The confinement of an annealed branched polymer by a potential well

• Published in: Физика низких температур
• Date: 2017
• Main Authors: Grosberg, A.Y., Kelly, Joshua, Bruinsma, Robijn
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2017
• Subjects: К 100-летию со дня рождения И.М. Лифшица
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/129359
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The confinement of an annealed branched polymer by a potential well / Alexander Y. Grosberg, Joshua Kelly, Robijn Bruinsma // Физика низких температур. — 2017. — Т. 43, № 1. — С. 122-131. — Бібліогр.: 20 назв. — англ.

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. 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/R⁴ 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.