Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is applied to the Hermitian analogue of the PT-symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a PT-symmetric extension of the one-parameter trigonometric Poschl-Teller potential.Comment: 13 pages, no figure, modified presentation, 6 additional references, published versio

General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space

In our previous work, we proposed a mathematical framework for PT-symmetric quantum theory, and in particular constructed a Krein space in which PT-symmetric operators would naturally act. In this work, we explore and discuss various general consequences and aspects of the theory defined in the Krein space, not only spectral property and PT symmetry breaking but also several issues, crucial for the theory to be physically acceptable, such as time evolution of state vectors, probability interpretation, uncertainty relation, classical-quantum correspondence, completeness, existence of a basis, and so on. In particular, we show that for a given real classical system we can always construct the corresponding PT-symmetric quantum system, which indicates that PT-symmetric theory in the Krein space is another quantization scheme rather than a generalization of the traditional Hermitian one in the Hilbert space. We propose a postulate for an operator to be a physical observable in the framework.Comment: 32 pages, no figures; explanation, discussion and references adde

Time evolution of non-Hermitian Hamiltonian systems

We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in addition in some cases also invariant under PT-symmetry. In particular, for the harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate explicitly various transition amplitudes, for the situation when these systems are exposed to a monochromatic linearly polarized electric field.Comment: 25 pages Latex, 1 eps figure, references adde

Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation

Witten's non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic Klein-Gordon equations. In such a class of models the requirement of supersymmetry is shown to lead to a certain "exceptional-point" instability of ground states.Comment: 20 page

Effect of sitagliptin on cardiovascular outcomes in type 2 diabetes

BACKGROUND: Data are lacking on the long-term effect on cardiovascular events of adding sitagliptin, a dipeptidyl peptidase 4 inhibitor, to usual care in patients with type 2 diabetes and cardiovascular disease. METHODS: In this randomized, double-blind study, we assigned 14,671 patients to add either sitagliptin or placebo to their existing therapy. Open-label use of antihyperglycemic therapy was encouraged as required, aimed at reaching individually appropriate glycemic targets in all patients. To determine whether sitagliptin was noninferior to placebo, we used a relative risk of 1.3 as the marginal upper boundary. The primary cardiovascular outcome was a composite of cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for unstable angina. RESULTS: During a median follow-up of 3.0 years, there was a small difference in glycated hemoglobin levels (least-squares mean difference for sitagliptin vs. placebo, -0.29 percentage points; 95% confidence interval [CI], -0.32 to -0.27). Overall, the primary outcome occurred in 839 patients in the sitagliptin group (11.4%; 4.06 per 100 person-years) and 851 patients in the placebo group (11.6%; 4.17 per 100 person-years). Sitagliptin was noninferior to placebo for the primary composite cardiovascular outcome (hazard ratio, 0.98; 95% CI, 0.88 to 1.09; P<0.001). Rates of hospitalization for heart failure did not differ between the two groups (hazard ratio, 1.00; 95% CI, 0.83 to 1.20; P = 0.98). There were no significant between-group differences in rates of acute pancreatitis (P = 0.07) or pancreatic cancer (P = 0.32). CONCLUSIONS: Among patients with type 2 diabetes and established cardiovascular disease, adding sitagliptin to usual care did not appear to increase the risk of major adverse cardiovascular events, hospitalization for heart failure, or other adverse events

Effect of sitagliptin on cardiovascular outcomes in type 2 diabetes

BACKGROUND Data are lacking on the long-term effect on cardiovascular events of adding sitagliptin, a dipeptidyl peptidase 4 inhibitor, to usual care in patients with type 2 diabetes and cardiovascular disease. METHODS In this randomized, double-blind study, we assigned 14,671 patients to add either sitagliptin or placebo to their existing therapy. Open-label use of antihyperglycemic therapy was encouraged as required, aimed at reaching individually appropriate glycemic targets in all patients. To determine whether sitagliptin was noninferior to placebo, we used a relative risk of 1.3 as the marginal upper boundary. The primary cardiovascular outcome was a composite of cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for unstable angina. RESULTS During a median follow-up of 3.0 years, there was a small difference in glycated hemoglobin levels (least-squares mean difference for sitagliptin vs. placebo, 120.29 percentage points; 95% confidence interval [CI], 120.32 to 120.27). Overall, the primary outcome occurred in 839 patients in the sitagliptin group (11.4%; 4.06 per 100 person-years) and 851 patients in the placebo group (11.6%; 4.17 per 100 person-years). Sitagliptin was noninferior to placebo for the primary composite cardiovascular outcome (hazard ratio, 0.98; 95% CI, 0.88 to 1.09; P<0.001). Rates of hospitalization for heart failure did not differ between the two groups (hazard ratio, 1.00; 95% CI, 0.83 to 1.20; P=0.98). There were no significant between-group differences in rates of acute pancreatitis (P=0.07) or pancreatic cancer (P=0.32). CONCLUSIONS Among patients with type 2 diabetes and established cardiovascular disease, adding sitagliptin to usual care did not appear to increase the risk of major adverse cardiovascular events, hospitalization for heart failure, or other adverse events. (Funded by Merck Sharp & Dohme; TECOS ClinicalTrials.gov number, NCT00790205.