Detailed analysis of the quantum relaxation features in the cell microtubules: Markovian and non-Markovian dynamics

Abstract

In the present work, the quantum relaxation processes in the microtubule dipole system are studied. The study is conducted in the Markovian and non-Markovian models. The research is based on the numerical simulation of the nonlinear system of differential equations. The detailed derivation of the non-Markovian analytical expressions has been made. The nonlinear character of the quantum relaxation processes has been established. It is shown that the quantum dynamics of the dipole moments has a different - ambivalent nature and depends on the critical values of the environmental factors such as: microtubule length, microtubule anisotropy, temperature. It is established that the dynamics in the non-Markovian model differs markedly from the Markovian one at a small temperature and at small relaxation time values.