SNAKE-LADDER GHOST IN COUPLED DIMER CHAIN

• Main Author: KINAMULEN, AULIA
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/72986
• Institution: Institut Teknologi Bandung

This final project studies the formulated coupled dimer chain model by H. Susanto (Susanto et al., 2018). In this model, a chain of atoms arranged in pairs to resemble a ladder. Coupled dimer chain arrangement so we will describe the bifurcation diagram to see the phenomenon snake-ladder. To describe the bifurcation diagram, it is necessary to look for stability from the model equation. Then using numerical continuity and uniform initial guess we will get a bifurcation diagram. Another result of this model were obtained by using localized initial guesses both onsite and offsite, so that we can describe a pattern resembling a snake called the snaking phenomenon and tiered line patterns resembling the so-called rungs ladder pattern. Meanwhile, there are conditions that cause symmetry breaking where the bifurcation parameter must be complex. This condition just happens with a certain variable value so that the imaginary part bifurcation parameter has a value non zero. This condition is what is called a ghost, which is a physical phenomenon not shown in the bifurcation diagram but can be explained mathematically. The influence of the variables in the equation of the coupled dimer chain model on the bifurcation parameter is also studied in this final project. Influence these variables can change the width and location of the two snaking patterns that are formed. The relationship is described by the pinning region or the rolled area is a graph of the variables observed against the bifurcation parameter.