Superfluidity versus disorder in the discrete nonlinear Schrödinger equation

Area of Science:

• Nonlinear dynamics
• Quantum physics
• Condensed matter physics

Background:

• The discrete nonlinear Schrödinger equation (DNLS) models wave propagation in various physical systems.
• Annular geometries and on-site defects introduce complexity to wave dynamics.
• Understanding wave behavior in disordered systems is crucial for applications.

Purpose of the Study:

• To investigate the dynamics of a traveling plane wave in a discrete nonlinear Schrödinger equation with on-site defects in an annular geometry.
• To identify and characterize different dynamical regimes, including a superfluid state.
• To establish a superfluidity criterion for this system and compare it to existing theories.

Main Methods:

• Mapping the DNLS dynamics to an effective nonrigid pendulum Hamiltonian.
• Analyzing the behavior of plane waves under varying nonlinearity and defect configurations.
• Comparing the observed superfluidity criterion with Landau's criteria for translationally invariant systems.

Main Results:

• Identified distinct dynamical regimes: complete reflection, refocusing, solitonic structures, and a superfluid state.
• Discovered a critical nonlinearity above which a plane wave propagates coherently through defects.
• Established a novel superfluidity criterion for the DNLS system.

Conclusions:

• The discrete nonlinear Schrödinger equation in annular geometry with defects exhibits complex dynamics, including a unique superfluid state.
• The identified superfluidity criterion offers new insights into wave coherence in disordered nonlinear systems.
• Findings have implications for Bose-Einstein condensates in optical potentials and optical fiber arrays.