present work, we find additional bifurcations at which edge states change from stable attractors to unstable repellers with increasing the strength of nonlinearity in nonlinear quantum walks, for the first time. The new bifurcations are unique to Floquet systems, since we take dynamical properties of Floquet systems into consideration by directly applying the time-evolution operator of the quantum walks to the linear stability analysis. Our results shed new light on nonlinear effects on topological edge states in Floquet systems.Comment: 28 pages, 11 figure

Uber die Legierungen des Nickels mit Alkali- und Erdalkalimetallen

In den Systemen Nickel-Barium und Nickel-Lithium befindet sich keine intermetallische Phase. Die beiden Bestandteile dieser Legierungen sind im flussigen Zustand nur teilweise mischbar und bilden in einem breiten Konzentrations-bereich eine Mischungslucke. Nickel vermag beispielsweise bei 1200°bis zu 0, 4% Lithium und nur 0, 08% Barium zu losen. Andererseits lost sich Nickel in der Bariumschmelze bei 1200℃ bis zu 20, 97% und in der Lithiumschmelze bei gleicher Temperatur bis zu 3, 47%. Ubereinstimmend mit H. Nowotny wurde intermetallische Phase Ni_5Ca (12, 02% Ca ; 87, 98% Ni) bestatigt. Ferner ergab sich, daβ im System Nickel-Kalzium noch eine bisher unbekannte intermetallische Phase, wahrscheinlich Ni_5Ca_2 (21, 2% Ca ; 78, 8% Ni) , vorhanden ist. Die Phase Ni_5Ca_2 bildet sich bei 1035℃ durch die peritektische Reaktion zwischen den primaren Ni_5Ca-Kristallen und der Restschmelze. Die beiden intermetallischen Phasen gehoren zu einem hexagonalen Kristall-system mit folgenden Gitterkonstanten ; Ni_5Ca ; a=4, 930A, c=3, 925A, c/a=0, 796 Ni_5Ca_2 ; a=5.039A, c=10, 280A, c/a=2, 040 Im System Nickel-Kalzium treten nachstehende drei Dreiphasengleichgewichte auf ; S=Ni+Ni_5Ca (eutektischer Punkt : 6%Ca und 1160℃) S+Ni_5Ca=Ni_5Ca_2 (Peritektikale : 12 bis 33%Ca bei 1035℃) S=Ni_5Ca_2+Ca (eutektischer Punkt : 78%Ca und 605℃) Im System Nickel-Strontium tritt eine intermetallische Verbindung auf, die sich bei 860℃ durch die peritektische Reaktion zwischen den primaren Nickel-Kristallen und der Restschmelze bildet. Diese intermetallische Phase, deren Zu-sammensetzung vermutlich als NiSr (59, 89% Sr, 40, 11% Ni) angegeben werden kann, kristallisiert in einer hexagonalen Struktur mit den Gitterkonstanten a=3, 332A, c=7, 009 A und c/a=2, 112. Die Phase NiSr und Strontium bilden ein eutektisches System. Der eutektische Punkt liegt bei 92% Sr und 660℃

Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms

We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble. This demonstrates a general feature which we clarify that a non-Hermitian Hamiltonian whose eigenvalues are purely real can be mapped to a Hermitian Hamiltonian which inherits the symmetries of the original Hamiltonian. When the spectrum contains imaginary eigenvalues, we show that the density of states (DOS) vanishes at the origin and diverges at the spectral edges on the imaginary axis. We show that the divergence of the DOS originates from the Dyson singularity in chiral-symmetric one-dimensional Hermitian systems and derive analytically the asymptotes of the DOS which is different from that in Hermitian systems.Comment: 10 pages, 8 figure

Topological Quantum Walk with Discrete Time-Glide Symmetry

Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary operators. Regarding each constituent unitary operator as a discrete time step, we formulate discrete space-time symmetry in quantum walks and evaluate the corresponding symmetry protected topological phases. In particular, we study chiral and/or time-glide symmetric topological quantum walks in this formalism. Due to discrete nature of time evolution,the topological classification is found to be different from that in conventional Floquet systems. As a concrete example, we study a two-dimensional quantum walk having both chiral and time-glide symmetries, and identify the anomalous edge states protected by these symmetries.Comment: 15 pages, 7 figure

Küttner's tumor of the sub-mandibular gland associated with fibrosclerosis and follicular hyperplasia of regional lymph nodes: a case report

<p>Abstract</p> <p>Introduction</p> <p>Küttner's tumor is characterized through histology by peri-ductal fibrosis, dense lymphocytic infiltration with lymphoid follicles, loss of acini, and occasional marked sclerosis of the salivary gland. On occasion, Küttner's tumor can be difficult to distinguish from malignant neoplasm.</p> <p>Case presentation</p> <p>A 58-year-old Japanese man was referred to our hospital with a three-month history of a painless swollen mass in the right sub-mandibular region. Histological findings revealed both lymphoid follicles with reactive germinal centers and variously sized lymphoid follicle-like nodules without definitive germinal centers or mantle zones. B-cells of similar size and shape occupied the lymphoid follicle-like nodules and stained positive for B-cell lymphoma. These cells were detected in the polyclonal B-cells by flow cytometric analysis and tested negative for CD10. Unusual B-cell proliferation was observed, but as there was no definitive evidence of B-cell lymphoma, the lesion was diagnosed as Küttner's tumor.</p> <p>Conclusion</p> <p>We report on a rare case of Küttner's tumor associated with fibrosclerosis and atypical lymphoid hyperplasia in both the sub-mandibular gland and regional lymph nodes. Although more cases need to be investigated, our findings might be helpful to further studies seeking to clarify the etiology of idiopathic sclerosing lesions arising in the organs and regional lymph nodes.</p

Dogs as Sentinels for Human Infection with Japanese Encephalitis Virus

Because serosurveys of Japanese encephalitis virus (JEV) among wild animals and pigs may not accurately reflect risk for humans in urban/residential areas, we examined seroprevalence among dogs and cats. We found that JEV-infected mosquitoes have spread throughout Japan and that dogs, but not cats, might be good sentinels for monitoring JEV infection in urban/residential areas