Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

Non-Hermitian topological edge states have many intriguing properties, but so far mainly been discussed in terms of bulk-boundary correspondence. Here we propose to use a bulk property diffusion coefficients for probing the and exploring their dynamics. The coefficient is found show unique features with phase transitions driven by paritytime( PT)-symmetric non-Hermitian discrete-time quantum walks as well Hermitian ones, despite artificial boundaries are not constructed inhomogeneous walk. For system, turning point abrupt change appears when system approaching transition, while it remains stable trivial state. except feature associated PT-symmetric-broken demonstrates an peak structure. In addition, Shannon entropy walk exhibit direct correlation coefficient. numerical results presented here may open up new avenue studying state systems.