One-Dimensional Many Boson System. IV : Condensation and Excitation Energy

概要

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The analysis for a one-dimensional many boson system with a repulsive delta-function potential is continued. It is shown that the expectation value of the number a_0*a_0 of bare bosons with zero momentum for the exact ground state ∣Ψ_<0,0,…,0>> is negligibly small compared with the total number n in the limit of an infinitely large coupling constant g; i.e., ≪Ψ_<0,…,0>∣a_0*a_0∣Ψ_<0,…,0>>/n→0(for n→∞, g→∞). This result shows a striking contrast to the result ≪Ψ_<0,…,0>∣A_0*A_0∣Ψ_<0,…,0>>/n=1 for an arbitrary g, where A_0*A_0 indicates the number operator of exactly dressed bosons with zero momentum. It is clarified that the energy of a dressed boson strongly depends upon the number distribution {n_q} of the other dressed bosons in the system. The excitation energy of a dressed boson has phonon character when n_0/n ≠0, where n_0 denotes the number of dressed bosons with zero momentum. When n_0/n tends to zero, the phonon character disappears in a drastic way. Some characteristic phenomena in liquid helium II are discussed on the basis of the results of our previous papers and the present paper.
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