Subdiffusive Lévy flights in quantum nonlinear Schrödinger lattices with algebraic power nonlinearity

Area of Science:

• Quantum physics
• Condensed matter theory
• Nonlinear dynamics

Background:

• Disordered quantum nonlinear lattices present complex dynamics.
• Understanding wave packet spreading is crucial for quantum transport.

Purpose of the Study:

• To investigate the theoretical dynamics of localized wave packets in disordered quantum nonlinear Schrödinger lattices.
• To elucidate the quantum mechanisms behind anomalous transport phenomena.

Main Methods:

• Theoretical analysis of subquadratic nonlinear lattices.
• Modeling wave packet dynamics using fractional-derivative equations.
• Investigating quasiparticle state formation and propagation.

Main Results:

• A purely quantum mechanism enables unlimited wave packet spreading, absent in classical analogs.
• Wave packet components form coupled states via tunneling, leading to Lévy flights.
• Subdiffusive transport arises from competing jumps and trapping phenomena, described by fractional-derivative equations.

Conclusions:

• The study reveals a unique quantum spreading mechanism in disordered nonlinear lattices.
• Lévy flights and subdiffusive transport are key features driven by quantum effects.
• The nonlinearity exponent dictates asymptotic laws for quantum transport.