Witnesses of Quantum Chaos and Nonlinear Kerr-Like Oscillator Model

Here, we present a brief insight into some current methods allowing for the detection of quantum chaos phenomena. In particular, we show examples of proposals of the parameters which could be applied as indicators of quantum-chaotic behavior and already were presented in the literature. We concentrate here on the quantum fidelity and the fidelity-like functions, defined for the wave functions describing system’s evolution. The definition of the fidelity-like parameter also involves the operator of the mean number of photons/phonons. Discussing such parameter, we show here how it is possible to take into account in the discussion of quantum-chaotic systems simultaneously the behavior of the divergence of wave functions and the energy of the system represented by the mean number of photons/phonons. Next, we discuss entropy-type parameter which can also be a good candidate for the indicators of quantum chaos’ phenomena. We show the ability of all considered here parameters to be witnesses of quantum-chaotic behavior for the systems of the quantum nonlinear Kerr-like oscillator—the classical counterpart of such system can exhibit chaotic evolution in its canonical form

Cardiac Rehabilitation in Heart Failure. Part I, Mechanism

Introduction Diagnosis and treatment issues among heart failure (HF) patients are becoming one of the most important points in public health of developed countries, largely due to the aging of population and the fact that HF affects mainly the elderly. In this review we would like to focus on pathophysiology of exercise intolerance in patients with heart failure and potential benefits of cardiac rehabilitation (CR). Material and Methods Analysis of articles in the EBSCO database using keywords: heart failure, cardiac rehabilitation, exercise training, pathophysiology. Results HF can be described as a composite syndrome which results from structural or functional impairment of ventricular filling or blood ejection. Patients have variety of symptoms which usually are nonspecific. The most frequently occurring symptoms of HF are dyspnea and fatigue, which may restrict exercise capacity, and fluid retention. There are many possible pathophysiological factors involved in the development of exercise intolerance. Based on the available literature pathological changes in central hemodynamic function, pulmonary system, skeletal muscles, endothelial function and neurohumoral system can be distinguished. They play a crucial role in the pathogenesis of HF symptoms and represent a potential curative object. Conclusions HF patients are characterized by diminished functional performance. Exercise training has many potential profits in patients with heart failure, including an increase in peak oxygen uptake, improvement in central hemodynamics, peripheral vascular and skeletal muscle function and has become part of evidence-based clinical therapy in these patients

The dependence of the ratio on <i>p</i> for Bi2212.

<p>The solid line with the open circles represents the theoretical calculation. The filled and half-filled symbols correspond to experimental results obtained by: (a) - Ch. Renner, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Renner1" target="_blank">[74]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Renner2" target="_blank">[75]</a>, (b) - A. Hoffmann, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Hoffmann1" target="_blank">[95]</a>, (c) - Y.G. Ponomarev, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Ponomarev1" target="_blank">[96]</a>, (d) - T. Oki, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Oki1" target="_blank">[97]</a>, (e) - V.M. Krasnov, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Krasnov1" target="_blank">[98]</a>, (f) - A.K. Gupta, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Gupta1" target="_blank">[99]</a>, (g) - A. Kanigel, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Kanigel1" target="_blank">[79]</a>, (h) - J.C. Campuzano, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Campuzano1" target="_blank">[100]</a>, K. Tanaka, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Tanaka1" target="_blank">[101]</a>, (i) - T. Nakano, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Nakano1" target="_blank">[102]</a>, (j) - M. Oda, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Oda1" target="_blank">[103]</a>, (k) - K. McElroy, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-McElroy1" target="_blank">[104]</a>, (l) - A. Matsuda, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Matsuda1" target="_blank">[105]</a>, (m) - J.E. Hoffman, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Hoffman1" target="_blank">[106]</a>, (n) - C. Howald, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Howald1" target="_blank">[107]</a>, (o) - H. Murakami, <i>et al................ </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Murakami2" target="_blank">[108]</a>. The lines (p) are obtained by using the empirical relation (33). The inset shows the dependence of the energy gap on the temperature; the filled region between the solid lines represents possible theoretical values of ; (r) - the experimental results <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Kanigel1" target="_blank">[79]</a>.</p

The four-body scattering event contributing to the interaction part of the Hamiltonian (10).

<p>The oval connecting the electron’s lines is an illustration of which denotes the effective potential.</p

The parameters and calculated by using and the mean values of .

a<p>The hole density <i>p</i> has been estimated as the doping .</p

The dependence of the ratio on <i>p</i> for Bi2212.

<p>The solid line with the open squares represents the theoretical calculation. The filled and half-filled symbols correspond to the experimental results obtained by: (a) - Renner, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Renner1" target="_blank">[74]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Renner2" target="_blank">[75]</a>, (b) - Hoffmann, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Hoffmann1" target="_blank">[95]</a>, (c) - Ponomarev, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Ponomarev1" target="_blank">[96]</a>, (d) - Oki, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Oki1" target="_blank">[97]</a>, (e) - Krasnov, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Krasnov1" target="_blank">[98]</a>, (f) - Gupta, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Gupta1" target="_blank">[99]</a>, (g) - Kanigel, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Kanigel1" target="_blank">[79]</a>, (h) - Campuzano, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Campuzano1" target="_blank">[100]</a>, Tanaka, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Tanaka1" target="_blank">[101]</a>, (i) - Nakano, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Nakano1" target="_blank">[102]</a>, (j) - Oda, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Oda1" target="_blank">[103]</a>, (k) - McElroy, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-McElroy1" target="_blank">[104]</a>, (l) - Matsuda, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Matsuda1" target="_blank">[105]</a>, (m) - Hoffman, <i>et al.............. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031873#pone.0031873-Hoffman1" target="_blank">[106]</a>. The lines (n) are obtained by using the empirical relation (33).</p

Figure 9

<p>(<i>A</i>) The dependence of the ratio on for ; we consider the case and . ( <i>B</i>) The dependence of the ratio on x for Pr-YBCO. ( <i>C</i>) The dependence of the ratio on x for Zn-YBCO.</p

The dependence of the energy gap amplitude on the temperature for the selected values of the EEPH potential.

<p>The solid line represents the physical stable solution; the dotted line corresponds to the unstable solution, where the thermodynamic potential is bigger than in the first case. The vertical line indicates the position of the critical temperature.</p