We study periodic, deterministic aperiodic (Thue-Morse, Fibonacci, Period Doubling, Rudin-Shapiro , Cantor, generalized Cantor , Kolakoski) and random binary sequences within the framework of the Tight-Binding wire model. We use B-DNA as our prototype system , where all sequences have purines  on the same strand and start with guanine.We investigate the interplay between structure, magnitude of parameters , and spectral, localization and charge transport properties. To this end, we comparatively study relevant quantities such as autocorrelation functions, integrated density of states, Lyapunov exponents, transmission coefficients and current-voltage curves , using the Landauer-Buttiker formalism. Our results reveal that there is a correspondence between the degree of structural complexity and the presence of correlations in the sequences and the aforementioned properties. Apart from periodic segments , which display enhanced transport properties , there are several cases of deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random segments represent the less efficient category . Finally, we discuss factors that influence the results and examine homogeneous sequences, for which transport efficiency is maximal .
We study periodic, quasi-periodic (Thue-Morse, Fibonacci, Period Doubling, Rudin-Shapiro ), fractal ( Cantor, generalized Cantor ), Kolakoski and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We use B-DNA as our prototype system . All sequences have purines , guanine (G) or adenine (A) on the same strand , i.e., our prototype binary alphabet is (G,A). Our aim is to examine the influence of sequence intricacy and magnitude of parameters on energy structure, localization and charge transport . We study quantities such as autocorrelation function, eigenspectra, density of states, Lyapunov exponents, transmission coefficients and current-voltage curves . We show that the degree of sequence intricacy and the presence of correlations decisively affect the aforementioned physical properties. Periodic segments have enhanced transport properties . Specifically, in homogeneous sequences transport efficiency is maximum. There are several deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random sequences is the less efficient category .
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