Selection of collective degrees of freedom in the boson space

F. Dönau, D. Janssen

Kenjiro Takada, S. Tazaki, Seiichi Yasumoto

In order to truncate a high-dimensional Hilbert space for a many-nucleon shell model to a small collective subspace, we carry out a Dyson-type boson mapping and select a small number of collective bosons. In this way, we can divide the Dyson boson Hamiltonian into collective and non-collective parts; the latter includes the renormalization of the coupling effects between the collective and non-collective degrees of freedom. The boson Hamiltonian thus obtained is written in terms of the selected collective bosons only. Diagonalizing this boson Hamiltonian and comparing the numerical results with those obtained from exact shell-model calculations for some sd- and pf-shell nuclei, we find that our method gives a good approximation of the exact shell model. It is shown that the coupling effect between the collective and non-collective degrees of freedom plays an essential role. This method is also applied to some heavier pfg-shell nuclei for which it is unfeasible to carry out exact shell-model calculation because of the very large number of dimensions of the Hilbert space. Our numerical results are in very good agreement with experiment.

D. Janssen, F. Dönau, S. Frauendorf +1 more

Yasser Omar, Nikola Paunković, Sougato Bose +1 more

Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of entanglement from the internal to the spatial degrees of freedom without any interaction between these degrees of freedom. Moreover, subensembles selected by local measurements of the path will, in general, have different amounts of entanglement in the internal degrees of freedom depending on the statistics (either fermionic or bosonic) of the particles involved.

Jean G. Valatin

Ching‐Teh Li

A variational principle of maximal decoupling between the collective and noncollective subspaces has recently been proposed to pin down the collective degrees of freedom of the nuclear many-body problem. This maximal-decoupling variational principle is further utilized here to determine in an optimal way the auxiliary Hamiltonians to be used in severely truncated boson-space calculations for nuclear collective motions. In the present method one treats the spurious-state problem in truncated boson-space calculations by using appropriate auxiliary boson Hamiltonians. The viability of the method is demonstrated through its application to a simplified shell model containing only the monopole pairing interactions.