Chiral Waves and Topological Novel States in Fermi

Subhamoy Singha Roy

doi:doi:10.11648/j.ijmsa.20221102.11

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Chiral Waves and Topological Novel States in Fermi

Subhamoy Singha Roy

Published in International Journal of Materials Science and Applications (Volume 11, Issue 2)

Received: 31 December 2021 Accepted: 17 January 2022 Published: 12 March 2022

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Abstract

This first show was that the spin system, the two nearest neighbour spin in the Entanglement of measuring compliance by the ground conditions are achieved Berry stage to the relation when it is a closed path developed is. It noted the need to share the stage in a kind of geometric phase as explained to go to which any deformations involved is not and it’s the first Stiefel-Whitney class which is to Z_z–cohomology value takes. However for polarized fermions we can relate the exchange phase as the celebrated Berry phase as in this case the Z_z-cohomology becomes irrelevant and is consistent with the first Chern class which involves curvature. This follows from the depiction of a fermion as a scalar particle attached with a magnetic flux line. As in this framework the measure of entanglement of two nearest neighbor spins in a spin system given by concurrence is found to be associated with the Berry phase acquired by a spin state when it evolves in a closed path we can consider that entanglement is a consequence of Fermi statistics. It has been noted that in terms of quantum field theory, the berry phase is related to the perpetual inconsistency caused by the breaking of the perpetual symmetry. As mentioned earlier the quantization procedure of a fermion in the framework of Nelson’s stochastic quantization procedure introduces an internal variable which appears as a direction vector and gives rise to spin degrees of freedom. It's pointing to is that when a spin- 1 state of two spin 1/2 state is a Entangle system as considered to be that, the most widely covered state longitudinal elements with the matching it.

Published in	International Journal of Materials Science and Applications (Volume 11, Issue 2)
DOI	10.11648/j.ijmsa.20221102.11
Page(s)	42-47
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Berry Phase, Entanglement, Chiral Anomaly, Quantum Field Theory

References

[1]	J. S. Bell: Physica, 1, 195 (1964).
[2]	J. R. Klauder: Ann. Phys., 180, 120 (1988); J. R. Klauder, E. Onofri: Int. J. Mod. Phys. A, 4, 3939 (1989).
[3]	N. Woodhouse: Geometric Quantization (Clarendon Press, Oxford, 1980).
[4]	P. Bandyopadhyay, K. Hajra: J. Math. Phys., 28, 711 (1987).
[5]	K. Hajra, P. Bandyopadhyay: Phys. Lett. A, 155, 7 (1991).
[6]	E. Nelson: Phys. Rev., 150, 1079 (1966); Dynamical theory of Brownian motion (Princeton University Press, 1967).
[7]	M. V. Berry: Proc. Roy. Soc. (London) A, 392, 45 (1984).
[8]	B. Simon: Phys. Rev. Lett., 51, 2167 (1983).
[9]	B. Basu: Europhys. Lett., 73, 833 (2006).
[10]	B. Basu, P. Bandyopadhyay: Int. J. Geo. Method. Mod. Phys., 4, 707 (2007).
[11]	B. Basu, P. Bandyopadhyay: J. Phys. AMath. Theor., 41, 055301 (2008).
[12]	D. Banerjee, P. Bandyopadhyay: J. Math. Phys., 33, 990 (1992).
[13]	A. Roy, P. Bandyopadhyay: J. Math. Phys., 30, 2366 (1989).
[14]	P. Bandyopadhyay: Int. J. Mod. Phys. A, 154107 (2000).
[15]	P. Bandyopadhyay: Proc. Roy. Soc. (London) A, 4662917 (2010).
[16]	M. V. Berry, J. M. Robbins: Proc. Roy. Soc. (London) A 453, 1771 (1997).
[17]	V. Vedral: Cent. Eur. J. Phys., 1, 284 (2003).
[18]	R. Jackiw: Phys. Rev. Lett., 54, 159 (1985).
[19]	A. Berard, H. Mohrbach: Phys. Rev. D, 69, 12701 (2004).
[20]	Y. S. WuandA. Zee: Phys. Lett. B, 152, 98 (1985).
[21]	M. Nakahara: Geometry, Topology and Physics, IOP, London, U. K.
[22]	W. K. Wooters: Phys. Rev. Lett, 80, 2245 (1998).
[23]	T. J. Osborne, M. A. Nielson, Phys. Rev. A, 66, 032110 (2002).
[24]	H. Casini, M. Huerta: Phys. Lett. B, 600, 142 (2004).
[25]	C. Holzhey, F. Larsen, F. Wilezek: Nucl. Phys. B, 424, 44 (1994).
[26]	P. Bandyopadhyay: Int. J. Mod. Phys. A, 15, 1415 (2000).
[27]	A. Zamolodchikov: JETPLett., 43, 731 (1986).
[28]	P. Bandyopadhyay: Proc. Roy. Soc. (London) A, 467, 427 (2011).
[29]	P. W. Anderson: Science, 235, 1196 (1987).
[30]	G. Goswami, P. Bandyopadhyay: J. Math. Phys., 38, 4451 (1997).
[31]	Basu, P. Bandyopadhyay and P. Majumdar, Phys. Rev. A 86, 022303 (2012).
[32]	P. Bandyopadhyay, Proc. Roy. Soc (Londan) A. 466 (2010) 2017.
[33]	S. Singha Roy, Theoretical Physics, 2, Number 3, 141 (2017).
[34]	S. Singha Roy and P. Bandyopadhyay,: Phys. Lett. A 382, 1973 (2018).

