The time-dependent Hamiltonians are a very important portion in the modeling of real systems. In fact, the dynamic description of an entangled quantum systems is reflected in full coherence with the resolution of a wave function, solution of the Schrödinger equation throughout the entire study path. In this regard, we specify in this paper the system of two-site Bose-Hubbard model that obeys tunnel behavior, as two coupled harmonic oscillators, to examine quantum entanglement. The dynamics of such a system is described by the Schrödinger equation have introduced to the solution, the non-linear Ermakov equations as well as through a passage to the Heisenberg picture approach and the general Lewis and Riesenfeld invariant method compute between coupled harmonic oscillators and the coupled Caldirola Kanai oscillators. We prove that a time exponential increase in the mass of the system brings back to an exponential increase of entanglement and the Heisenberg picture approach is the most stable method to quantum entanglement because, this last has reached very large values. Also, we specify a cyclic time evolution, we find analytically the nonadiabatic Berry phases. In a particular case, such an entangled system acquired a nonadiabatic Berry phases that exhibits the same behavior as the Schmidt parameter.
| Published in | American Journal of Physics and Applications (Volume 12, Issue 2) |
| DOI | 10.11648/j.ajpa.20241202.12 |
| Page(s) | 27-39 |
| 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 |
Two-site Bose-Hubbard Model, Schmidt Mode, Entanglement, Nonadiabatic Berry Phases
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APA Style
Abidi, A., Trabelsi, A. (2024). The Schmidt Decomposition for Entangled System and Nonadiabatic Berry Phases. American Journal of Physics and Applications, 12(2), 27-39. https://doi.org/10.11648/j.ajpa.20241202.12
ACS Style
Abidi, A.; Trabelsi, A. The Schmidt Decomposition for Entangled System and Nonadiabatic Berry Phases. Am. J. Phys. Appl. 2024, 12(2), 27-39. doi: 10.11648/j.ajpa.20241202.12
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Download@article{10.11648/j.ajpa.20241202.12,
author = {Ahlem Abidi and Adel Trabelsi},
title = {The Schmidt Decomposition for Entangled System and Nonadiabatic Berry Phases},
journal = {American Journal of Physics and Applications},
volume = {12},
number = {2},
pages = {27-39},
doi = {10.11648/j.ajpa.20241202.12},
url = {https://doi.org/10.11648/j.ajpa.20241202.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20241202.12},
abstract = {The time-dependent Hamiltonians are a very important portion in the modeling of real systems. In fact, the dynamic description of an entangled quantum systems is reflected in full coherence with the resolution of a wave function, solution of the Schrödinger equation throughout the entire study path. In this regard, we specify in this paper the system of two-site Bose-Hubbard model that obeys tunnel behavior, as two coupled harmonic oscillators, to examine quantum entanglement. The dynamics of such a system is described by the Schrödinger equation have introduced to the solution, the non-linear Ermakov equations as well as through a passage to the Heisenberg picture approach and the general Lewis and Riesenfeld invariant method compute between coupled harmonic oscillators and the coupled Caldirola Kanai oscillators. We prove that a time exponential increase in the mass of the system brings back to an exponential increase of entanglement and the Heisenberg picture approach is the most stable method to quantum entanglement because, this last has reached very large values. Also, we specify a cyclic time evolution, we find analytically the nonadiabatic Berry phases. In a particular case, such an entangled system acquired a nonadiabatic Berry phases that exhibits the same behavior as the Schmidt parameter. },
year = {2024}
}
TY - JOUR T1 - The Schmidt Decomposition for Entangled System and Nonadiabatic Berry Phases AU - Ahlem Abidi AU - Adel Trabelsi Y1 - 2024/10/31 PY - 2024 N1 - https://doi.org/10.11648/j.ajpa.20241202.12 DO - 10.11648/j.ajpa.20241202.12 T2 - American Journal of Physics and Applications JF - American Journal of Physics and Applications JO - American Journal of Physics and Applications SP - 27 EP - 39 PB - Science Publishing Group SN - 2330-4308 UR - https://doi.org/10.11648/j.ajpa.20241202.12 AB - The time-dependent Hamiltonians are a very important portion in the modeling of real systems. In fact, the dynamic description of an entangled quantum systems is reflected in full coherence with the resolution of a wave function, solution of the Schrödinger equation throughout the entire study path. In this regard, we specify in this paper the system of two-site Bose-Hubbard model that obeys tunnel behavior, as two coupled harmonic oscillators, to examine quantum entanglement. The dynamics of such a system is described by the Schrödinger equation have introduced to the solution, the non-linear Ermakov equations as well as through a passage to the Heisenberg picture approach and the general Lewis and Riesenfeld invariant method compute between coupled harmonic oscillators and the coupled Caldirola Kanai oscillators. We prove that a time exponential increase in the mass of the system brings back to an exponential increase of entanglement and the Heisenberg picture approach is the most stable method to quantum entanglement because, this last has reached very large values. Also, we specify a cyclic time evolution, we find analytically the nonadiabatic Berry phases. In a particular case, such an entangled system acquired a nonadiabatic Berry phases that exhibits the same behavior as the Schmidt parameter. VL - 12 IS - 2 ER -
National Higher School of Engineers of Tunis, Tunis University, Tunisia; Department of Physics, Faculty of Sciences of Tunis, Tunis El Manar University, Tunis, Tunisia
National Center for Nuclear Science and Technology Technological Pole, Sidi Thabet, Tunisia
