Non-Hermitian delocalization from Hermitian Hamiltonians

Area of Science:

• Physics
• Mathematical Physics
• Condensed Matter Physics

Background:

• Non-Hermitian delocalization is a phenomenon observed in diverse fields, including bacterial population dynamics (e.g., Bacillus subtilis), vortex pinning in superconductors, and hydrodynamical stability.
• Previous studies often involve complex numerical methods, such as calculating left and right eigenfunctions of non-Hermitian Hamiltonians or using supermatrices with complex frequencies.

Purpose of the Study:

• To present a novel method for obtaining non-Hermitian delocalization using Galilean transformations.
• To simplify the study of non-Hermitian delocalization by avoiding complex numerical instabilities and computational overhead.

Main Methods:

• Application of Galilean transformations to derive non-Hermitian phenomena from Hermitian systems.
• Solving the time-dependent Schrödinger equation with a Hermitian Hamiltonian.

Main Results:

• Successfully reproduced non-Hermitian delocalization using a Hermitian Hamiltonian via Galilean transformations.
• Circumvented the need for calculating non-Hermitian eigenfunctions or employing large supermatrices.
• Eliminated the use of complex frequencies as variational parameters, simplifying eigenvalue determination.

Conclusions:

• Galilean transformations offer a more computationally stable and efficient method for studying non-Hermitian delocalization.
• This approach provides a new perspective on the relationship between Hermitian and non-Hermitian systems.
• The findings have potential implications for understanding phenomena in condensed matter physics, hydrodynamics, and population dynamics.