Ground state(s) of the spin-boson hamiltonian

Masao Hirokawa

An expression of the ground state energy E SB of the spin-boson Hamiltonian H SB is considered. The expression in the cases of both massive and massless bosons is given by a nonperturbative method.

Anton Amann

Asao Arai, Masao Hirokawa

The existence and uniqueness of ground states of the spin-boson Hamiltonian $H_{\mathrm{S}\mathrm{B}}$ are con- sidered.The main results in the case of massive bosons include: $(\mathrm{i})(\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e})$ there exists a ground state without restriction for the strength of the coupling constant; $(\mathrm{i}\mathrm{i})(\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s})$ under a mild (nonperturbative) condition for the parameters contained in $H_{\mathrm{S}\mathrm{B}},$ $H_{\mathrm{S}\mathrm{B}}$ has only one ground state ; (iii) (degeneracy) under a certain condition for the parameters of $H_{\mathrm{S}\mathrm{B}}$which is weaker than that of (ii), the number of the ground states is at most two.In the case of massless bosons, the existence of a ground state of $H_{\mathrm{S}\mathrm{B}}$ is shown as a limit of ground states of the massive case.The methods used are nonperturbative.A generalization of the model is proposed.

Naotaka Yoshinaga, A. Arima, Y. M. Zhao

In this report we study the origin of spin-zero ground-state dominance for even-even nuclei in the presence of random two-body interactions. We evaluate the ground-state energy in terms of the energy centroid and the width of the random Hamiltonian. For both fermions and bosons in a single orbital, we obtain excellent agreement between the spin-I ground state probabilities predicted by using our formula and those obtained by diagonalizing the random Hamiltonian.

David Hasler, Ira Herbst