The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent $s$-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.

• Received 30 July 2009

DOI:https://doi.org/10.1103/PhysRevA.81.013612