Statistical mechanics of bosons with attractive interaction
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In order to obtain meaningful results for a system of bosons interacting via a potential containing a long-ranged attraction, the coupling of low momentum particles with high momentum particles has to be taken into account. The method of thermal Green’s functions applied to this problem leads to involved graphical calculations even for temperatures close to the absolute zero. It is shown that the problem can be tackled much more simply and profitably by obtaining an effective hamiltonian for low momentum particles in a manner similar to that adopted in the recent renormalisation group approach to critical phenomena. The occurrence of anomalous pairings is avoided by performing suitable Bogolubov transformations. The procedure gives the quasiparticle spectrum besides yielding an explicit expression for the free energy in the low temperature limit. The results agree with those derived by Green’s function methods using partial summations.
KeywordsBosons attractive interaction renormalisation group Green’s functions
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