Dear Surender,

The inverse participation ratio is a quantity that provides a measure of localization for a system with disorder and/or nonlinearity. There are several such systems of interest (e.g. the discrete nonlinear schrodinger equation with disorder) , in which we provide a localized excitation (i.e., we excite a particular lattice site) and then let the system evolve for long time intervals. An important question is weather an initially localized excitation will remain localized or it will be spread out in the long term (there are many works on that and similar issues, e.g. by S. Flach, with extensive numerical simulations).

Anyway, value of the inverse participation number (IPN) at time t, if properly normalized, roughly gives the number of sites on which the excitation occupies at that time. For that reason the IPN is usually monitored in time during such numerical simulations. In a real experiment, perhaps there are other ways to decide about the degree of localization in a given system at some time t.

Best regards,

Nick L.

See e.g., the chapter by S. Flach,

"Nonlinear Lattice Waves in Random Potentials"

Springer International Publishing Switzerland 2015

C. Besse, J.-C. Garreau (eds.),

Nonlinear Optical and Atomic Systems, pp. 1-48

,

Lecture Notes in Mathematics 2146, DOI 10.1007/978-3-319-19015-0_

Thanks Nikos for our kind reply.Even i have seen many people are calculating IPR or say PR also in graphene system also,with applied strain.Or even some people are GIPR or NIPR,as i have seen that when we are looking at PR with sample sites,we used to see that states a e loalized near band center only,which is physically acceptable also,can you please refer me some papers where people have calculated IPR ,with proper explanation.

Warm regards

Surender Pratap