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Physics & Astronomy International Journal

A simple theoretical analysis of quantum biomathematical model of DNA and heisenberg spin chain model

Subhamoy Singha Roy

Published Feb 5, 2019• 0 citations
Publisher

Abstract

We have considered here that the conformational properties of a DNA molecule can be mapped onto a Heisenberg spin system when spins are located on the axis forming an antiferromagnatic chain.This helps us to study the topological and elastic properties of a DNA molecule in terms of SU(2) gauge fields.The entanglement entropy of the spin system in a supercoil has been determined and it is pointed out that this effectively corresponds to the thermodynamic entropy.The model reproduces salient features of the Rod-Like-Chain model avoiding the "RLC model crisis".

DOI
10.15406/paij.2019.03.00155

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We have considered here that the conformational properties of a DNA molecule can be mapped onto a Heisenberg spin system when spins are located on the axis forming an antiferromagnatic chain.This helps us to study the topological and elastic properties of a DNA molecule in terms of SU(2) gauge fields.The entanglement entropy of the spin system in a supercoil has been determined and it is pointed out that this effectively corresponds to the thermodynamic entropy.The model reproduces salient features of the Rod-Like-Chain model avoiding the "RLC model crisis".
In this paper we have considered here that the DNA molecule can be treated as a spin system when spins are located on the axis forming an antiferromagnetic chain.When spins are described in the Lie algebra of ( ) 2 SU the linking number can be ascertained from the Chern-Simons topology associated with the spin system.It is shown that bend and twist are not two separate entities but one depends on the other, also other hand entanglement of two DNA molecule inserting spin-echo to one of them marks the transform of Berry phase that can be exact as a calculate of entanglement.This formalism helps us to depict the thermodynamic entropy as entanglement entropy and the entanglement of spin can be used as a resource for genetic information and the transcription of genetic information can be considered in the framework of quantum information theory.
It is observed that when the conformational properties of DNA molecule are mapped onto an antiferromagnetic spin system we can realize the specific properties of the rod-like-chain (RLC) model where the analytically continued partition function corresponds to the symmetric top Hamiltonian.The relevant path integral represents a charge particle in the field of a non-quantized monopole which suggests that angular momentum is not quantized.However in a spin chain the nonquantized monopole charge appears in the renormalization group flow and corresponds to the Barry phase required by a spin ½ state in an entangled spin system.Thus avoids the RLC model crisis.
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.
One approach to imagine spins on the axis generating an antiferomagnatic chain is described as simulating a DNA molecule as a Heisenberg spin system. In a DNA molecule, the entanglement entropy of the spin system is shown to be in good agreement with the thermodynamic entropy. At times when the impact of temperature is included during the time of quench, It is shown that denaturation corresponds to a quantum phase change triggered by a quench. The critical point is attained and When the entanglement entropy is eliminated, it equates to a critical torsonal energy. DNA loops now appear as solitonic (skyrmionic) excitations upon base pair opening.
When a DNA molecules conformational characteristics are charted adjacent to a Heisenberg-spin-system, the denaturation shift be able to be expressed in stipulations of a QFT (quantum-phase-transition) brought on through a quench, in which the external field is torsion and the temperature effect is integrated into the quench time. When the spin system's entanglement entropy disappears, the denaturation transition takes place. The energy of torsion includes temperature, stress, and torque, the latter of which is correlated with the twist angle. A DNA molecule put on the Heisenberg spin chain experiences torsion as the outer field. When the EE (entanglement entropy) disappears, the transition to denaturation takes place. The entanglement entropy steadily drops as the proportion of unlock stand pairs gradually increases, the two strands split until the entropy disappears, since the dangerous area corresponding to a 2-boundary actions. The melting profiles of specific DNA molecules have been examined, and the findings show great agreement with biotechnology.
The conformational properties of a DNA molecule when mapped onto a Heisenberg spin system denaturation transition can be formulated in terms of quantum phase transition induced by a quench where the temperature effect is incorporated in the quench time. Here torsion takes on the role of the external field. The denaturation transition occurs when the entanglement entropy of the spin system vanishes. As the critical region corresponds to a two-limit behaviour the entanglement entropy gradually decreases with the gradual increase in the fraction of open base pairs and when the entropy vanishes the two strands are separated. The sequence heterogeneity interplays with the entropy effects and we have the onset of denaturation bubbles. We have studied the melting profiles for different sequence-specific DNA molecules and the results are found to be in excellent agreement with experiment.