Narrow Results

We describe the primitive ideal space of the C*-algebra of a row-finite k-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute the primitive ideal space of two examples. In order to do this we prove some new results on aperiodicity. Our computations indicate that when every ideal is gauge invariant, the primitive ideal space only depends on the 1-skeleton of the k-graph in question.

We investigated the influence of the distribution of bimodal bonds on phase transition in 8-state Potts model in two dimensions. We show that there is a finite size dependent threshold value of the introduced quenched randomness in the bond distribution for rounding the first-order phase transition.

The effect of aperiodicity on the charge transfer process through DNA molecules is investigated using a tight-binding model. Single-stranded aperiodic Fibonacci polyGC and polyAT sequences along with aperiodic Rudin–Shapiro poly(GCAT) sequences are used in the study. Based on the tight-binding model, molecular orbital calculations of the DNA chains are performed and ionization potentials compared, as this might be relevant to understanding the charge transfer process. Charges migrate through the sequences in a multistep hopping process. Results for current conduction through aperiodic sequences are compared with those for the corresponding periodic sequences. We find that dinucleotide aperiodic Fibonacci sequences decrease the current while tetranucleotide aperiodic Rudin–Shapiro sequences increase the current when compared with the corresponding periodic sequences. The conductance in all cases decays exponentially as the sequence length increases.