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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Quantum Levy Flights and Multifractality of Dipolar Excitations in a Random System
X Deng1, B L Altshuler2,3, G V Shlyapnikov3,4,5,6,7
1Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany.
Physical Review Letters
|July 23, 2016
Summary
Dipolar excitations exhibit Levy flight propagation in disordered lattices. While localized in 1D/2D, 3D states are extended but can transition from ergodic to nonergodic, especially at low lattice filling.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Disordered systems
Background:
- Dipolar excitations propagate via dipole-induced exchange in molecular lattices.
- Randomly spaced immobile molecules lead to complex excitation dynamics.
- Long-range hops, or Levy flights, characterize propagation.
Purpose of the Study:
- Analyze eigenenergy spectra and multifractal wave function structure.
- Investigate excitation behavior in 1D, 2D, and 3D lattices.
- Determine conditions for ergodic and nonergodic states.
Main Methods:
- Analysis of eigenenergy spectra.
- Multifractal analysis of wave functions.
- Theoretical modeling of excitation propagation in disordered lattices.
Main Results:
- In 1D and 2D, all states are localized; 2D systems show large localization lengths, suggesting a crossover.
- In 3D, eigenstates are extended but can be ergodic or nonergodic.
- Reduced lattice filling induces a transition from ergodic to nonergodic states, with nonergodic behavior dominant at low filling.
Conclusions:
- Lattice dimensionality and filling critically influence excitation localization and dynamics.
- Understanding these transitions is key for designing materials with specific transport properties.
- The study reveals complex behavior in disordered systems, bridging localization and delocalization phenomena.
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