Phase transitions of wave packet dynamics in disordered non-Hermitian systems

Transport in Hermitian systems is a property of single frequencies due to the conservation of energy. Starting from the works of Hatano and Nelson, phase transitions in disordered non-Hermitian systems are studied using a single-frequency framework. However, energy is not conserved in non-Hermitian systems, and therefore wave packet dynamics in these systems are not described by single energies. In disordered non-Hermitian systems, wave packets with arbitrary initial conditions will converge to the maximally amplified waveform. This waveform can depend discontinuously on the system parameters, and therefore can undergo transitions directly between two distinct propagating phases. Metal-insulator transitions also exist in these systems, but have a different behavior from single-frequency metal-insulator transitions.