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Wave packet dynamics in one-dimensional linear and nonlinear generalized Fibonacci lattices
Zhenjun Zhang1, Peiqing Tong, Jiangbin Gong
1Department of Physics, Nanjing Normal University, Nanjing, Jiangsu 210046, People's Republic of China.
Summary
Wave packet spreading in generalized Fibonacci lattices was numerically studied. Results show distinct spreading behaviors in linear and nonlinear lattices, offering insights for cold atom experiments in quasiperiodic optical lattices.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Nonlinear dynamics
Background:
- Generalized Fibonacci (GF) lattices are quasiperiodic structures with unique spectral and transport properties.
- Wave packet spreading dynamics are crucial for understanding transport phenomena in disordered and quasiperiodic systems.
- The Pisot-Vijayaraghavan property influences the localization and delocalization of states in such lattices.
Purpose of the Study:
- To numerically investigate the spreading dynamics of localized wave packets in one-dimensional linear and nonlinear GF lattices.
- To classify GF lattices based on the Pisot-Vijayaraghavan property and analyze their impact on wave packet spreading.
- To explore the influence of nonlinear effects and on-site potentials on wave packet dynamics.
Main Methods:
- Numerical simulations were employed to study wave packet evolution.
- Analysis focused on the time evolution of the second moment and participation number of the wave packet.
- Two classes of GF lattices were considered, distinguished by the Pisot-Vijayaraghavan property.
Main Results:
- In linear GF lattices, wave packet spreading depends on the lattice class and potential strength, exhibiting ballistic diffusion or stairlike growth.
- Nonlinear GF lattices show modified spreading: the second moment may grow while the participation number does not, especially in the first class.
- Strong on-site potentials in nonlinear GF lattices of the second class lead to self-trapping, inhibiting wave packet spreading.
Conclusions:
- The Pisot-Vijayaraghavan property critically dictates wave packet spreading in both linear and nonlinear GF lattices.
- Nonlinear effects can significantly alter spreading dynamics, leading to phenomena like partial delocalization or self-trapping.
- Findings provide guidance for experiments involving cold atoms in quasiperiodic optical lattices, relevant for quantum simulation and transport studies.
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