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Network analysis of chaotic dynamics in fixed-precision digital domain
When implemented in the digital domain with time, space and value discretized
in the binary form, many good dynamical properties of chaotic systems in
continuous domain may be degraded or even diminish. To measure the dynamic
complexity of a digital chaotic system, the dynamics can be transformed to the
form of a state-mapping network. Then, the parameters of the network are
verified by some typical dynamical metrics of the original chaotic system in
infinite precision, such as Lyapunov exponent and entropy. This article reviews
some representative works on the network-based analysis of digital chaotic
dynamics and presents a general framework for such analysis, unveiling some
intrinsic relationships between digital chaos and complex networks. As an
example for discussion, the dynamics of a state-mapping network of the Logistic
map in a fixed-precision computer is analyzed and discussed.Comment: 5 pages, 9 figure
Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6
Kondo insulator samarium hexaboride (SmB6) has been intensely studied in
recent years as a potential candidate of a strongly correlated topological
insulator. One of the most exciting phenomena observed in SmB6 is the clear
quantum oscillations appearing in magnetic torque at a low temperature despite
the insulating behavior in resistance. These quantum oscillations show multiple
frequencies and varied effective masses. The origin of quantum oscillation is,
however, still under debate with evidence of both two-dimensional Fermi
surfaces and three-dimensional Fermi surfaces. Here, we carry out
angle-resolved torque magnetometry measurements in a magnetic field up to 45 T
and a temperature range down to 40 mK. With the magnetic field rotated in the
(010) plane, the quantum oscillation frequency of the strongest oscillation
branch shows a four-fold rotational symmetry. However, in the angular
dependence of the amplitude of the same branch, this four-fold symmetry is
broken and, instead, a twofold symmetry shows up, which is consistent with the
prediction of a two-dimensional Lifshitz-Kosevich model. No deviation of
Lifshitz-Kosevich behavior is observed down to 40 mK. Our results suggest the
existence of multiple light-mass surface states in SmB6, with their mobility
significantly depending on the surface disorder level.Comment: 15 pages, 9 figure
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