A fundamental property of wave propagation is Anderson localization, which affects the transfer of information, energy, mass, and charge in disordered media. This localization can manifest itself via, e.g., the metal-insulator transition. We exactly map the behavior of a quantum particle moving in a potential with correlated disorder to the sub-terahertz wave propagation in either Josephson chains or superconducting multilayers. When the Josephson junction parameters vary randomly, the sub-THz electromagnetic waves cannot propagate through these Josephson structures due to localization. For parameter variations with long-range correlations, we predict sharp transitions from transparent to reflective frequency regions for Josephson plasma waves. With appropriate choices of the correlation function, frequency windows with targeted or designed transparencies for THz or sub-THz electromagnetic waves could be achieved. This could be useful for tailoring the electromagnetic wave spectrum of Josephson arrays within the THz frequency range, which is important for applications in physics, astronomy, chemistry, biology, and medicine.
We analyze the structure of DNA molecules of different organisms by using the additive Markov chain approach. Transforming nucleotide sequences into binary strings, we perform statistical analysis of the corresponding "texts". We develop the theory of N-step additive binary stationary ergodic Markov chains and analyze their differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain by means of the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses two point correlators instead of probability of block occurring, it makes possible to calculate the entropy of subsequences at much longer distances than with the use of the standard methods. We utilize the obtained analytical result for numerical evaluation of the entropy of coarse-grained DNA texts. We believe that the entropy study can be used for biological classification of living species.
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