Bosonic behavior of entangled fermions

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson states. We derive the two-fermion-states that extremize the normalization ratio for a fixed single-fermion purity P, and establish general tight bounds for this indicator. For very small purities, P<1/N^2, the upper and lower bounds converge, which allows to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.Comment: 9 pages, 5 figures, accepted by PR

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Classic wisdom about ways to happiness: How does it apply today?

__Abstract__ Since we humans have some choice in how we live our lives, there has always been ideas about what constitutes a good life. Written reflections on that subject focus typically on moral issues, but there have always been ideas about what constitutes a satisfying life. Interest in this classic wisdom is increasing today, as part of the rising concern about happiness. This begs the question of what we can learn from this ancient wisdom. Does it hold universal truth? Or are these views specific for the historical conditions from which they emerged? In this paper I consider some classic beliefs about happiness and inspect how well these apply in contemporary society. The following five beliefs are considered: 1) Happiness is found in fame and power: follow the path of the warrior. 2) Happiness is found in wealth and involvement: follow the path of the merchant. 3) Happiness is found in intellectual development: follow the path of the philosopher. 4) Happiness is found in simplicity: follow the path of the peasant. 5) Happiness is not of this world: follow the path of the monk. Each of these ways to happiness will manifest in specific behaviors and attitudes and I inspected to what extent these go together with happiness today. To do this. I selected relevant research findings from the World Database of Happiness. The classic beliefs 1 and 2 seem to apply fairly well today, but 3 and 4 not. The advice to seek happiness in other-worldly detachment (5) may have been more sensible in the brutish conditions of feudal society, in which it emerged

ILIOTIBIAL BAND SYNDROME INJURED RUNNERS INCREASE FLEXIBILITY USING SOFT TISSUE MOBILIZATION AND INCREASE FUNCTIONAL STRENGTH USING A HEAT PACK-IMPLICATIONS FOR FASTER RECOVERY

The purpose of this study was to quantify the effects of two independent treatments, soft tissue mobilization and a localized heat pack, upon iliotibial band syndrome injured runner. Iliotibial band injured runners (n=5) who were actively seeking soft tissue mobilization as a treatment were recruited. These runners received one of three randomized treatments during three consecutive visits - (1) soft tissue mobilization (2) an iliotibial band isolating heat pack (3) rest. Iliotibial band flexibility and functional abductor strength measures were taken before and after each treatment. Flexibility was quantified by determining the hip and knee abduction moments generated during the iliotibial band stretch. Each active treatment resulted in significant changes when compared to the treatment of rest. Soft tissue mobilization increased flexibility at the hip and knee while the heat pack increased functional abductor strength

Random walk generated by random permutations of {1,2,3, ..., n+1}

We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the \text{rise-and-descent} sequences characterizing random permutations $\pi$ of $[n+1] = \{1,2,3, ...,n+1\}$. We determine exactly the probability of finding the end-point $X_n = X^{(n)}_n$ of the trajectory of such a permutation-generated random walk (PGRW) at site $X$, and show that in the limit $n \to \infty$ it converges to a normal distribution with a smaller, compared to the conventional P\'olya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identic to the distribution of the intermediate points $X^{(n)}_l$, $l < n$, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of "turns" of the PGRW trajectories.Comment: text shortened, new results added, appearing in J. Phys.

Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

Exact expressions for correlations in the ground state of the dense O(1) loop model

Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary conditions have been considered before. We give many new conjectures for these two cases and review some of the existing results. We also consider boundaries on which loops can end. We call such boundaries ''open''. We have obtained expressions for correlations when both boundaries are open, and one is open and the other one is reflecting. Also, we formulate a conjecture relating the ground state of the model with open boundaries to Fully Packed Loop models on a finite square grid. We also review earlier obtained results about this relation for the three other types of boundary conditions. Finally, we construct a mapping between the ground state of the dense O$(1)$ loop model and the XXZ spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA

Follow-up of blood-pressure lowering and glucose control in type 2 diabetes.

BACKGROUND In the Action in Diabetes and Vascular Disease: Preterax and Diamicron Modified Release Controlled Evaluation (ADVANCE) factorial trial, the combination of perindopril and indapamide reduced mortality among patients with type 2 diabetes, but intensive glucose control, targeting a glycated hemoglobin level of less than 6.5%, did not. We now report results of the 6-year post-trial follow-up. METHODS We invited surviving participants, who had previously been assigned to perindopril–indapamide or placebo and to intensive or standard glucose control (with the glucose-control comparison extending for an additional 6 months), to participate in a post-trial follow-up evaluation. The primary end points were death from any cause and major macrovascular events. RESULTS The baseline characteristics were similar among the 11,140 patients who originally underwent randomization and the 8494 patients who participated in the post-trial follow-up for a median of 5.9 years (blood-pressure–lowering comparison) or 5.4 years (glucose-control comparison). Between-group differences in blood pressure and glycated hemoglobin levels during the trial were no longer evident by the first post-trial visit. The reductions in the risk of death from any cause and of death from cardiovascular causes that had been observed in the group receiving active blood-pressure–lowering treatment during the trial were attenuated but significant at the end of the post-trial follow-up; the hazard ratios were 0.91 (95% confidence interval [CI], 0.84 to 0.99; P=0.03) and 0.88 (95% CI, 0.77 to 0.99; P=0.04), respectively. No differences were observed during follow-up in the risk of death from any cause or major macrovascular events between the intensive-glucose-control group and the standard-glucose-control group; the hazard ratios were 1.00 (95% CI, 0.92 to 1.08) and 1.00 (95% CI, 0.92 to 1.08), respectively. CONCLUSIONS The benefits with respect to mortality that had been observed among patients originally assigned to blood-pressure–lowering therapy were attenuated but still evident at the end of follow-up. There was no evidence that intensive glucose control during the trial led to long-term benefits with respect to mortality or macrovascular events