Exact Results in Quantum Theory

A lot of interesting physical and mathematical information about quantum gases at zero temperature in large volume is encoded in the spectral properties of their Hamiltonian and their total momentum. The joint spectrum of these commuting self-adjoint operators after the subtraction of the ground state energy can be called the excitation spectrum. One can conjecture that in some situations the excitation spectrum should have an interesting shape characterized by a positive critical velocity, which is related to superfluidity.