In analogy with a symmetry-restoring treatment of rotational invariance for deformed Hamiltonians, we discuss the case of a separable monopole pairing Hamiltonian in the quasiparticle basis. The results are compared to estimates of a conventional treatment based on the quasiparticle random phase approximation.
The ground state of a many body Hamiltonian considered in the quasiparticle representation is redefined by accounting for the quasiparticle quadrupole pairing interaction. The residual interaction of the newly defined quasiparticles is treated by the quasiparticle random phase approximation (QRPA). Solutions of the resulting equations exhibit specific features. In particular, there is no interaction strength where the first root is vanishing. A comparison with other renormalization methods is presented. Application to a single [Formula: see text]-shell allows for the results interpretation by comparing them with those obtained by exact calculations.
A brief description of excited and ground states in two-dimensional quantum dots and rotating nuclei is presented within a mean field approach and a random-phase approximation (RPA). We discuss the procedure to restore the rotational symmetry broken at the mean field, which can be extended for other symmetry breaking cases. We propose to consider a disappearance of collective excitations in the rotating frame as a manifestation of symmetry breaking phenomena of the rotating mean field. In particular, we demonstrate that the disappearance of a collective octupole mode in the rotating frame in 162 Yb gives rise to the nonaxial octupole deformation.
A nonlinear generalization of the quasiparticle random phase approximation is constructed with the aim of describing anharmonic effects in the low-lying spectra of vibrational nuclei. Angular momentum zero pairing correlations of the ground state are described by a generalized BCS calculation based on a variational method. The dynamics of the vibrational states are described by the Heisenberg equations of motion for fermion pair operators; matrix elements of products of pair operators are treated by sum rule methods. Kinematical constraints are expressed by the algebra of the pair operators and by boson-like polynomial expansions for the quasiparticle conserving multipole operators in terms of the quasiparticle pair changing operators, these expansions enforcing the content of the Pauli principle. The physical basis for the choice of approximations is described. The final algorithm is organized so as to involve little more than repeated BCS-like and RPA-like calculations, converging to a self-consistent solution of the full nonlinear scheme. Detailed discussion is carried out for a modified form of the pairing plus quadrupole interaction Hamiltonian, but the method is not confined to this model.NUCLEAR STRUCTURE Approximate many-body methods applied to modified pairing plus quadrupole model. Description of vibrational spectrum of single closed shell nuclei. Equations of motion and algebraic methods.
The study of symmetry restoration has recently emerged as a fruitful means to extract high-level information on the relaxation of quantum many-body systems. However, while the restoration of internal symmetries has been investigated intensively, that of spatial symmetries has hitherto only been considered in the context of random unitary circuits. Here, we present a complementary study of translation symmetry restoration in integrable systems. In particular, we consider a one-dimensional chain of spinless, noninteracting fermions quenched from a ν > 1 shift invariant state, and follow the local restoration of one-site shift invariance using the Frobenius distance Δ F A between the state on a subsystem and its symmetrized counterpart. Distinct from the case of random unitary circuits, where symmetry restoration occurs abruptly for times proportional to the subsystem size, we find that symmetry here is restored smoothly and over timescales of the order of the subsystem size squared. We also find that the so-called ‘‘quantum Mpemba effect’’ is readily observed. Most importantly, we show that—in contrast to the case of continuous internal symmetries—this discrete symmetry restoration is not qualitatively described by a quasiparticle picture for Δ F A , and therefore goes beyond the hydrodynamic description. Our results can be directly extended to higher dimensions.