Bose-Einstein condensation in quasi2D trapped gases

We discuss BEC in (quasi)2D trapped gases and find that well below the transition temperature $T_c$ the equilibrium state is a true condensate, whereas at intermediate temperatures $T<T_c$ one has a quasicondensate (condensate with fluctuating phase). The mean-field interaction in a quasi2D gas is sensitive to the frequency $\omega_0$ of the (tight) confinement in the "frozen" direction, and one can switch the sign of the interaction by changing $\omega_0$. Variation of $\omega_0$ can also reduce the rates of inelastic processes, which opens prospects for tunable BEC in trapped quasi2D gases.