Regularity-Induced Separation of Intrinsic and Collective Dynamics

We propose that the adiabatic separation of collective and intrinsic motions in many-body systems is related to increased regularity of the intrinsic dynamics. The surmise is verified on the separation of rotations from intrinsic vibrations in the interacting boson model of nuclear structure.

Figure 1

The SU(3) decomposition of selected rotational-like (a)–(c) and nonrotational (d) sequences of states in the spectrum of a transitional Hamiltonian (1) with $(\eta ,\chi )=(0.5,-0.9)$ and $N=30$. The bars grouped above each ($\lambda ,\mu$) represent squared amplitudes (only the largest components shown) of the respective SU(3) basis state in a sequence of eigenstates with angular momenta $l=0,2,4,6$ ($l_j$ denoting the $j$th eigenstate with given $l$). The sequence in each panel was chosen to maximize the correlation with the respective $0_i$ state. Coherent patterns in  (a)–(c) indicate a common intrinsic structure for each of these bands.

Figure 2

Quantities $C(2,4{)}_i$ (a) and $R(4/2{)}_i$ (b) for $l=0,2,4,\dots$ sequences at energy $E(0_i)$ (arb. units), and the classical regular fraction $f_{\mathrm{reg}}(E)$ (c). Calculation done for $(\eta ,\chi )=(0.5,-0.9)$ and $N=30$. Symbols I, II, and III demarcate regions with high, medium, and low degree of regularity, respectively, showing a tendency for the corresponding occurrence of rotational sequences. The energy axis in (c), with $N\to \infty$, was linearly transformed to keep link with the upper panels. The $f_{\mathrm{reg}}$ curve ends below the maximal energy because of a numerical instability above the asymptotic value of the potential energy [16].

Figure 3

The same as in Fig. 2 but for $(\eta ,\chi )=(0.5,-0.5)$.