Atomic Compton profiles within different exchange-only theories

The Impulse Compton Profiles (CP's) J(q) and the - expectation values for some inert gas atoms (He-Kr) are computed and compared within the Harbola-Sahni (HS), Hartree-Fock(HF) theories and a Self Interaction Corrected (SIC) density functional model. The Compton profiles for excited states of Helium atom are also calculated. While the calculated CP's are found to generally agree, they differ slightly from one another for small values of the Compton parameter q and are in good agreement for large q values. The expectation values within the three theories are also found to be comparable. The HS formalism seem to mimic HF reasonably well in the momentum space, establishing the logical consistency of the former.Comment: 15 page

Exactly solvable PT\mathcal{PT}-symmetric models in two dimensions

Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $\mathcal{PT}$ symmetry threshold can be tuned by introducing a second gain-loss potential or its hermitian counterpart. Our results explicitly demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $\mathcal{PT}$ symmetric phases.Comment: 6 pages, 6 figure

Momentum space properties from coordinate space electron density

Electron density and electron momentum density, while independently tractable experimentally, bear no direct connection without going through the many-electron wave function. However, invoking a variant of the constrained-search formulation of density functional theory, we develop a general scheme (valid for arbitrary external potentials) yielding decent momentum space properties, starting exclusively from the coordinate space electron density. Numerical illustration of the scheme is provided for the closed-shell atomic systems He, Be and Ne and for $1s^1~2s^1$ singlet electronic excited state for Helium by calculating the Compton profiles and the $$ expectation values derived from given coordinate space electron densities.Comment: 4 pages, 1 figur

Nonexistence of local maxima in molecular electrostatic potential maps

It has been rigorously established by means of classical electrostatic arguments, that molecular electrostatic potential maps are devoid of local maxima. This forms a generalization of the earlier works of Politzer and co-workers which were restricted to the case of atoms

Spatiotemporal characteristics of atrial fibrillation electrograms: a novel marker for arrhythmia stability and termination

Background: Sequentially mapped complex fractionated atrial electrograms (CFAE) and dominant frequency (DF) sites have been targeted during catheter ablation for atrial fibrillation (AF). However, these strategies have yielded variable success and have not been shown to correlate consistently with AF dynamics. Here, we evaluated whether the spatiotemporal stability of CFAE and DF may be a better marker of AF sustenance and termination. Methods: Eighteen sheep with 12 weeks of "one-kidney, one-clip" hypertension underwent open-chest studies. A total of 42 self-terminating (28–100 s) and 6 sustained (>15 min) AF episodes were mapped using a custom epicardial plaque and analyzed in 4-s epochs for CFAE, using the NavX CFE-m algorithm, and DF, using a Fast Fourier Transform. The spatiotemporal stability index (STSI) was calculated using the intraclass correlation coefficient of consecutive AF epochs. Results: A total of 67,733 AF epochs were analyzed. During AF initiation, mean CFE-m and the STSI of CFE-m/DF were similar between sustained and self-terminating episodes, although median DF was higher in sustained AF (p=0.001). During sustained AF, the STSI of CFE-m increased significantly (p=0.02), whereas mean CFE-m (p=0.5), median DF (p=0.07), and the STSI of DF remained unchanged (p=0.5). Prior to AF termination, the STSI of CFE-m was significantly lower (p<0.001), with a physiologically non-significant decrease in median DF (−0.3 Hz, p=0.006) and no significant changes in mean CFE-m (p=0.14) or the STSI of DF (p=0.06). Conclusions: Spatiotemporal stabilization of CFAE favors AF sustenance and its destabilization heralds AF termination. The STSI of CFE-m is more representative of AF dynamics than are the STSI of DF, sequential mean CFE-m, or median DF

Characteristics of the phenotype of mixed cardiomyopathy in patients with implantable cardioverter-defibrillators

OnlinePublBackground or Purpose The prognosis of mixed cardiomyopathy (CMP) in patients with implanted cardioverter-defbrillators (ICDs) has not been investigated. We aim to study the demographic, clinical, device therapies and survival characteristics of mixed CMP in a cohort of patients implanted with a defbrillator. Methods The term mixed CMP was used to categorise patients with impaired left ventricular ejection fraction attributed to documented non-ischemic triggers with concomitant moderate coronary artery disease. This is a single center observational cohort of 526 patients with a mean follow-up of 8.7±3.5 years. Results There were 42.5% patients with ischemic cardiomyopathy (ICM), 26.9% with non-ischemic cardiomyopathy (NICM) and 30.6% with mixed CMP. Mixed CMP, compared to NICM, was associated with higher mean age (69.1 ± 9.6 years), atrial fibrillation (55.3%) and greater incidence of comorbidities. The proportion of patients with mixed CMP receiving device shocks was 23.6%, compared to 18.4% in NICM and 27% in ICM. The VT cycle length recorded in mixed CMP (281.6 ± 43.1 ms) was comparable with ICM (282.5 ± 44 ms; p = 0.9) and lesser than NICM (297.7±48.7 ms; p=0.1). All-cause mortality in mixed CMP (21.1%) was similar to ICM (20.1%; p=0.8) and higher than NICM (15.6%; p = 0.2). The Kaplan–Meier curves revealed hazards of 1.57 (95% CI: 0.91, 2.68) for mixed CMP compared to NICM. Conclusion In a cohort of patients with ICD, the group with mixed CMP represents a phenotype predominantly comprised of the elderly with a higher incidence of comorbidities. Mixed CMP resembles ICM in terms of number of device shocks and VT cycle length. Trends of long-term prognosis of patients with mixed CMP are worse than NICM and similar to ICM.Deep Chandh Raja, Indira Samarawickrema, Sarat Krishna Menon, Rikvin Singh, Abhinav Mehta, Lukah Q. Tuan, Ulhas Pandurangi, Sanjiv Jain, David J. Callans, Francis E. Marchlinski, Walter P. Abhayaratna, Prashanthan Sanders, Rajeev K. Patha