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We present rigorous results on the diagonalization of Bogoliubov Hamiltonian for a soliton condensate. Using the complete and orthonormalized set of eigenfunction for the Bogoliubovde Gennes equations, we calculate exactly the quantum depletion of the condensate and show that two degenerate zero-modes, which originate from a U(1) gauge- and a translational-symmetry breaking of the system, induce the quantum diffusion and transverse instability of the soliton condensate.
Deng, L.
and Huang, G.
(2006),
Quantum depletion of a soliton condensate, Physics Letters, [online], https://doi.org/10.1016/j.physleta.2006.04.023
(Accessed November 29, 2023)