You can read an overview of Georgia's eviction process here. The article addresses situations in which a property appears to be (but may not in fact be) abandoned.

The safe way to go is to serve a proper notice to vacate for non-payment of rent. When they ignore the notice, file a dispossessory affidavit and get a court order permitting the eviction.

If you can find the tenant and convince the tenant to sign and date a document indicating that they've moved out and that everything left behind in the rental property is trash, that's faster -- but the odds of it happening are low.