In this work it is pointed out that the phase transitions of the d+1 Gross-Neveu (fermionic) and CPN−1 (bosonic) models at finite temperature and imaginary chemical potential can be mapped to transformations of Hubbard-like regular hexagonal to square lattice with the intermediate steps to be specific surfaces (irregular hexagonal kind) with an ordered construction based on the even indexed Bloch-Wigner-Ramakrishnan polylogarithm function. The zeros and extrema of the Clausen Cld(θ) function play an important role to the analysis since they allow us not only to study the fermionic and bosonic theories and their phase transitions but also the possibility to explore the existence of conductors arising from the correspondence between the partition functions of the two models and the Bloch and Wannier functions that play a crucial role in the tight-binding approximation in solid state physics. The main aim of this work is not only to unveil the relevance of the canonical partition functions of a fermionic and a bosonic model to Bloch states by using an imaginary chemical potential but also to examine the overlap between two Bloch wave-functions that differ by a lattice momentum that calculates the momentum transfer of a Bloch wave during the interaction with a lattice point of a hexagonal construction.
| Published in | American Journal of Modern Physics (Volume 13, Issue 2) |
| DOI | 10.11648/j.ajmp.20241302.12 |
| Page(s) | 17-26 |
| 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), 2024. Published by Science Publishing Group |
Fermion-boson Map, Hubbard Lattice, Conductor, Bloch Function, Wannier Function
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APA Style
Filothodoros, E. G. (2024). Fermionic and Bosonic Partition Functions at Imaginary Chemical Potential as Bloch Functions. American Journal of Modern Physics, 13(2), 17-26. https://doi.org/10.11648/j.ajmp.20241302.12
ACS Style
Filothodoros, E. G. Fermionic and Bosonic Partition Functions at Imaginary Chemical Potential as Bloch Functions. Am. J. Mod. Phys. 2024, 13(2), 17-26. doi: 10.11648/j.ajmp.20241302.12
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Download@article{10.11648/j.ajmp.20241302.12,
author = {Evangelos Georgiou Filothodoros},
title = {Fermionic and Bosonic Partition Functions at Imaginary Chemical Potential as Bloch Functions},
journal = {American Journal of Modern Physics},
volume = {13},
number = {2},
pages = {17-26},
doi = {10.11648/j.ajmp.20241302.12},
url = {https://doi.org/10.11648/j.ajmp.20241302.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20241302.12},
abstract = {In this work it is pointed out that the phase transitions of the d+1 Gross-Neveu (fermionic) and CPN−1 (bosonic) models at finite temperature and imaginary chemical potential can be mapped to transformations of Hubbard-like regular hexagonal to square lattice with the intermediate steps to be specific surfaces (irregular hexagonal kind) with an ordered construction based on the even indexed Bloch-Wigner-Ramakrishnan polylogarithm function. The zeros and extrema of the Clausen Cld(θ) function play an important role to the analysis since they allow us not only to study the fermionic and bosonic theories and their phase transitions but also the possibility to explore the existence of conductors arising from the correspondence between the partition functions of the two models and the Bloch and Wannier functions that play a crucial role in the tight-binding approximation in solid state physics. The main aim of this work is not only to unveil the relevance of the canonical partition functions of a fermionic and a bosonic model to Bloch states by using an imaginary chemical potential but also to examine the overlap between two Bloch wave-functions that differ by a lattice momentum that calculates the momentum transfer of a Bloch wave during the interaction with a lattice point of a hexagonal construction.},
year = {2024}
}
TY - JOUR T1 - Fermionic and Bosonic Partition Functions at Imaginary Chemical Potential as Bloch Functions AU - Evangelos Georgiou Filothodoros Y1 - 2024/06/12 PY - 2024 N1 - https://doi.org/10.11648/j.ajmp.20241302.12 DO - 10.11648/j.ajmp.20241302.12 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 17 EP - 26 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.20241302.12 AB - In this work it is pointed out that the phase transitions of the d+1 Gross-Neveu (fermionic) and CPN−1 (bosonic) models at finite temperature and imaginary chemical potential can be mapped to transformations of Hubbard-like regular hexagonal to square lattice with the intermediate steps to be specific surfaces (irregular hexagonal kind) with an ordered construction based on the even indexed Bloch-Wigner-Ramakrishnan polylogarithm function. The zeros and extrema of the Clausen Cld(θ) function play an important role to the analysis since they allow us not only to study the fermionic and bosonic theories and their phase transitions but also the possibility to explore the existence of conductors arising from the correspondence between the partition functions of the two models and the Bloch and Wannier functions that play a crucial role in the tight-binding approximation in solid state physics. The main aim of this work is not only to unveil the relevance of the canonical partition functions of a fermionic and a bosonic model to Bloch states by using an imaginary chemical potential but also to examine the overlap between two Bloch wave-functions that differ by a lattice momentum that calculates the momentum transfer of a Bloch wave during the interaction with a lattice point of a hexagonal construction. VL - 13 IS - 2 ER -
Institute of Theoretical Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece
