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We consider the Bouchaud trap model on the integers in the case that the trapdistribution has a slowly varying tail at infinity. We prove that the modeleventually localises on exactly two sites with overwhelming probability. Thisis a stronger form of localisation than has previously been established in theliterature for the Bouchaud trap model on the integers in the case of regularlyvarying traps. Underlying this result is the fact that the sum of a sequence ofi.i.d. random variables with a slowly varying tail is asymptotically dominatedby the maximal term.

Two-site localisation in the Bouchaud trap model with slowly varying traps