Bose-Einstein condensation in an Einstein universe
Journal of Physics A: Mathematical and General, 1978
The condensation of a non-relativistic ideal Bose gas in an Einstein universe is investigated. Ex... more The condensation of a non-relativistic ideal Bose gas in an Einstein universe is investigated. Explicit expressions for the condensate fraction N0/N and the specific heat are obtained by using the Poisson summation formula to express the summations as integrations plus corrections. It is shown that the finiteness of the system smoothes out the cusp-like singularity of the infinite system. A rigorous asymptotic analysis of the critical temperature and the specific heat maximum are given, and the relation with the scaling theory of finite size effects is briefly discussed.
Uploads
Papers by Basil Altaie
This article presents a comprehensive overview of the introduction of AI techniques in Quranic studies, highlighting key areas that could form the core of such investigations. The suggested venues and examples presented here need discussion from both technical and contextual perspectives. While many studies and experiments using AI in Quranic studies are available in the published literature, some crucial remarks and precautions need to be considered regarding the involvement of AI in the study of the Qur’ān and Hadith.
It is crucial to acknowledge that our contemporary era has a vast spectrum of information in natural sciences compared to past ages. The development of the two pillars of modern biology and modern physics has dramatically altered our understanding of life and the universe. The discovery of extraterrestrial planetary systems harboring Earth-like planets presents a challenge to theology and philosophy, requiring us to understand the impact of these discoveries on our comprehension of religion.
The Qur’ān, being considered the word of Allah in Islamic belief, must align with the correct implications of natural sciences. Verses of the Qur’ān are revealed to express the truth, and the exact understanding of the physical world must be truthful. Therefore, it is expected that science may elevate our understanding of the Qur’ān, while the Qur’ān illuminates our path towards scientific exploration. This dialectic relationship between science and the Qur’ān should be investigated by knowledgeable individuals who are well-versed in both domains. Through my own research, I have repeatedly seen this relationship reflecting the authenticity of the Qur’ān's origin as a divine source. Several examples are provided in my book (The Divine Word and the Grand Design), offering profound evidence for the authenticity of the Qur’ān's divine origin.