Bose–Einstein Condensation in a One-Dimensional System of Interacting Bosons

Abstract

Using the Vakarchuk formulae for the density matrix, we calculate the number Nk of atoms with momentum ħk for the ground state of a uniform one-dimensional periodic system of interacting bosons. We obtain for impenetrable point bosons N0≈2N and Nk=2πj/L≃0.31N0/√|j|. That is, there is no condensate or quasicondensate on low levels at large N. For almost point bosons with weak coupling ((Formula presented.)), we obtain (Formula presented.) and (Formula presented.). In this case, the quasicondensate exists on the level with k=0 and on low levels with k≠0, if N is large and β is small (e.g., for N∼1010, β∼0.01). A method of measurement of such fragmented quasicondensate is proposed.