Phase extraction in disordered isospectral shapes.

Area of Science:

• Quantum mechanics
• Condensed matter physics

Background:

• The phase of electronic wave functions is not directly measurable.
• Isospectral shapes offer a novel experimental approach to access wave function phase information.
• The transplantation property relates eigenfunctions of isospectral pairs.

Purpose of the Study:

• To numerically simulate and analyze the phase extraction procedure in the presence of disorder.
• To investigate the robustness of the phase extraction method against Anderson disorder and edge roughness.
• To explore the behavior of the extracted phase at higher disorder amplitudes.

Main Methods:

• Numerical simulation of phase extraction from isospectral shapes.
• Introduction of Anderson disorder and edge roughness.
• Definition of extracted phase as that minimizing wave function misfit.
• Adaptation of transplantation to discrete models and proof of preserved isospectrality.

Main Results:

• The phase extraction method demonstrates robustness against moderate disorder levels (up to ~5% wave function misfit).
• The extracted phase closely matches the disorder-free phase within this range.
• At higher disorder amplitudes, the extracted phase exhibits a puzzle structure, losing correlation with the disorder-free phase.
• Discretization is shown to preserve isospectrality and allow adaptation of the transplantation method.

Conclusions:

• The phase extraction method using isospectral shapes is resilient to certain levels of disorder.
• Disordered systems can still yield meaningful phase information, albeit with limitations.
• Discrete models are suitable for analyzing disorder effects in this context.