Rebesh A. Non-standerd deformed quantum oscillators and their applications

Using the criterion of validity of the Fibonacci-like relation for any three consecutive energy levels of quantum deformed oscillators we have separated diverse models of deformed oscillators into two classes: Fibonacci oscillators and quasi-Fibonacci oscillators. In the framework of p,q-Bose gas model, at high temperatures dealing with the equation of state we obtain the virial expansion and correspondingly derive the five nontrivial virial coeffcients. At low temperatures we find the critical temperature of condensation. In the framework of mu-Bose gas model we obtain the intercepts of two- and three-particle correlation functions and their asymptotics.