1,613 research outputs found
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 at both their pitchfork and tangent
bifurcations. These functions have the form of -exponentials as proposed in
Tsallis' generalization of statistical mechanics. We determine the -indices
that characterize these universality classes and perform for the first time the
calculation of the -generalized Lyapunov coefficient . 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 ânew philosophersâ 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 overmanâs (Ubermensch) âwill to power.â While Nietzsche is opening a necessary and legitimate door, in reality this mindset is akin to Ivan Karamazovâs âeverything is permittedâ 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 Nietzscheâs 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 oneâs 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 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 A 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 , the dynamics
rigorously obeys the Tsallis statistics. We account for the -indices and the
generalized Lyapunov coefficients 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 . 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 -phase transitions of rapidly
decreasing strength, each associated to a discontinuity in Feigenbaum's
trajectory scaling function . The value of at each transition
corresponds to the same special value for the entropic index , such that the
resultant sets of -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
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