On the statistics of generalized Gaussian structures: collapse and random external fields

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Abstract
We consider the statistics of generalized Gaussian structures (GGS) exposed to a random external field. A GGS comprises N monomers connected to each other by harmonic potentials. When the spectral dimension d, of a GGS exceeds the value of two its radius of gyration R becomes independent of its mass N. The cross-over into this collapse can be treated continuously by cross-linking m precursor chains of length n in the stretched state to an object which we call a polymer bundle. We demonstrate that an external field f applied to each monomer can `unfold` such a collapsed state. In the case where every monomer has an individual, randomly distributed, charge the critical spectral dimension for the collapse is raised to four. R scales like fNalpha with alpha =(4-ds)/(2ds) for ds<4.