On the infimum of the energy-momentum spectrum of a homogeneous Bose gas

We consider second quantized homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature, and in the grand canonical setting (the chemical potential μ is fixed, the number of particles can vary). We investigate upper bounds on the infimum of the energy for a fixed total momentum k given by the expectation value at one-particleexcitations over a squeezed state. We show that the results of the Bogoliubov approach (usually derived heuristically) coincide with the results of the firstiteration of our method (which leads to rigorous upper bounds).We consider second quantized homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature, and in the grand canonical setting (the chemical potential μ is fixed, the number of particles can vary). We investigate upper bounds on the infimum of the energy for a fixed total momentum k given by the expectation value at one-particleexcitations over a squeezed state. We show that the results of the Bogoliubov approach (usually derived heuristically) coincide with the results of the firstiteration of our method (which leads to rigorous upper bounds)