Energy confinement in imperfect periodic systems

The energy fraction Delta(avg) is developed as a measure of energy confinem ent in periodic systems of finite extent. Based on the response of a system to uniform broadband forcing, Delta(avg) is experimentally measurable but can be expensive to calculate. It is shown that a norm f the eigenvector ma trix Delta'(avg) is a good approximation for Delta(avg) when damping is lig ht. Delta(avg) is almost three orders of magnitude faster to calculate than Delta(avg) which makes detailed Monte Carlo studies of imperfections pract ical. One-dimensional linear-chain and cyclic systems of a range of sizes a re studied. In line with previous research, it is found that a periodic sys tem's propensity to confine energy increases with system size. It is also f ound that cyclic systems are less likely to suffer energy confinement than (otherwise equivalent) linear-chain systems. (C) 2000 Academic Press.