Prog. Theor. Phys. Vol. 81 No. 6 (1989) pp. 1158-1173
Energy Spectrum of One-Dimensional Many Boson System
Department of Physics, College of General Education,
Osaka University, Toyonaka 560
(Received March 1, 1989)
An energy spectrum is exactly examined for a one-dimensional many boson system where bosons are interacting to each other through a delta-functional repulsive potential. After a unitary transformation, the Hamiltonian is diagonalized to be the following compact form ∑p(p2/2m)np + (π\hbar/2mL) ×∑p,q|p - q|npnq + (1/6m)(π\hbar/L)2[(∑pnp)3 - ∑pnp)] at the infinitely large limit of the coupling constant. This form is non-linear with respect to the numbers np of quasi-particles. The non-linear terms are Galilean-invariant and produce a phonon-like spectrum. In a case of a finite coupling contant g, the total energy is expanded to power series of (1/g).
DOI : 10.1143/PTP.81.1158
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Citing Article(s) :
Journal of the Physical Society of Japan 59 (1990) pp. 1593-1599
Thermodynamic Functions of One-Dimensional Many-Boson System
Shosuke Sasaki and Tosaku Kunimasa