Applied Science and Innovative Research ISSN 2474-4972 (Print) ISSN 2474-4980 (Online) Vol. 6, No. 4, 2022 www.scholink.org/ojs/index.php/asir 137 Original Paper Exploring the Effect of DNA Noise and Current on the Berry Phase Effects Subhamoy Singha Roy1 1 Department of Physics, JIS College of Engineering, West Bengal University of Technology, Kalyani, Nadia -741235, India Received: November 9, 2022 Accepted: November 15, 2022 Online Published: November 27, 2022 doi:10.22158/asir.v6n4p137 URL: http://doi.org/10.22158/asir.v6n4p137 Abstract We have studied here 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 in order. This implies that the transcription of genetic in order can be considered in the structure of quantum in sequence hypothesis. Keywords antiferromagnetic spin, entanglement entropy, DNA molecule, DNA noise, Berry phase. 1. Introduction We consider that as two polynucleotide chains are coiled about the same axis with a specific helical sense in a DNA molecule, this can be viewed as if a spin with a specific orientation is inserted on the axis of the coil such that two adjacent coils have opposite orientations of the spin. In fact with each turn two strands move in the opposite side of the axis and so the spin orientation assigned for the two adjacent coils should be opposite to each other. Thus a DNA supercoil may be viewed as a long chain of an antiferromagnetic spin system when the spin is considered to be located on the axis of the supercoil. A unit vector depicting the tangent rt s   where )(sr  is a space curve parameterized by the arc length s can be associated with a spin vector when the spin is located at the spatial point x on the axis. A spin vector in the Lie algebra of  2SU representation can be constructed with bosonic or fermionic oscillators. We write the spin vector )(xS as    xxxS   †)(  (1) www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 6, No. 4, 2022 138 Published by SCHOLINK INC. where   † is the fermionic oscillator function and   is the vector of Pauli matrices. A unit vector n  is constructed as          2 1* 2 * 1     n (2) with   2 1 2 cos   i e (3.a)   2 2 2 sin   i e   (3.b) We now will study the appearance of Berry phase in the entanglement of two identical spin 2/1 quantized particles. The antisymmetric Bell State of two spin 2/1 DNA molecules is 112 )( 2 1 cos    downup  (3.c) By the difference of Berry phase factor. The most general antisymmetric Bell state for two particles A and B situated at the points x and y becomes  )()()()(()(2 ttttt  (3.d) Where  and  are two complex coefficients, With the idea of one DNA molecule rotation of one fermion for a time interval  the spinor comes to its orginal state acquiring only Berry phase and loosing the dynamical phase., We have the new form of the entangle state as   )()()()(()( 2 2 ttettt upi  (3.e) As we consider   the Berry phase is removed along with dynamical phase in the ’spin-echo’ method. This helps us to write        xxS †23)(  (4) We can now construct a unit vector n with 3,2,1,0 in 3+1 dimensions incorporating the unit vector n  given by eqn. (2)             2 1* 2 * 121    n (5) with I0  , I being the identity matrix and   are Pauli matrices. We now construct the topological current   dcbaabcd nnnnJ    2121 (6) www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 6, No. 4, 2022 139 Published by SCHOLINK INC. where (a, b, c, d) correspond to (0, 1, 2, 3) and   ,,, correspond to space-time indices. The current J can be written in the form [1]   ))()((241 1112 ggggggTrJ     (7) with   .n I0 ing  which belongs to the group  2SU . If we now demand that in Euclidean 4- dimensional space-time the field strength F of a gauge potential A vanishes at all points on the boundary 3S of a certain volume 4V inside which 0F the gauge potential tends to a pure gauge towards the boundary and we write ggA   1 (8) with  2SUg . We can now write the topological current given by (7) as [2]         AAAFATrJ 32161 2  (9) with A given by eqn.