(Received December 9, 1982)
In a series of papers, we shall consider a class of simple Hamiltonians of interacting bosons with degenerate ground states. As the simplest example, we treat here a system composed of a single kind of boson interacting with a special cubic and quartic self-interactions. The conventional perturbation, when applied in a simple-minded manner, does not work at all because of the degeneracy of the ground state. We study the spectrum of our Hamiltonian analytically as well as numerically. We find a very rapid transition from the weak coupling region to the strong coupling region, which takes place at a rather small value of the coupling constant.
An application of this study to the problem of nuclear rotation from the standpoint of “spontaneous break-down of rotation symmetry” will be presented in a forthcoming paper.
URL : http://ptp.ipap.jp/link?PTP/69/1146/
DOI : 10.1143/PTP.69.1146