Study of Different Random Walk Simulations of Boson Kinetics in 1-D Lattices

Robert M. Mazo, Christian Van den Broeck

The spectrum of a spectroscopically active particle which makes a random walk on a finite one-dimensional lattice, upon each of whose n sites the particle radiates or absorbs radiation with a different frequency, is discussed. The correlation function of the radiating dipole is found to decay asymptotically as a Gaussian times ${t}^{\mathrm{\ensuremath{-}}(n\mathrm{\ensuremath{-}}1)/2}$ in the case when the site frequencies are independent Gaussian random variables. Numerical simulations of the random walk confirm the asymptotic result. The difference between these results for a finite system and previous results for an infinite system are discussed.

Pier Paolo Delsanto, G. Kaniadakis, Marco Scalerandi

N. Fjeldso, John Midtdal, F. Ravndal

When the quantum planar rotor is put on a lattice its dynamics can be approximated by random walks on a circle. This allows for fast and accurate Monte Carlo simulations to determine the topological charge of different configurations of the system and thereby the theta dependence of the lowest energy levels.

V. Apaja, Olav F. Syljuåsen

Pier Paolo Delsanto, G. Kaniadakis, M. And Scalerandi

Stefano Longhi

Random walks (RW) behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the photon can be destroyed and the walk terminates. While for a classical random walk, the photon is unavoidably destroyed by the traps. For a quantum walk, the photon can remain alive, and the walk continues forever. Such an intriguing behavior is illustrated by considering photonic random walks in synthetic mesh lattices with controllable decoherence, which enables the switch from quantum to classical random walks.