On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with complex electric(magnetic) field, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of Physics A(v3

Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-hermitian supersymmetric quantum systems with a special emphasis on rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigen functions and eigenvalues. The Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum system related to short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References, Version to appear in Jouranl of Physics A: Mathematical and Theoretical (Commissioned Topical Review Article

A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field

We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turns out to be unique with the sole assumption that the Dyson map is Hermitian. Finally we compute the magnetization of the chain in the z and x direction

Sphingosine-1-phosphate receptor-1 (S1P1) is expressed by lymphocytes, dendritic cells, and endothelium and modulated during inflammatory bowel disease

The sphingosine-1-phosphate receptor-1 (S1P1) agonist ozanimod ameliorates ulcerative colitis, yet its mechanism of action is unknown. Here, we examine the cell subsets that express S1P1 in intestine using S1P1-eGFP mice, the regulation of S1P1 expression in lymphocytes after administration of dextran sulfate sodium (DSS), after colitis induced by transfer of CD4+CD45RBhi cells, and by crossing a mouse with TNF-driven ileitis with S1P1-eGFP mice. We then assayed the expression of enzymes that regulate intestinal S1P levels, and the effect of FTY720 on lymphocyte behavior and S1P1 expression. We found that not only T and B cells express S1P1, but also dendritic (DC) and endothelial cells. Furthermore, chronic but not acute inflammatory signals increased S1P1 expression, while the enzymes that control tissue S1P levels in mice and humans with inflammatory bowel disease (IBD) were uniformly dysregulated, favoring synthesis over degradation. Finally, we observed that FTY720 reduced T-cell velocity and induced S1P1 degradation and retention of Naïve but not effector T cells. Our data demonstrate that chronic inflammation modulates S1P1 expression and tissue S1P levels and suggests that the anti-inflammatory properties of S1PR agonists might not be solely due to their lymphopenic effects, but also due to potential effects on DC migration and vascular barrier function

Ectopic synaptic ribbons in dendrites of mouse retinal ON- and OFF-bipolar cells

The ectopic distribution of synaptic ribbons in dendrites of mouse retinal bipolar cells was examined by using genetic ablation of metabotropic glutamate receptor subtype 6 (mGluR6), electron microscopy, and immunocytochemistry. Ectopic ribbons were observed in dendrites of rod and ON-cone bipolar cells in the mGluR6-deficient mouse but not in those of wild-type mice. The number of rod spherules facing the ectopic ribbons in mGluR6-deficient rod bipolar dendrites increased gradually during early growth and reached a plateau level of about 20% at 12 weeks. These ectopic ribbons were immunopositive for RIBEYE, a ribbon-specific protein, but the associated vesicles were immunonegative for synaptophysin, a synaptic-vesicle-specific protein. The presence of ectopic ribbons was correlated with an increase in the roundness of the invaginating dendrites of the rod bipolar cells. We further confirmed ectopic ribbons in dendrites of OFF-cone bipolar cells in wild-type retinas. Of the four types of OFF-cone bipolar cells (T1–T4), only the T2-type, which had a greater number of synaptic ribbons at the axon terminal and a thicker axon cylinder than the other types, had ectopic ribbons. Light-adapted experiments revealed that, in wild-type mice under enhanced-light adaptation (considered similar to the mGluR6-deficient state), the roundness in the invaginating dendrites and axon terminals of rod bipolar cells increased, but no ectopic ribbons were detected. Based on these findings and known mechanisms for neurotransmitter release and protein trafficking, the possible mechanisms underlying the ectopic ribbons are discussed on the basis of intracellular transport for the replenishment of synaptic proteins