Transport in deformed centrosymmetric networks.

Area of Science:

• Quantum physics
• Complex systems theory
• Random matrix theory

Background:

• Centrosymmetry is crucial for perfect state transfer (PST) in diverse systems.
• Controlling centrosymmetry in complex networks is challenging.

Purpose of the Study:

• Introduce a novel framework, the deformed centrosymmetric ensemble (DCE), for tunable centrosymmetry.
• Investigate the relationship between centrosymmetry and transport properties in complex networks.

Main Methods:

• Defined DCE using random matrices H(λ) = H_{+} + λH_{-}, with H_{+} centrosymmetric and H_{-} skew-centrosymmetric.
• Introduced quantitative measures P and C for centro- and skew-centrosymmetry.
• Analyzed phase transitions at γP ≡ 1 and γC ≡ -1, and an ergodic transition at γE ≡ 0.
• Constructed random networks from DCE eigenvectors.

Main Results:

• Established precise control over centrosymmetry extent via the parameter γ.
• Demonstrated second-order phase transitions in centrosymmetry and skew-centrosymmetry.
• Showed that maximum transfer fidelity (FT) directly correlates with the degree of centrosymmetry (P).

Conclusions:

• DCE provides a powerful tool to study the impact of centrosymmetry on system dynamics.
• The findings establish a direct link between network structure (centrosymmetry) and transport efficiency.
• This work offers insights into designing complex networks for optimal information transfer.