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Bose-Einstein Condensation of Ideal Gas with a Fixed Total Momentum

Student: Petrukhina Mariia

Supervisor: Alexey Alexeevich Sokolik

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Mathematical Methods of Modelling and Computer Technologies (Master)

Year of Graduation: 2019

The paper deals with the Bose-Einstein condensation of an ideal gas with a fixed total momentum. Such a statement of the problem is due to the fact that the state of a system with all sorts of fluctuating momentums traditionally enters the statistical ensemble, while, from a physical point of view, a Bose gas in free space must have a fixed momentum by virtue of the law of conservation of momentum. To calculate the characteristics of a system with a full fixed momentum, the method of recurrent relations is used. Similar relations are used to consider a Bose gas in a canonical ensemble. This paper derives the recurrence relation for a Bose gas in a canonical ensemble with a fixed total momentum, on the basis of which the thermodynamic characteristics of the system are calculated as a function of the total momentum: free energy, the fraction of particles in the condensate, and the chemical potential at different temperatures.

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