64 research outputs found
Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
Schroedinger equation H \psi=E \psi with PT - symmetric differential operator
H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on
L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at
a>0. The proof of this non-variational construction is given. Our Taylor series
form of \psi complements and completes the recent terminating solutions as
obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J.
Phys. A: Math. Gen., to appea
Study of a class of non-polynomial oscillator potentials
We develop a variational method to obtain accurate bounds for the
eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the
nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in
(-infinity,\infinity), g>0. The variational bounds are compared with results
previously obtained in the literature. An infinite set of exact solutions is
also obtained and used as a source of comparison eigenvalues.Comment: 16 page
PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
For any central potential V in D dimensions, the angular Schroedinger
equation remains the same and defines the so called hyperspherical harmonics.
For non-central models, the situation is more complicated. We contemplate two
examples in the plane: (1) the partial differential Calogero's three-body model
(without centre of mass and with an impenetrable core in the two-body
interaction), and (2) the Smorodinsky-Winternitz' superintegrable harmonic
oscillator (with one or two impenetrable barriers). These examples are solvable
due to the presence of the barriers. We contemplate a small complex shift of
the angle. This creates a problem: the barriers become "translucent" and the
angular potentials cease to be solvable, having the sextuple-well form for
Calogero model and the quadruple or double well form otherwise. We mimic the
effect of these potentials on the spectrum by the multiple, purely imaginary
square wells and tabulate and discuss the result in the first nontrivial
double-well case.Comment: 21 pages, 5 figures (see version 1), amendment (a single comment
added on p. 7
Eigenvalues from power--series expansions: an alternative approach
An appropriate rational approximation to the eigenfunction of the
Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the
eigenvalue accurately as the limit of a sequence of roots of Hankel
determinants. The convergence rate of this approach is greater than that for a
well--established method based on a power--series expansions weighted by a
Gaussian factor with an adjustable parameter (the so--called Hill--determinant
method)
Pathophysiology of resistant hypertension: The role of sympathetic nervous system
Resistant hypertension (RH) is a powerful risk factor for cardiovascular morbidity and mortality. Among the characteristics of patients with RH, obesity, obstructive sleep apnea, and aldosterone excess are covering a great area of the mosaic of RH phenotype. Increased sympathetic nervous system (SNS) activity is present in all these underlying conditions, supporting its crucial role in the pathophysiology of antihypertensive treatment resistance. Current clinical and experimental knowledge points towards an impact of several factors on SNS activation, namely, insulin resistance, adipokines, endothelial dysfunction, cyclic intermittent hypoxaemia, aldosterone effects on central nervous system, chemoreceptors, and baroreceptors dysregulation. The further investigation and understanding of the mechanisms leading to SNS activation could reveal novel therapeutic targets and expand our treatment options in the challenging management of RH. Copyright © 2011 Costas Tsioufis et al
Parallel deterioration of albuminuria, arterial stiffness and left ventricular mass in essential hypertension: Integrating target organ damage
Background: Albuminuria, arterial stiffening and left ventricular hypertrophy (LVH) constitute target organ damage. We estimated whether increased urinary albumin excretion, assessed by albumin-to-creatine ratio (ACR), and carotid to femoral pulse wave velocity (c-f PWV) were accompanied by augmented left ventricular (LV) mass index (LVMI) in hypertension. Methods: In 428 non-diabetic untreated hypertensives (257 men, mean age = 52 years, office blood pressure (BP) = 146/93 mm Hg) the distributions of ACR and c-f PWV were split by the median (8 mg/g and 7.8 m/s, respectively). Results: Age, male sex, 24 h systolic BP, ACR and c-f PWV were the independent predictors of LVMI (R 2 = 0.478, p < 0.0001). Among patients with low ACR (n = 198), those with high c-f PWV (n = 84) compared to those with low c-f PWV (n = 114) were characterized by increased LVMI (by 8.9 g/m 2, p = 0.012) and prevalence of LVH (30 vs. 14%, p = 0.015). Similarly among patients with high ACR (n = 230), those with high c-f PWV (n = 123) compared to those with low c-f PWV (n = 107) exhibited heightened LVMI (by 13.6 g/m 2, p = 0.001). Conclusions: Increased ACR in conjunction with pronounced arterial stiffness is accompanied by augmented LV mass and higher LVH rates. Furthermore, the interrelationships between albuminuria, c-f PWV and LVMI suggest parallel target organ damage progression. Copyright © 2011 S. Karger AG, Basel
On dynamical mass generation and asymptotic freedom in nonabelian gauge theories
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