Bose gas of small density in a random field

Bose gas in a random external field is considered. The effective action both for weak and strong random fields, compared with the interaction between particles, is derived in the framework of the path integral Keldysh-Schwinger technique. Using this effective action the properties of the system in strongly fluctuating random field are analyzed. Used approximation shows a gap in the chemical potential, when it flows from negative to positive values.