(8). It is noted that as the spin vector is constructed from the unit vector n  given by (2) which is incorporated in the current J as is evident from eqn. (6), we can associate spin with this current J . In fact we can consider the topological Lagrangian in terms of the  2SU gauge fields in affine spece     FFTrL 41 (10.a) Now the gauge connection associated with the Lagrangian in this equation )(2/(iLup eff   )Cos (10.b) due to any change in  , , resulting a gauge transformation, this equation giving rise to Berry phase. Now the necessary geometrical phase of the only quantized spinor      )cos1()cos)(2/1()(  dddAidtLi upup eff up (10.c) This gives rise to the topological current [3]       ffaJ    (11) where we have taken the  2SU gauge field A and corresponding field strength F as    .aA and    .fF (12)   being vector of Pauli matrices. From this it appears that the spin vector )(xS  can be depicted as www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 6, No. 4, 2022 140 Published by SCHOLINK INC. the topological current  J given by eqn.(11). In terms of this current a spin system on a lattice can be viewed as if currents are located on the vertices when gauge fields lie on links [10]. This helps us to consider the spin system associated with a DNA supercoil in terms of the Chern-Simons topology as will be discussed in the next section. We find the effect of noise in the Berry phase of quantized spinor and in its entangled state both in the presence and the absence of spin –echo method, on the influence of classical fluctuation of field on Berry phase of spin ½ particle [4,5]. We define noise by a shift like residual dipolar couplings crucially (RDCs). If we consider that with the lapse of time, the parameter  suffer a deviation   due to any change in  , , resulting a gauge transformation.        )( )()( Z ZZ (13) Here )(Z is the gauge connection associated with the Lagrangian in this eqn.10.b, this equation giving rise to Berry phase. This fluctuation of gauge relations by the parameter  , is the extremely cause of transfer in magnetic flux line equivalent chiral equilibrium contravention. Now the necessary geometrical phase of the only quantized spinor eqn. 10.c, This shows that for quantized spinorthe Berry Phase is a solid angle subtended about the quantization axis. For 0 the minimum value of up is 0 and   maximum. Spin up case we have )cos1)(2/1()(  upZ (14) This leads to have the noise dependent Berry Connection of the quantized spinor )sincos1)(2/1()(  upZ (15) Now the result a modification of Berry phase )sincos1(  up (16) And similar for down spinor )sincos1(  down (17) Where we consider up , down as the noise induced Berry phase for the spin up and spin down quantized practices in that order [5-7]. Now the entangled state of two identical spinor, as we find in eqn.3.c, that the evolution of the state at a exacting instant depends on the distinction of up and down which implies boost of noise by twice. The effect of noise in the entangled state formed after ’spin-echo’ will be less as realized from eqn. 3.e. On the conclusion, we similar to observation that here the noise is accountable for the fluctuation of quantization that can be practical for the entanglement of Quantum Hall particles in the non-plateau and plateau area. 2. Discussion We have formulated bending (curvature) and twisting (torsion) in terms of these gauge fields. A significant result of this formalism is that bending and twisting are not independent entities. In fact www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 6, No. 4, 2022 141 Published by SCHOLINK INC. bending influences the propagation of twisting strain along the DNA which has been supported by experiments. Also the dynamical phase of DNA molecule can be separate in the spin-echo system. During this process the addition of Berry phase in the entangled state is accountable for the calculate of entanglement. Variation in DNA molecule helicity is considered as noise that change the fixed significance of Berry phase [8-9]. The consequence of noise doubles as two pure identical spinor entangle. We like to study further this effect of noise, decoherence and entanglement in association with quantization feature of Berry phase in previous quantum aspect DNA molecule development. References [1] A.I.Abanov and P.B.Wiegmann, Nucl.Phys.B 570(2000) 685 [2] P.Bandyopadhyay, Proc.Roy.Soc(Londan) A.466(2010) 2917. [3] M.Carmeli and S.Malin, Ann.Phys. 103(1977) 208. [4] G.P Berman, G.D Doolen, R. Mainnier and V.I Tsifrinovich; Introduction to Quantum Computers, World Scientific, 1998. [5] S.Singha Roy: Theoretical Physics, 2, Number 3, 141(2017). [6] S.Singha Roy and P.Bandyopadhyay,: Phys. Lett. A 382, 1973 (2018). [7] S.S. Roy and P.Bandyopadhyay, Phys. Lett. A 337, 2884 (2013). [8] B.Basu, P.Bandyopadhyay and P. Majumdar, Phys. Rev.A 86, 022303 (2012). [9] S.S.Roy and P. Bondyopadhyay, Euro. Phys. Lett. 109(4), 48002 (2015). [10] G.Goswami and P.Bandyopadhyay, J.Math. Phys. 34(1995) 749