Algebraic statistics of Poincare recurrences in DNA molecule
Résumé
Statistics of Poincar ́e recurrences is studied for the base-pair breathing dynamics of an all-atom
DNA molecule in realistic aqueous environment with thousands of degrees of freedom. It is found
that at least over five decades in time the decay of recurrences is described by an algebraic law
with the Poincar ́e exponent close to β = 1.2. This value is directly related to the correlation decay
exponent ν = β − 1, which is close to ν ≈ 0.15 observed in the time resolved Stokes shift exper-
iments. By applying the virial theorem we analyse the chaotic dynamics in polynomial potentials
and demonstrate analytically that exponent β = 1.2 is obtained assuming the dominance of dipole-
dipole interactions in the relevant DNA dynamics. Molecular dynamics simulations also reveal the
presence of strong low frequency noise with the exponent η = 1.6. We trace parallels with the
chaotic dynamics of symplectic maps with a few degrees of freedom characterized by the Poincar ́e
exponent β ∼ 1.5.