Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCluster Identification and Characterization of Physical Fields
82
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from various methods. Main steps are as follows. We first divide the space using face or volume elements from discrete points. Then, combine the elements with the same and/or similar properties to construct clusters with special physical characterizations. In the algorithm, we adopt administrative structure of hierarchy-tree for spatial bodies such as points, lines, faces, blocks, and clusters. Two fast search algorithms with the complexity are realized. The establishing of the hierarchy-tree and the fast searching of spatial bodies are general, which are independent of spatial dimensions. Therefore, it is easy to extend the skill to other fields. As a verification and validation, we treated with and analyzed some two-dimensional and three-dimensional random data.
rate research
Read More
Physical spin configurations corresponding to topological excitations expected to be present in the XY limit of a purely quantum spin 1/2 Heisenberg ferromagnet, are probed on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed in terms of coherent spin field components as limiting case of meronic (anti-meronic) configurations. The crucial role of the associated Wess-Zumino term is highlighted in our procedure. It is shown that this term can identify a large class of vortices (anti-vortices). In particular the excitations having odd topological charges form this class and also exihibit a self-similar pattern regarding the internal charge distribution. This manifestation of different behaviour of the odd and the even topological sectors is very prominent in the strongly quantum regime but fades away as we go to higher spins. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices).
Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice . Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations . The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure . The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice . It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices) .
A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the Information-Processing Second Law (IPSL): the physical entropy of the universe can decrease if compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate information-carrying degrees of freedom. In particular, the asymptotic-rate IPSL precisely delineates the thermodynamic functioning of autonomous Maxwellian demons and information engines. How do these systems begin to function as engines, Landauer erasers, and error correctors? Here, we identify a minimal, inescapable transient dissipation engendered by physical information processing not captured by asymptotic rates, but critical to adaptive thermodynamic processes such as found in biological systems. A component of transient dissipation, we also identify an implementation-dependent cost that varies from one physical substrate to another for the same information processing task. Applying these results to producing structured patterns from a structureless information reservoir, we show that retrodictive generators achieve the minimal costs. The results establish the thermodynamic toll imposed by a physical systems structure as it comes to optimally transduce information.
We consider the smallest eigenvalues of perturbed Hermitian operators with zero modes, either topological or system specific. To leading order for small generic perturbation we show that the corresponding eigenvalues broaden to a Gaussian random matrix ensemble of size $ utimes u$, where $ u$ is the number of zero modes. This observation unifies and extends a number of results within chiral random matrix theory and effective field theory and clarifies under which conditions they apply. The scaling of the former zero modes with the volume differs from the eigenvalues in the bulk, which we propose as an indicator to identify them in experiments. These results hold for all ten symmetric spaces in the Altland-Zirnbauer classification and build on two facts. Firstly, the broadened zero modes decouple from the bulk eigenvalues and secondly, the mixing from eigenstates of the perturbation form a Central Limit Theorem argument for matrices.
The standard map, paradigmatic conservative system in the $(x,p)$ phase space, has been recently shown to exhibit interesting statistical behaviors directly related to the value of the standard map parameter $K$. A detailed numerical description is achieved in the present paper. More precisely, for large values of $K$, the Lyapunov exponents are neatly positive over virtually the entire phase space, and, consistently with Boltzmann-Gibbs (BG) statistics, we verify $q_{text{ent}}=q_{text{sen}}=q_{text{stat}}=q_{text{rel}}=1$, where $q_{text{ent}}$ is the $q$-index for which the nonadditive entropy $S_q equiv k frac{1-sum_{i=1}^W p_i^q}{q-1}$ (with $S_1=S_{BG} equiv -ksum_{i=1}^W p_i ln p_i$) grows linearly with time before achieving its $W$-dependent saturation value; $q_{text{sen}}$ characterizes the time increase of the sensitivity $xi$ to the initial conditions, i.e., $xi sim e_{q_{text{sen}}}^{lambda_{q_{text{sen}}} ,t};(lambda_{q_{text{sen}}}>0)$, where $e_q^z equiv[1+(1-q)z]^{1/(1-q)}$; $q_{text{stat}}$ is the index associated with the $q_{text{stat}}$-Gaussian distribution of the time average of successive iterations of the $x$-coordinate; finally, $q_{text{rel}}$ characterizes the $q_{text{rel}}$-exponential relaxation with time of the entropy $S_{q_{text{ent}}}$ towards its saturation value. In remarkable contrast, for small values of $K$, the Lyapunov exponents are virtually zero over the entire phase space, and, consistently with $q$-statistics, we verify $q_{text{ent}}=q_{text{sen}}=0$, $q_{text{stat}} simeq 1.935$, and $q_{text{rel}} simeq1.4$. The situation corresponding to intermediate values of $K$, where both stable orbits and a chaotic sea are present, is discussed as well. The present results transparently illustrate when BG or $q$-statistical behavior are observed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
