Major overhaul: All sections have been changed and improved.
Added: Computation of the condensate fraction
Added: Discussion and plots of correlation function and momentum distribution
Added: Section on numerical computation
Added: Appendices on functional analysis
Added: Detailed analysis of the operator K_e
Change: Parameters for numerical simulations.
Change: Renamed "Simplified approach" to "Lieb's simplified approach"
Added: More bibliography
Added: Acknowledgements
Ian Jauslin
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