New theory of diffusive and coherent nature of optical wave via a   quantum walk
  We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave mechanics. Using the recent result of a localization phenomenon in a one-dimensional quantum walk (Konno, Quantum Inf. Proc. (2010) 9, 405-418), we numerically show that the randomized localized matrices suppress the coherence and give diffusive nature. 
Yusuke Ide, Norio Konno, Shigeki Matsutani, Hideo Mitsuhashi
quant-ph