So a collection of enough Bose particles in thermal equilibrium will mostly be in the ground state, with only a few in any excited state, no matter how small the energy difference.
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When a gas of Bose particles is cooled to temperatures very close to absolute zero, then its kinetic energy decreases down to a negligible amount and the particles condense into the lowest energy state.
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Ivan Vakarchuk has the rank of Doctor of Physical and Mathematical Sciences, Professor, PhD with the thesis : " Application of the method of displacements and collective variables in the study of interacting Bose particles near absolute zero " ( Institute for Theoretical Physics, Academy of Sciences of USSR, 1974 ) doctoral thesis on " Microscopic theory of Bose liquid'( Institute for Theoretical Physics, USSR Academy of Sciences, 1980 ).
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