Tan's adiabatic sweep theorem from the variational theorem for the scattering length

Abstract

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.

8 pages, 2 figures, misprints corrected

References in corpus (9)

• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Verification of universal relations in a strongly interacting Fermi gas
• Number of closed-channel molecules in the BEC-BCS crossover
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Virial theorems for trapped cold atoms
• Universal contact of strongly interacting fermions at finite temperatures
• Strongly correlated Bose gases
• Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation