161 research outputs found

### About "On certain incomplete statistics" by Lima et al

Lima et al recently claim that ({\em Chaos, Solitons & Fractals,}
2004;19:1005)the entropy for the incomplete statistics based on the
normalization$\sum_ip_i^q=1$ should be $S=-\sum_ip_i^{2q-1}\ln_qp_i$ instead
of$S=-\sum_ip_i^{q}\ln_qp_i$ initially proposed by Wang. We indicate here that
thisconclusion is a result of erroneous use of temperature definition for the
incompletestatistics

### A nonextensive approach to Bose-Einstein condensation of trapped interacting boson gas

In the Bose-Einstein condensation of interacting atoms or molecules such as
87Rb, 23Na and 7Li, the theoretical understanding of the transition temperature
is not always obvious due to the interactions or zero point energy which cannot
be exactly taken into account. The S-wave collision model fails sometimes to
account for the condensation temperatures. In this work, we look at the problem
within the nonextensive statistics which is considered as a possible theory
describing interacting systems. The generalized energy Uq and the particle
number Nq of boson gas are given in terms of the nonextensive parameter q. q>1
(q<1) implies repulsive (attractive) interaction with respect to the perfect
gas. The generalized condensation temperature Tcq is derived versus Tc given by
the perfect gas theory. Thanks to the observed condensation temperatures, we
find q ~ 0.1 for 87Rb atomic gas, q ~ 0.95 for 7Li and q ~ 0.62 for 23Na. It is
concluded that the effective interactions are essentially attractive for the
three considered atoms, which is consistent with the observed temperatures
higher than those predicted by the conventional theory

### Fractal geometry, information growth and nonextensive thermodynamics

This is a study of the information evolution of complex systems by
geometrical consideration. We look at chaotic systems evolving in fractal phase
space. The entropy change in time due to the fractal geometry is assimilated to
the information growth through the scale refinement. Due to the incompleteness
of the state number counting at any scale on fractal support, the incomplete
normalization $\sum_ip_i^q=1$ is applied throughout the paper, where $q$ is the
fractal dimension divided by the dimension of the smooth Euclidean space in
which the fractal structure of the phase space is embedded. It is shown that
the information growth is nonadditive and is proportional to the trace-form
$\sum_ip_i-\sum_ip_i^q$ which can be connected to several nonadditive
entropies. This information growth can be extremized to give power law
distributions for these non-equilibrium systems. It can also be used for the
study of the thermodynamics derived from Tsallis entropy for nonadditive
systems which contain subsystems each having its own $q$. It is argued that,
within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can
be preserved.Comment: Final version, 10 pages, no figures, Invited talk at the
international conference NEXT2003, 21-28 september 2003, Villasimius
(Cagliari), Ital

### Generalized algebra within a nonextensive statistics

By considering generalized logarithm and exponential functions used in
nonextensive statistics, the four usual algebraic operators : addition,
subtraction, product and division, are generalized. The properties of the
generalized operators are investigated. Some standard properties are preserved,
e.g., associativity, commutativity and existence of neutral elements. On the
contrary, the distributivity law and the opposite element is no more universal
within the generalized algebra.Comment: 11 pages, no figure, TeX. Reports on Mathematical Physics (2003), in
pres

### Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems

We propose an experimentally feasible scheme to achieve quantum computation
based on a pair of orthogonal cyclic states. In this scheme, quantum gates can
be implemented based on the total phase accumulated in cyclic evolutions. In
particular, geometric quantum computation may be achieved by eliminating the
dynamic phase accumulated in the whole evolution. Therefore, both dynamic and
geometric operations for quantum computation are workable in the present
theory. Physical implementation of this set of gates is designed for NMR
systems. Also interestingly, we show that a set of universal geometric quantum
gates in NMR systems may be realized in one cycle by simply choosing specific
parameters of the external rotating magnetic fields. In addition, we
demonstrate explicitly a multiloop method to remove the dynamic phase in
geometric quantum gates. Our results may provide useful information for the
experimental implementation of quantum logical gates.Comment: 9 pages, language revised, the publication versio

### Quantum computing with four-particle decoherence-free states in ion trap

Quantum computing gates are proposed to apply on trapped ions in
decoherence-free states. As phase changes due to time evolution of components
with different eigenenergies of quantum superposition are completely frozen,
quantum computing based on this model would be perfect. Possible application of
our scheme in future ion-trap quantum computer is discussed.Comment: 10 pages, no figures. Comments are welcom

### Quantum control of $^{88}$Sr$^+$ in a miniature linear Paul trap

We report on the construction and characterization of an apparatus for
quantum information experiments using $^{88}$Sr$^+$ ions. A miniature linear
radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1
MHz in all directions are obtained with 50 V on the trap end-caps and less than
1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the
$S_{1/2}$ electronic ground-state of the ion. We constructed all the necessary
laser sources for laser cooling and full coherent manipulation of the ions'
external and internal states. Oscillating magnetic fields are used for coherent
spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are
demonstrated. Following resolved sideband cooling the average axial vibrational
quanta of a single trapped ion is $\bar n=0.05$ and a heating rate of
$\dot{\bar n}=0.016$ ms$^{-1}$ is measured.Comment: 8 pages,9 figure

### Efficient photoionization for barium ion trapping using a dipole-allowed resonant two-photon transition

Two efficient and isotope-selective resonant two-photon ionization techniques
for loading barium ions into radio-frequency (RF)-traps are demonstrated. The
scheme of using a strong dipole-allowed transition at \lambda=553 nm as a first
step towards ionization is compared to the established technique of using a
weak intercombination line (\lambda=413 nm). An increase of two orders of
magnitude in the ionization efficiency is found favoring the transition at 553
nm. This technique can be implemented using commercial all-solid-state laser
systems and is expected to be advantageous compared to other narrowband
photoionization schemes of barium in cases where highest efficiency and
isotope-selectivity are required.Comment: 8 pages, 5 figure

### Band crossings in Ta166

High-spin states in the odd-odd nucleus Ta166 are investigated through the 5n channel of the V51+Sn120 reaction. Four new bands are observed and linked into the previous level scheme. Configurations for the bands are proposed, based on measured alignments and B(M1)/B(E2) transition strength ratios

### Rotational structures and the wobbling mode in Ta167

Excited states in the neutron-deficient nucleus Ta167 were studied through the Sn120(V51,4n) reaction. Twelve rotational bands have been observed and the relative excitation energy of each sequence is now known owing to the multiple interband connections. Several quasineutron alignments were observed that aided in the quasiparticle assignments of these bands. The resulting interpretation is in line with observations in neighboring nuclei. Trends in the wobbling phonon energy seen in Lu161,163,165,167 and Ta167 are also discussed and particle-rotor model calculations (assuming constant moments of inertia) are found to be inconsistent with the experimental data

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