Quantum Walk and Dressed Photon

A physical model called dressed photons, a composite system of photons and excitation of electrons in the nano-particles, is effectively used in the realm of near-field optics. Many interesting behaviors of dressed photons are known, especially the rapid energy transfer and the accumulation to singular points, e.g., points with strong dissipation. We propose a new modelling of dressed photons based on quantum walks, especially Grover walks on semi-infinite graphs which we call jellyfish graphs, and show a universal accumulation phenomena around the point with strong dissipation.