Quantum Depletion of a Soliton Condensate
Guoxiang Huang, L. Deng, Jiaren Yan, and Bambi Hu
TL;DR
This paper rigorously diagonalizes the Bogoliubov Hamiltonian for a soliton condensate, calculating exact quantum depletion and revealing how zero-modes cause diffusion and instability.
Contribution
It provides an exact calculation of quantum depletion in a soliton condensate using complete eigenfunctions of the Bogoliubov equations, highlighting the role of zero-modes.
Findings
Exact quantum depletion calculated for soliton condensate
Zero-modes induce quantum diffusion and transverse instability
Complete eigenfunctions enable precise analysis
Abstract
We present rigorous results on the diagonalization of Bogoliubov Hamilto- nian for a soliton condensate. Using the complete and orthonomalized set of eigenfunction for the Bogoliubov de Gennes equations, we calculate ex- actly the quantum depletion of the condensate and show that two degenerate zero-modes, which originate from a U(1) guage- and a translational-symmetry breaking of the system, induce the quantum diffusion and transverse instabil- ity of the soliton condensate.
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