ON THE STATISTICS OF GENERALIZED GAUSSIAN STRUCTURES - COLLAPSE AND RANDOM EXTERNAL FIELDS

We consider the statistics of generalized Gaussian structures (GGS) ex posed to a random external field. A GGS comprises N monomers connected to each other by harmonic potentials. When the spectral dimension d(s ) of a GGS exceeds the value of two its radius of gyration R becomes i ndependent of its mass N. The cross-over into this collapse can be tre ated continuously by cross-linking m precursor chains of length n in t he stretched state to an object which we call a polymer bundle. We dem onstrate that an external field f applied to each monomer can 'unfold' such a collapsed state. In the case where every monomer has an indivi dual, randomly distributed, charge the critical spectral dimension for the collapse is raised to four. R scales like fN(alpha) with alpha = (4 - d(s))/(2d(s)) for d(s) < 4.