TY - JOUR

T1 - The confinement of an annealed branched polymer by a potential well

AU - Grosberg, Alexander Y.

AU - Kelly, Joshua

AU - Bruinsma, Robijn

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

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U2 - 10.1063/1.4974189

DO - 10.1063/1.4974189

M3 - Article

AN - SCOPUS:85012308652

VL - 43

SP - 101

EP - 109

JO - Low Temperature Physics

JF - Low Temperature Physics

SN - 1063-777X

IS - 1

ER -