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We have study here the topological properties as w ell as the elastic and thermodynamical properties of DNA molecules from an analysis of an antiferromagnetic spin chain system. The topological property such as the linking number can be derived from the Chem-Simons topology associated with a quantum spin and two indistinguishable fermions are made relatively diverse earlier entanglement, through giving one qubit spin to one of them done the circularly split attractive field that plays the character of shifting the path of quantization axis. Therefore the reverberation arise and the spin must development the transformation of entangled state from symmetric to antisymmetric state finished the closed path. This spin of the attractive field efficiently corresponds near the variation in the path of the flux line. It is exposed that the entanglement of two DNA molecule place spin-echo to one of them marks the transform of Berry phase that can be exact as a analyse of entanglement photon echo technique. If we apply this technique to one spinor previously entanglement by other then the Berry phase is surrounded in the entangled state, consequential the exclusion of dynamical time. This is found to be in good agreement with the thermodynamic entropy as entanglement entropy, charge of encircle a inelastic polymer string bounded by a fine tube.

Surface <i>Free Energy</i> of <i>Photon echo on</i> DNA Molecules: Theoretical Study