A Modified Bogoliubov Approximation

Jacob Katriel

O. Litt, William H. Bassichis

We use a non-gauge-invariant modification of the exact Hamiltonian to obtain a new Hamiltonian-like operator for a simple exactly solvable boson model. The eigenvalues of the new operator are close to those of the original Hamiltonian. We make a one-body approximation of the new two-body operator in the spirit of the Bogoliubov approximation. Because only the number operator appears, the c-number approximation is not required individually for the creation or annihilation operators in the ground state. For the simple model, the results using the new approximation are closer to the exact results than the usual Bogoliubov results over a wide range of parameters. The improvement increases dramatically as the model interaction strength increases.

Mohsen Razavy, Edward S. Krebes

The Bassichis–Foldy model of a simple interacting boson is solved numerically and the results are compared with those obtained by the Bogoliubov approximation and by the Brueckner–Sawada t-matrix formalism. In the normal region, contrary to the widely held view, the Brueckner–Sawada approximation for the energy of the ground state is not reliable for strong, well-behaved, repulsive forces. The Bogoliubov approximation, on the other hand, remains valid for a wide range of values of the coupling constant. In the inverted region, the attractive force causes a population inversion in the levels of the system. For this case a modified Brueckner–Sawada approximation is developed. This method is applied to the calculation of the transition point and the energies of the ground and the first excited states of the system. Here most of the predictions of the modified Brueckner–Sawada approximation are quite accurate. By a simple change in the Bassichis–Foldy model it is shown that even, for two bosons there can be a phase transition. In this model, the derivative of the ground state energy with respect to the coupling constant is discontinuous at the transition point.

John M. Blatt

Petarpa Boonserm, Matt Visser

Baoqing Sun, M. S. Pindzola

Bogoliubov modes and the static structure factor for a two-species Bose–Einstein condensate were investigated within the framework of mean field approximation. We find that both quantities are strongly affected due to atomic collisions between the two species. The inter-species interaction not only changes the density distributions of the two species, but also modifies the Bogoliubov modes. As a consequence, the static structure factor exhibits a measurable difference. For a binary mixture of 87Rb and 23Na, our numerical results suggest that such an effect can be observed experimentally.