S. De Baerdemacker

In the present paper, we discuss the differences that underlie a topic of current intensive research and debate, e.g., the appearance of phase transitions and shape coexistence in atomic nuclei. Besides a formulation of the basic differences, we discuss on one hand some typical examples of shape coexistence (near the Sn and Pb closed shell regions) and, on the other hand, of phase transitions. The present discussion should allow a more transparent way to analyze nuclear structure changes in particular mass regions.

The quantum many-body problem can be rephrased as a variational determination of the two-body reduced density matrix, subject to a set of N-representability constraints. The mathematical problem has the form of a semidefinite program. We adapt a standard primal–dual interior point algorithm in order to exploit the specific structure of the physical problem. In particular the matrix-vector product can be calculated very efficiently. We have applied the proposed algorithm to a pairing-type Hamiltonian and studied the computational aspects of the method. The standard N-representability conditions perform very well for this problem.
Keywords: Density matrix; Variational; Semidefinite programming