  It is shown that variation of the one-particle dispersion in a universal
many-body system enables us to obtain Tan's adiabatic sweep theorem and its
generalization. The derivation is based on the Hellmann-Feynman theorem and the
variational theorem for the scattering length suggested in our previous paper
[Cherny and Shanenko, Phys. Rev. E 62, 1646 (2000)]. As an example, the
universal effects in the system of spinless bosons are considered. With the
help of the variational theorem, we obtain the mean kinetic and interaction
energies and derive the virial theorem for the homogeneous and trapped bosons.
The results can easily be generalized to the two-component fermions with
interactions between opposite spins.
