Non-uniform ground state for the Bose gas
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چکیده
We study the ground state Ψ0 = aX |X of N hard-core bosons on a finite lattice in configu-aY can be interpreted as probabilities Pa(X). Let E0 denote the energy of the ground state and |∂X| the number of nearest-neighbour particle-hole pairs in the configuration X. We prove the concentration of Pa onto X with |∂X| in a |E0|-neighbourhood of |E0|, show that the average of aX over configurations with |∂X| = n increases exponentially with n, discuss fluctuations about this average, derive upper and lower bounds on E0 and give an argument for off-diagonal long-range order in the ground state.
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