Two stories outside Boltzmann-Gibbs statistics: Mori's q-phase transitions and glassy dynamics at the onset of chaos

First, we analyze trajectories inside the Feigenbaum attractor and obtain the atypical weak sensitivity to initial conditions and loss of information associated to their dynamics. We identify the Mori singularities in its Lyapunov spectrum with the appearance of a special value for the entropic index q of the Tsallis statistics. Secondly, the dynamics of iterates at the noise-perturbed transition to chaos is shown to exhibit the characteristic elements of the glass transition, e.g. two-step relaxation, aging, subdiffusion and arrest. The properties of the bifurcation gap induced by the noise are seen to be comparable to those of a supercooled liquid above a glass transition temperature.Comment: Proceedings of: 31st Workshop of the International School of Solid State Physics, Complexity, Metastability and Nonextensivity, Erice (Sicily) 20-26 July 2004 World Scientific in the special series of the E. Majorana conferences, in pres

Rheology of a sonofluidized granular packing

We report experimental measurements on the rheology of a dry granular material under a weak level of vibration generated by sound injection. First, we measure the drag force exerted on a wire moving in the bulk. We show that when the driving vibration energy is increased, the effective rheology changes drastically: going from a non-linear dynamical friction behavior - weakly increasing with the velocity- up to a linear force-velocity regime. We present a simple heuristic model to account for the vanishing of the stress dynamical threshold at a finite vibration intensity and the onset of a linear force-velocity behavior. Second, we measure the drag force on spherical intruders when the dragging velocity, the vibration energy, and the diameters are varied. We evidence a so-called ''geometrical hardening'' effect for smaller size intruders and a logarithmic hardening effect for the velocity dependence. We show that this last effect is only weakly dependent on the vibration intensity.Comment: Accepted to be published in EPJE. v3: Includes changes suggested by referee

Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: rigorous nonextensive solutions

Using the Feigenbaum renormalization group (RG) transformation we work out exactly the dynamics and the sensitivity to initial conditions for unimodal maps of nonlinearity $\zeta >1$ at both their pitchfork and tangent bifurcations. These functions have the form of $q$-exponentials as proposed in Tsallis' generalization of statistical mechanics. We determine the $q$-indices that characterize these universality classes and perform for the first time the calculation of the $q$-generalized Lyapunov coefficient $\lambda_{q}$. The pitchfork and the left-hand side of the tangent bifurcations display weak insensitivity to initial conditions, while the right-hand side of the tangent bifurcations presents a `super-strong' (faster than exponential) sensitivity to initial conditions. We corroborate our analytical results with {\em a priori} numerical calculations.Comment: latex, 4 figures. Updated references and some general presentation improvements. To appear published in Europhysics Letter

Life at the Meridian: The Subjectivity of Ethics in the Works of Albert Camus and Friedrich Nietzsche

This paper endeavors to respond to the questions: can ethics can be unbound from its traditional rootedness in religious systems? If so, what contributions did Nietzsche make to liberate value from the shackles of Western morality? To what degree is Camus one of the “new philosophers” Nietzsche calls for in On the Genealogy of Morals? In an attempt to demonstrate that ethics can and do exist vividly in the realm of the non-religious, this paper will begin by illustrating the metaphysical door Nietzsche opens through his use of aphorisms in Thus Spoke Zarathustra and his investigation of the history of Western values in On the Genealogy of Morals. In these nihilistic inquiries Nietzsche collects and sorts values, razes traditional morals of the religious to the ground, and constructs a worldview based on an overman’s (Ubermensch) “will to power.” While Nietzsche is opening a necessary and legitimate door, in reality this mindset is akin to Ivan Karamazov’s “everything is permitted” declaration that allows all actions, even those as extreme as murder. At this point Albert Camus responds to Nietzsche in his books The Stranger, The Myth of Sisyphus, and The Rebel by re-imagining the deserted space beyond Nietzsche’s door. By actively rejecting any type of unifying principle, be it nihilism, religion, or objective conclusions about the world, Camus advocates for an individualistic and ultimately subjective mode of thought. Within this imagined space one is fundamentally free but proportionally lonely and responsible for one’s actions. Void of eternal hope and set free from traditional values, an individual is filled with the opportunity for creativity and constructs a universe for oneself

Shape evolution and shape coexistence in Pt isotopes: comparing interacting boson model configuration mixing and Gogny mean-field energy surfaces

The evolution of the total energy surface and the nuclear shape in the isotopic chain $^{172-194}$Pt are studied in the framework of the interacting boson model, including configuration mixing. The results are compared with a self-consistent Hartree-Fock-Bogoliubov calculation using the Gogny-D1S interaction and a good agreement between both approaches shows up. The evolution of the deformation parameters points towards the presence of two different coexisting configurations in the region 176 $\leq$ A $\leq$ 186.Comment: Submitted to PR

Intermittency at critical transitions and aging dynamics at edge of chaos

We recall that, at both the intermittency transitions and at the Feigenbaum attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the generalized Lyapunov coefficients $\lambda_{q}$ that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the edge of chaos with the appearance of a special value for the entropic index $q$. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.Comment: Proceedings of: STATPHYS 2004 - 22nd IUPAP International Conference on Statistical Physics, National Science Seminar Complex, Indian Institute of Science, Bangalore, 4-9 July 2004. Pramana, in pres

Tsallis' q index and Mori's q phase transitions at edge of chaos

We uncover the basis for the validity of the Tsallis statistics at the onset of chaos in logistic maps. The dynamics within the critical attractor is found to consist of an infinite family of Mori's $q$-phase transitions of rapidly decreasing strength, each associated to a discontinuity in Feigenbaum's trajectory scaling function $\sigma$. The value of $q$ at each transition corresponds to the same special value for the entropic index $q$, such that the resultant sets of $q$-Lyapunov coefficients are equal to the Tsallis rates of entropy evolution.Comment: Significantly enlarged version, additional figures and references. To be published in Physical Review

Control and coherence of the optical transition of single defect centers in diamond

We demonstrate coherent control of the optical transition of single Nitrogen-Vacancy defect centers in diamond. On applying short resonant laser pulses, we observe optical Rabi oscillations with a half-period as short as 1 nanosecond, an order of magnitude shorter than the spontaneous emission time. By studying the decay of Rabi oscillations, we find that the decoherence is dominated by laser-induced spectral jumps. By using a low-power probe pulse as a detuning sensor and applying post-selection, we demonstrate that spectral diffusion can be overcome in this system to generate coherent photons.Comment: 5 pages,4 figure