The confinement of an annealed branched polymer by a potential well

Alexander Y. Grosberg, Joshua Kelly, Robijn Bruinsma
2017 Low temperature physics (Woodbury, N.Y., Print)  
The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The harmonic oscillator potential results from the repulsion of the many branches from the potential walls.
more » ... otential walls. Mathematically, it must be obtained from the solution of the equation of motion of a second, now classical, particle in a non-linear potential that depends self-consistently on the eigenvalue of the quantum oscillator. The resulting confinement energy has a 1/R 4 dependence on the confinement radius R, in agreement with scaling arguments. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids. PACS: 36.20.-r Macromolecules and polymer molecules; 87.15.H-Dynamics of biomolecules.
doi:10.1063/1.4974189 fatcat:mgypcrr7ojg4fazyux6hvmfaze