Lokalisierungs- und Transportphänomene in ungeordneten exzitonischen (English shop)

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Markus Grimm’s dissertation “Lokalisierungs- und Transportphänomene in ungeordneten exzitonischen Systemen” investigates how structural disorder influences excitation localization and thermal transport in quantum systems. The research focuses on excitonic models used to describe transport properties in amorphous materials and quasiperiodic structures. A central motivation is the unusual temperature dependence of thermal conductivity in nonmetallic amorphous solids, particularly at low temperatures. To investigate these phenomena, the study develops a theoretical formalism that describes thermal transport through the temporal evolution of spatially localized excitations without requiring explicit calculation of all eigenvalues and eigenvectors. The analysis of one-dimensional excitonic systems demonstrates that statistical disorder in onsite and transfer energies causes localization and suppresses ballistic transport. Depending on disorder strength, sub-ballistic and diffusive transport regimes are identified. The investigation is extended to higher-dimensional systems, addressing critical dimensionality and the existence of mobility edges. Quasiperiodic structures are examined using the Fibonacci chain, revealing anomalous transport behavior. Additionally, the single-state diagonalization method provides approximate eigenstates and transport quantities. The dissertation contributes to the theoretical understanding of localization mechanisms and thermal transport in disordered quantum systems.