Non-uniform ground state for the Bose gas

Details Non-uniform ground state for the Bose gas Non-uniform ground state for the Bose gas

2000-11-20

arxiv.org/abs/cond-mat/0011334v3

J. Phys. A: Math. Gen. 34 (2001) 37-55, ibid. 34 (2001) 6209

Physics

Condensed Matter

Statistical Mechanics

Equation (77) corrected

Scientific paper

We study the ground state, sum a_X |X>, of N hard-core bosons on a finite lattice in configuration space, X={x_1,...,x_N}. All a_X being positive, the ratios a_X / sum a_Y can be interpreted as probabilities P_a (X). Let E denote the energy of the ground state and B_X the number of nearest-neighbor particle-hole pairs in the configuration X. We prove the concentration of P_a to X's with B_X in a sqrt(|E|)-neighborhood of |E|, show that the average of a_X over configurations with B_X=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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