Initial wave packets and the various power-law decreases of scattered wave packets at long times

The long time behavior of scattered wave packets $\psi (x,t)$ from a finite-range potential is investigated, by assuming $\psi (x,t)$ to be initially located outside the potential. It is then shown that $\psi (x,t)$ can asymptotically decrease in the various power laws at long time, according to its initial characteristics at small momentum. As an application, we consider the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can also appear for another $\psi (x,t)$.Comment: 5 pages, 1 figur

Cosmic acceleration in a model of scalar-tensor gravitation

In this paper we consider a model of scalar-tensor theory of gravitation in which the scalar field, $\phi$ determines the gravitational coupling G and has a Lagrangian of the form, $\mathcal{L}_{\phi} =-V(\phi)\sqrt{1 - \partial_{\mu}\phi\partial^{\mu}\phi}$. We study the cosmological consequence of this theory in the matter dominated era and show that this leads to a transition from an initial decelerated expansion to an accelerated expansion phase at the present epoch. Using observational constraints, we see that the effective equation of state today for the scalar field turns out to be $p_{\phi}=w_{\phi}{\rho}_{\phi}$, with $w_{\phi}=-0.88$ and that the transition to an accelerated phase happened at a redshift of about 0.3.Comment: 12 pages, 2 figures, matches published versio

A note on perfect scalar fields

We derive a condition on the Lagrangian density describing a generic, single, non-canonical scalar field, by demanding that the intrinsic, non-adiabatic pressure perturbation associated with the scalar field vanishes identically. Based on the analogy with perfect fluids, we refer to such fields as perfect scalar fields. It is common knowledge that models that depend only on the kinetic energy of the scalar field (often referred to as pure kinetic models) possess no non-adiabatic pressure perturbation. While we are able to construct models that seemingly depend on the scalar field and also do not contain any non-adiabatic pressure perturbation, we find that all such models that we construct allow a redefinition of the field under which they reduce to pure kinetic models. We show that, if a perfect scalar field drives inflation, then, in such situations, the first slow roll parameter will always be a monotonically decreasing function of time. We point out that this behavior implies that these scalar fields can not lead to features in the inflationary, scalar perturbation spectrum.Comment: v1: 11 pages; v2: 11 pages, minor changes, journal versio

Finding Common Interests: Using Social Media to boost Retention in Voluntary Professional Associations

Attrition is one of the most important challenges faced by Professional Associations like the Project Management Institute (PMI). According to publicly available data, 90,000 members joined PMI in 2005. In the month of April 2006 alone, 33,751 new members were added, which leads to the logical conclusion that the PMI membership must have grown by over 115,750 during the period 2005-2006. However, records show that the growth has been by only 70,000. PMI’s reported growth of 5% would have been much higher had it not been for their attrition of 23%. Similarly, ISACA’s growth during 2014 dropped to 4% due to their attrition of 19%. In this paper, we combine the social identity theory and communication ecology theory to propose a Social Identity Theory (SITPA) for professionals. We argue that by leveraging the social media, Voluntary Professional Associations (VPAs) can provide “value” to their members, increasing their retention rates

Heat shock protein 70 gene polymorphism and hospital outcomes in patients with acute pancreatitis.

