Dr. Michael Hilke, a researcher at the University of Oregon, has been exploring the intriguing world of quantum topology and its potential applications in the energy sector. His recent work focuses on the Su-Schrieffer-Heeger (SSH) model, a theoretical framework that describes the behavior of certain quantum systems.
The SSH model is notable for its two distinct topological phases: a trivial phase with no edge states and a non-trivial phase with zero-energy edge states. These phases are characterized by integer invariants that remain robust despite some deformations and types of disorder. The energy dispersion of the SSH model is dominated by a gap around zero energy, which significantly suppresses the transmission of energy through the system. This suppression is quantified by the Lyapunov exponent, a measure that describes how chaotic a system is.
In his research, Dr. Hilke derived an analytical expression for the Lyapunov exponent as a function of energy, considering both diagonal and off-diagonal disorder. This was achieved by establishing a recurrence relation for the local density, which could then be averaged over different disorder configurations. The results showed excellent agreement between the analytical expression and numerical simulations across a wide range of disorder strengths and types.
The practical implications of this research for the energy sector are significant. Understanding the behavior of quantum systems under disorder can help in the development of more robust and efficient energy transmission and storage technologies. For instance, the zero-energy edge states in the non-trivial phase of the SSH model could potentially be harnessed to create highly conductive materials that are less susceptible to disruptions.
Moreover, the real space winding number, a topological invariant, was evaluated as a function of off-diagonal and on-site disorder. This could provide insights into the design of new materials with tailored topological properties for energy applications.
Dr. Hilke’s work was published in the journal Physical Review B, a leading publication in the field of condensed matter physics. This research not only advances our fundamental understanding of quantum topology but also paves the way for innovative solutions in the energy industry.
Source: Physical Review B
This article is based on research available at arXiv.