Berlin 2024 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Poster: Statistical Physics

DY 31.1: Poster

Wednesday, March 20, 2024, 15:00–18:00, Poster C

Localisation in one-dimensional random tight-binding models — •Luca Schäfer and Barbara Drossel — Technische Universität Darmstadt, Darmstadt, Germany

We compare the localisation characteristics of three different one-dimensional disordered quantum systems described by the tight-binding model, using exact and partial diagonalisation of the Hamiltonian to obtain the eigenvalue spectrum and the associated participation ratios (P), and the transfer-matrix method to determine the localisation length (ξ). The degree of localisation is evaluated based on the scaling of P and ξ with the system size. The first model is the well-known Anderson model (AM) featuring on-site disorder, for which all states are localised. The second model has no on-site disorder, but random couplings (RCM). In this scenario, solely the state with E=0 is extended, and ξ increases proportional to the negative logarithm of E. We show that the eigenstate in the band centre can be mapped on a random walk, thus explaining its properties. The third model can be represented as a harmonic chain with random coupling (HCM), where the on-site potential is correlated with the coupling strengths such that the model has a conserved quantity. This choice is motivated by applications in ecological and diffusion networks. We find, in agreement with existing analytical calculations, that the number of extended states for E≈ 0 grows proportional to the square root of the system size, and we related this power law to the power laws that characterise the statistics of P and E and ξ and the relation between them.

Keywords: Anderson localisation; random media; disorder; harmonic chain