BCS thermal vacuum of fermionic superfluids and its perturbation theory

The thermal field theory is applied to fermionic superfluids by doubling the degrees of freedom of the BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon results from the perturbation theory. The BCS thermal vacuum is shown to be a generalized coherent and squeezed state. The correspondence between the thermal vacuum and purification of the density matrix allows a unitary transformation, and we found the geometric phase in the parameter space associated with the transformation.Comment: 14 pages, 2 figure

Continuous Selections For Almost Lower Semicontinuous Multifunctions

[[abstract]]In this paper, we obtain several new continuous selection theorems for almost lower semicontinuous multifunctions T on a paracompact topological space X, in the general noncompact and/or nonconvex settings. We consider three interesting topics in the selection theory; each of these topics deals with a broad class of selection problems. One is to introduce and analyze some well known selection theorems. Based on Deutsch-Kenderov theorem and an equicontinuous property, we first establish a generalized selection theorem for the multifunctions, even without requiring lower semicontinuity on T, but merely an almost lower semicontinuous multifunction. Secondly, we establish some relationships between abstract convexity and the selection property. Under a mild condition of one point extension property, we show that a C-set structure on a metric space without convexity still has the continuous selection property. Finally, we modify our selection theorems by adjusting a closed subset Z of X with its covering dimension less or equal to 0. These results derived here generalize and unify various earlier ones from classic continuous selection theory.

One-dimensional polymers in random environments: stretching vs. folding

In this article we study a \emph{non-directed polymer model} on $\mathbb Z$, that is a one-dimensional simple random walk placed in a random environment. More precisely, the law of the random walk is modified by the exponential of the sum of ``rewards'' (or penalities) $\beta \omega_x -h$ sitting on the range of the random walk, where $(\omega_x)_{x\in \mathbb Z}$ are i.i.d.\ random variables (the disorder), and where $\beta\geq 0$ (disorder strength) and $h\in \mathbb{R}$ (external field) are two parameters. When $\beta=0,h>0$, this corresponds to a random walk penalized by its range; when $\beta>0, h=0$, this corresponds to the ``standard'' polymer model in random environment, except that it is non-directed. In this work, we allow the parameters $\beta,h$ to vary according to the length of the random walk, and we study in detail the competition between the \emph{stretching effect} of the disorder, the \emph{folding effect} of the external field (if $h\ge 0$), and the \emph{entropy cost} of atypical trajectories. We prove a complete description of the (rich) phase diagram. For instance, in the case $\beta>0, h=0$ of the non-directed polymer, if $\omega_x$ ha a finite second moment, we find a transversal fluctuation exponent $\xi=2/3$, and we identify the limiting distribution of the rescaled log-partition function.Comment: 28 pages, 5 figure

THE EFFECTS OF KINESIO TAPING ON RATE OF FORCE DEVELOPMENT IN SQUAT JUMP AND COUNTER MOVEMENT JUMP

Kinesio tape (KT) has been widely used to prevent muscle pain and to improve strength and sports performance. Therefore, the aim of this study was to investigate the effect of KT in rate of force development (RFD). To compare with KT or non-KT in squat jump (SJ) and counter movement jump (CMJ). The RFD was improved or not improved by using KT. Six healthy female was recruited in this study. The kistler force plate was used to measure the RFD. There is no significant improve in SJ and CMJ. The results showed that KT did not affect RFD