Non-uniform ground state for the Bose gas
Abstract
We study the ground state, sum aX |X>, of N hard-core bosons on a finite lattice in configuration space, X=x1,...,xN. All aX being positive, the ratios aX / sum aY can be interpreted as probabilities Pa (X). Let E denote the energy of the ground state and BX the number of nearest-neighbor particle-hole pairs in the configuration X. We prove the concentration of Pa to X's with BX in a sqrt(|E|)-neighborhood of |E|, show that the average of aX over configurations with BX=n increases exponentially with n, discuss fluctuations about this average, derive upper and lower bounds on E and give an argument for off-diagonal long-range order in the ground state.
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