INTRODUCTION : Acute pancreatitis is defined as a process involving inflammation of pancreas, the surrounding tissues as well as distant organs. Incidence of acute pancreatitis differ in different parts of the world, possibly due to the differnce in the consumption of alcohol in different places as well as difference in the incidence of gall stones in different parts of world. Previous studies reported the occurence of acute pancreatitis ranging from 4.9 to 35 per 1 lakh populations. Severe disease was reported in about 20% of individuals and may be associated with mortality close to 20%. There are varied aetiologies for acute pancreatitis. In one study Steer M L et al, found that in 45 percent of cases, cholelithiasis was the cause followed by ethanol in 35 percent ,rest in 10%. In about 10%, a specific cause could not be found and was grouped under idiopathic(5) . In India, the aetiological spectrum of mild pancreatitis included the following: alcoholism in 41.1%, gallstones in 23.5%, trauma in 17.6%, idiopathic in 11.7% and post-endoscopic retrograde cholangiopancreatography in 5.8%. Acute pancreatitis patients, usually present with pain abdomen and vomiting. Pain typically starts in epigastrium and may be radiating to the back also. Abdominal examination may reveal tenderness in the epigastrium. In mild cases, usually there will be an uneventful recovery and may require only few days of admission in hospital. In severe cases, pain may be severe with increase in heart rate, tachypnoea, decreased urine output and hypotension. There can be various signs on abdominal examination like cullens and Gray Turners signs. In severe cases death also can occur. Such patients can be grouped as severe acute pancreatitis when they present with /develop organ failure and or with local complications such as fluid collections, necrosis, abscess, or pseudocyst. AIM : To determine whether there is any association between Heat Shock Protein 70 gene polymorphisms and severity of illness and hospital outcomes in patients with acute pancreatitis admitted to a tertiary care hospital. CONCLUSIONS : Alcohol was the most common cause for acute pancreatitis in this study followed by biliary stones.Male gender is affected more than females.Severe Acute Pancreatitis were observed in more than half of the study population.Local complications were present in 41.73% of study population of which acute fluid collection was the commonest followed by pseudocyst, necrosis and abscess. Organ failure was present in one fourth of the study population. Respiratory insufficiency was the most common organ failure followed by cardiovascular, renal and gastrointestinal complication Klebsiella was the most common organism grown in patient with infection. The mortality in acute severe pancreatitis was 20 %. One tenth of the total population studied had recurrent acute pancreatitis with biliary stones as the most common aetiology after excluding the idiopathic group. Homozygous TT rs 2227956 gene polymorphism showed statistically significant correlation with the need for pressure support ,length of ICU stay and it also showed a trend towards significance for overall organ failure, overall severity of the disease and pulmonary insufficiency. There is a possibility that those who are having homozygous TT allele with rs 2227956 genetic polymorphism are at risk for a severe course of disease if they have an episode of acute pancreatitis

Free initial wave packets and the long-time behavior of the survival and nonescape probabilities

The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both S(t) and P(t) asymptotically exhibit the same power-law decrease at long times, when the initial wave packet in momentum representation behaves as O(1) or O(k) at small momentum. On the other hand, if the integer m becomes greater than 1, S(t) and P(t) decrease in different power-laws at long times.Comment: 4 pages, 3 figures, Title and organization changed, however the results not changed, To appear in Phys. Rev.

The various power decays of the survival probability at long times for free quantum particle

The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator at long times, in terms of the integral operators. This enables us to obtain the asymptotic formula for the survival probability of the initial state $\psi (x)$, which is assumed to decrease sufficiently rapidly at large $|x|$. We then show that the behaviour of the survival probability at long times is determined by that of the initial state $\psi$ at zero momentum $k=0$. Indeed, it is proved that the survival probability can exhibit the various power-decays like $t^{-2m-1}$ for an arbitrary non-negative integers $m$ as $t \to \infty$, corresponding to the initial states with the condition $\hat{\psi} (k) = O(k^m)$ as $k\to 0$.Comment: 15 pages, to appear in J. Phys.

Scalar Field Dark Energy Perturbations and their Scale Dependence

We estimate the amplitude of perturbation in dark energy at different length scales for a quintessence model with an exponential potential. It is shown that on length scales much smaller than hubble radius, perturbation in dark energy is negligible in comparison to that in in dark matter. However, on scales comparable to the hubble radius ($\lambda_{p}>1000\mathrm{Mpc}$) the perturbation in dark energy in general cannot be neglected. As compared to the $\Lambda$CDM model, large scale matter power spectrum is suppressed in a generic quintessence dark energy model. We show that on scales $\lambda_{p} < 1000\mathrm{Mpc}$, this suppression is primarily due to different background evolution compared to $\Lambda$CDM model. However, on much larger scales perturbation in dark energy can effect matter power spectrum significantly. Hence this analysis can act as a discriminator between $\Lambda$CDM model and other generic dark energy models with $w_{de} \neq -1$.Comment: 12 pages, 13 figures, added new section, accepted for publication in Phys. Rev.

Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200