Collective Phenomea In Highly Excited Bose Gas

e}wij:ed gas is meant a 90."1 in which thet'e exisi: a s.i9nificantrnnumber of exalted particles. Tlw number of ~jxcited part 1clesrndepends on external sources (la.ser illumination, electron beams,rnetc.) and can be arbitrary. In typical case" the number of excitedrnatoms N .i" smaller than the number of pal;t.icles .in thern1rnground state. As.is '1e11 lmoVin the energy of interactionrnbetween pa,'ticles in the same quantum Bt_ate is proportional tornlid' ~Ihere R 1s the distance between partlcles. 'I'his shortrangerninteraction is responslblc 1:or tho coll()ct:i,ve propertiesrnof 1:he convelltional gas Huch as condensation and pha"e transitions.rn'1'he int_m:action hel:vl8cn dlf ferently·-exci'ced particles 1srnproportional to I/n 3 and can be 21ttnlctive as Vlell as repulsive.rn'rhus, t_he ava:llab.il.ity of even a comparaU.vely small number ofrnexcited -paxticles can and does l(-lad to 21 signU'icant change ofrnthe propertles of th,~ gas compared ~i til the non-(~xcited gas.rnThe properties of Huch exc:l.tec1 (jas are invest.i.gated onrnthe basis of the second'-quantJzecl Hilmil tonian and the method ofrnequations of IUo-tion of Green functions. 1~hiB method yields I inrna most natural and direct "THY, the enor(w~spectrulU of elllmentaryrnexcitations and t:he t:hGl:l!lodynaroiGCll functions of excitedrngas

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