ENERGY CONFINEMENT IN IMPERFECT PERIODIC SYSTEMS

The energy fraction Δavgis developed as a measure of energy confinement in periodic systems of finite extent. Based on the response of a system to uniform broadband forcing,Δavg is experimentally measurable but can be expensive to calculate. It is shown that a norm of the eigenvector matrix Δ′avgis a good approximation forΔavg when damping is light. Δ′avgis almost three orders of magnitude faster to calculate than Δavg, which makes detailed Monte Carlo studies of imperfections practical. One-dimensional linear-chain and cyclic systems of a range of sizes are studied. In line with previous research, it is found that a periodic systemʹs propensity to confine energy increases with system size. It is also found that cyclic systems are less likely to suffer energy confinement than (otherwise equivalent) linear-chain systems.