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Subhamoy Singha Roy. (2022). Chiral Waves and Topological Novel States in Fermi. International Journal of Materials Science and Applications, 11(2), 42-47. https://doi.org/10.11648/j.ijmsa.20221102.11

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Subhamoy Singha Roy. Chiral Waves and Topological Novel States in Fermi. Int. J. Mater. Sci. Appl. 2022, 11(2), 42-47. doi: 10.11648/j.ijmsa.20221102.11

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Subhamoy Singha Roy. Chiral Waves and Topological Novel States in Fermi. Int J Mater Sci Appl. 2022;11(2):42-47. doi: 10.11648/j.ijmsa.20221102.11

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@article{10.11648/j.ijmsa.20221102.11,
  author = {Subhamoy Singha Roy},
  title = {Chiral Waves and Topological Novel States in Fermi},
  journal = {International Journal of Materials Science and Applications},
  volume = {11},
  number = {2},
  pages = {42-47},
  doi = {10.11648/j.ijmsa.20221102.11},
  url = {https://doi.org/10.11648/j.ijmsa.20221102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20221102.11},
  abstract = {This first show was that the spin system, the two nearest neighbour spin in the Entanglement of measuring compliance by the ground conditions are achieved Berry stage to the relation when it is a closed path developed is. It noted the need to share the stage in a kind of geometric phase as explained to go to which any deformations involved is not and it’s the first Stiefel-Whitney class which is to Zz–cohomology value takes. However for polarized fermions we can relate the exchange phase as the celebrated Berry phase as in this case the Zz-cohomology becomes irrelevant and is consistent with the first Chern class which involves curvature. This follows from the depiction of a fermion as a scalar particle attached with a magnetic flux line. As in this framework the measure of entanglement of two nearest neighbor spins in a spin system given by concurrence is found to be associated with the Berry phase acquired by a spin state when it evolves in a closed path we can consider that entanglement is a consequence of Fermi statistics. It has been noted that in terms of quantum field theory, the berry phase is related to the perpetual inconsistency caused by the breaking of the perpetual symmetry. As mentioned earlier the quantization procedure of a fermion in the framework of Nelson’s stochastic quantization procedure introduces an internal variable which appears as a direction vector and gives rise to spin degrees of freedom. It's pointing to is that when a spin- 1 state of two spin 1/2 state is a Entangle system as considered to be that, the most widely covered state longitudinal elements with the matching it.},
 year = {2022}
}

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TY  - JOUR
T1  - Chiral Waves and Topological Novel States in Fermi
AU  - Subhamoy Singha Roy
Y1  - 2022/03/12
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmsa.20221102.11
DO  - 10.11648/j.ijmsa.20221102.11
T2  - International Journal of Materials Science and Applications
JF  - International Journal of Materials Science and Applications
JO  - International Journal of Materials Science and Applications
SP  - 42
EP  - 47
PB  - Science Publishing Group
SN  - 2327-2643
UR  - https://doi.org/10.11648/j.ijmsa.20221102.11
AB  - This first show was that the spin system, the two nearest neighbour spin in the Entanglement of measuring compliance by the ground conditions are achieved Berry stage to the relation when it is a closed path developed is. It noted the need to share the stage in a kind of geometric phase as explained to go to which any deformations involved is not and it’s the first Stiefel-Whitney class which is to Zz–cohomology value takes. However for polarized fermions we can relate the exchange phase as the celebrated Berry phase as in this case the Zz-cohomology becomes irrelevant and is consistent with the first Chern class which involves curvature. This follows from the depiction of a fermion as a scalar particle attached with a magnetic flux line. As in this framework the measure of entanglement of two nearest neighbor spins in a spin system given by concurrence is found to be associated with the Berry phase acquired by a spin state when it evolves in a closed path we can consider that entanglement is a consequence of Fermi statistics. It has been noted that in terms of quantum field theory, the berry phase is related to the perpetual inconsistency caused by the breaking of the perpetual symmetry. As mentioned earlier the quantization procedure of a fermion in the framework of Nelson’s stochastic quantization procedure introduces an internal variable which appears as a direction vector and gives rise to spin degrees of freedom. It's pointing to is that when a spin- 1 state of two spin 1/2 state is a Entangle system as considered to be that, the most widely covered state longitudinal elements with the matching it.
VL  - 11
IS  - 2
ER  -

