The internal energy and thermodynamic behaviour of a boson gas below the Bose–Einstein temperature

2011 ◽  
Vol 375 (15) ◽  
pp. 1637-1639 ◽  
Author(s):  
F.A. Deeney ◽  
J.P. OʼLeary
Keyword(s):  
Internal Energy ◽  
Thermodynamic Behaviour ◽  
Einstein Temperature ◽  
Bose Einstein

scholarly journals Dimensional Crossover in the Bose–Einstein Condensation Confined to Anisotropic Three-Dimensional Lattices

2020 ◽  
Vol 201 (3-4) ◽  
pp. 340-372
Author(s):  
K. K. Witkowski ◽  
T. K. Kopeć
Keyword(s):  
Specific Heat ◽  
Internal Energy ◽  
Three Dimensional ◽  
Einstein Condensation ◽  
Thermodynamic Quantities ◽  
Dimensional Crossover ◽  
Bose Einstein Condensation ◽  
Energy Entropy ◽  
Bose Einstein ◽  
1D Chains

Abstract The Bose–Einstein condensation (BEC) in three-dimensional (3D) anisotropic lattices is studied. We present theoretical results for the critical temperature for BEC, chemical potential, condensate fraction and relevant thermodynamic quantities like: internal energy, entropy, specific heat and compressibility as a function of anisotropy parameter being the ratio of the nearest-neighbor in-plane ($$t_\parallel$$ t ‖ ) and out-of-plane ($$t_\perp$$ t ⊥ ) hopping amplitudes. In particular, considered scenarios include weakly coupled two-dimensional (2D) planes ($$t_\perp /t_\parallel \ll 1$$ t ⊥ / t ‖ ≪ 1 , relevant for layered structures) as well as a rod-like geometry of interacting one-dimensional (1D) chains ($$t_\parallel /t_\perp \ll 1$$ t ‖ / t ⊥ ≪ 1 ). The impact of the dimensional crossover as the system is tuned away from a set of disconnected 2D layers, or traverses from a set of separate 1D chains to a regime where a fully isotropic 3D structure emerges is elucidated. Both numerical and analytic approaches are employed, (the latter in a form of series expansions involving $$t_\parallel ,t_\perp$$ t ‖ , t ⊥ amplitudes) for internal energy, entropy, specific heat and isothermal compressibility. The theoretical outcome of the present study may be of interest to a number of scenarios in solid-state physics, where the relevant quasi-particles are bosonic-like, as well as might be applicable to the physics of cold bosons loaded in artificially engineered 3D optical lattices.

Refroidissement sympathique et doubles condensats de Bose-Einstein

2002 ◽  
Vol 12 (5) ◽  
pp. 133-134 ◽  
Author(s):  
G. Delannoy ◽  
S. G. Murdoch ◽  
V. Boyer ◽  
V. Josse ◽  
P. Bouyer ◽  
...  
Keyword(s):  
Bose Einstein

Challenges, Concerns, and Perspectives for Poland's Energy Transition during Global COVID-19 Pandemic

2020 ◽  
Vol 1 (2) ◽  
pp. 169-173
Author(s):  
Andrzej Lorkowski ◽  
Robert Jeszke
Keyword(s):  
Internal Energy ◽  
Energy Transition ◽  
Energy Transformation ◽  
Modern Times ◽  
Current Discussion ◽  
The Face ◽  
National Governments ◽  
The Eu ◽  
At Home

The whole world is currently struggling with one of the most disastrous pandemics to hit in modern times – Covid-19. Individual national governments, the WHO and worldwide media organisations are appealing for humanity to universally stay at home, to limit contact and to stay safe in the ongoing fight against this unseen threat. Economists are concerned about the devastating effect this will have on the markets and possible outcomes. One of the countries suffering from potential destruction of this situation is Poland. In this article we will explain how difficult internal energy transformation is, considering the long-term crisis associated with the extraction and usage of coal, the European Green Deal and current discussion on increasing the EU 2030 climate ambitions. In the face of an ongoing pandemic, the situation becomes even more challenging with each passing day.

Bose-Einstein condensates

1997 ◽  
Vol 167 (6) ◽  
pp. 649 ◽  
Author(s):  
Boris B. Kadomtsev ◽  
Mikhail B. Kadomtsev
Keyword(s):  
Bose Einstein

Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov
Keyword(s):  
Internal Energy ◽  
Hamiltonian Systems ◽  
Classical Mechanics ◽  
Motion Equation ◽  
Holonomic Constraints ◽  
Dissipative Processes ◽  
Motion Energy ◽  
Analytical Review ◽  
History Of ◽  
Material Points

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

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