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Author Information

Subhamoy Singha Roy

Department of Physics, JIS College of Engineering, Kalyani, India

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Plain Text BibTeX RIS

APA Style

Subhamoy Singha Roy. (2022). Chiral Waves and Topological Novel States in Fermi. International Journal of Materials Science and Applications, 11(2), 42-47. https://doi.org/10.11648/j.ijmsa.20221102.11

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ACS Style

Subhamoy Singha Roy. Chiral Waves and Topological Novel States in Fermi. Int. J. Mater. Sci. Appl. 2022, 11(2), 42-47. doi: 10.11648/j.ijmsa.20221102.11

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AMA Style

Subhamoy Singha Roy. Chiral Waves and Topological Novel States in Fermi. Int J Mater Sci Appl. 2022;11(2):42-47. doi: 10.11648/j.ijmsa.20221102.11

Copy | Download

@article{10.11648/j.ijmsa.20221102.11,
  author = {Subhamoy Singha Roy},
  title = {Chiral Waves and Topological Novel States in Fermi},
  journal = {International Journal of Materials Science and Applications},
  volume = {11},
  number = {2},
  pages = {42-47},
  doi = {10.11648/j.ijmsa.20221102.11},
  url = {https://doi.org/10.11648/j.ijmsa.20221102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20221102.11},
  abstract = {This first show was that the spin system, the two nearest neighbour spin in the Entanglement of measuring compliance by the ground conditions are achieved Berry stage to the relation when it is a closed path developed is. It noted the need to share the stage in a kind of geometric phase as explained to go to which any deformations involved is not and it’s the first Stiefel-Whitney class which is to Zz–cohomology value takes. However for polarized fermions we can relate the exchange phase as the celebrated Berry phase as in this case the Zz-cohomology becomes irrelevant and is consistent with the first Chern class which involves curvature. This follows from the depiction of a fermion as a scalar particle attached with a magnetic flux line. As in this framework the measure of entanglement of two nearest neighbor spins in a spin system given by concurrence is found to be associated with the Berry phase acquired by a spin state when it evolves in a closed path we can consider that entanglement is a consequence of Fermi statistics. It has been noted that in terms of quantum field theory, the berry phase is related to the perpetual inconsistency caused by the breaking of the perpetual symmetry. As mentioned earlier the quantization procedure of a fermion in the framework of Nelson’s stochastic quantization procedure introduces an internal variable which appears as a direction vector and gives rise to spin degrees of freedom. It's pointing to is that when a spin- 1 state of two spin 1/2 state is a Entangle system as considered to be that, the most widely covered state longitudinal elements with the matching it.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Chiral Waves and Topological Novel States in Fermi
AU  - Subhamoy Singha Roy
Y1  - 2022/03/12
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmsa.20221102.11
DO  - 10.11648/j.ijmsa.20221102.11
T2  - International Journal of Materials Science and Applications
JF  - International Journal of Materials Science and Applications
JO  - International Journal of Materials Science and Applications
SP  - 42
EP  - 47
PB  - Science Publishing Group
SN  - 2327-2643
UR  - https://doi.org/10.11648/j.ijmsa.20221102.11
AB  - This first show was that the spin system, the two nearest neighbour spin in the Entanglement of measuring compliance by the ground conditions are achieved Berry stage to the relation when it is a closed path developed is. It noted the need to share the stage in a kind of geometric phase as explained to go to which any deformations involved is not and it’s the first Stiefel-Whitney class which is to Zz–cohomology value takes. However for polarized fermions we can relate the exchange phase as the celebrated Berry phase as in this case the Zz-cohomology becomes irrelevant and is consistent with the first Chern class which involves curvature. This follows from the depiction of a fermion as a scalar particle attached with a magnetic flux line. As in this framework the measure of entanglement of two nearest neighbor spins in a spin system given by concurrence is found to be associated with the Berry phase acquired by a spin state when it evolves in a closed path we can consider that entanglement is a consequence of Fermi statistics. It has been noted that in terms of quantum field theory, the berry phase is related to the perpetual inconsistency caused by the breaking of the perpetual symmetry. As mentioned earlier the quantization procedure of a fermion in the framework of Nelson’s stochastic quantization procedure introduces an internal variable which appears as a direction vector and gives rise to spin degrees of freedom. It's pointing to is that when a spin- 1 state of two spin 1/2 state is a Entangle system as considered to be that, the most widely covered state longitudinal elements with the matching it.
VL  - 11
IS  - 2
ER  -

Copy | Download