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Le Journal de Physique Colloques

THE BERRY PHASE AND DIABOLIC PAIR TRANSFER IN ROTATING NUCLEI

Peter A. Ring, R. S. Nikam

Published Jun 1, 1987• 0 citations
Publisher

Abstract

A new manifestation of the Berry-Phase is presented in the theory of fast rotating superfluid nuclei : Diabolic Pair Transfer, i.e. oscillations of the pair transfer matrix elements as a function of the angular velocity, is shown to be the direct consequence the Berry-Phase, giving a non-trivial contribution at the diabolical points of cranked Hartree-Fock-Bogoliubov (HFB) spectra.

DOI
10.1051/jphyscol:1987251

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A new manifestation of the Berry-Phase is presented in the theory of fast rotating superfluid nuclei : Diabolic Pair Transfer, i.e. oscillations of the pair transfer matrix elements as a function of the angular velocity, is shown to be the direct consequence the Berry-Phase, giving a non-trivial contribution at the diabolical points of cranked Hartree-Fock-Bogoliubov (HFB) spectra.
The quantum mechanical Berry phase is a topological contribution to the adiabatic response as system parameters are varied. It is the root of many fascinating topological phenomena in physics. Here, the authors consider spatiotemporal adiabatic response for many-body quantum systems in any dimension, and find analogous topological contributions they dub the ``higher Berry phase''. These contributions constrain the global structure of the phase diagrams of these systems and imply the existence of boundary modes at special parameter values.
The time-dependent Schr\"odinger equation for a spin particle in a rotating magnetic field is solved analytically by the cranking method, and the exact solutions are employed to study the nonadiabatic Berry's phase. An alternative expression for Berry's phase is given, which shows that Berry's phase is related to the expectation value of spin along the rotating axis and gives Berry's phase a physical explanation besides its gauge geometric interpretation. This expression also presents a simple algorithm for calculating the nonadiabatic Berry's phase for Hamiltonians that are nonlinear functions of the SU(2) generators. It is shown that nonadiabaticity alters the time evolution ray and in turn changes its Berry's phase. For the SU(2) dynamical group, the nonadiabatic effect on Berry's phase manifests itself as spin alignment (a phenomenon in nuclear physics), and spin-alignment quantization (observed recently in high-spin nuclear physics) is related to Berry's-phase quantization.
A new numerical method of calculating the Hartree-Fock-Bogoliubov (HFB) and time-dependent HFB (TDHFB) with the Gogny interaction is proposed. The three-dimensional harmonic-oscillator (3DHO) basis functions are replaced by one-dimensional spatial grid points of Lagrange mesh plus two-dimensional harmonic-oscillator basis functions in the perpendicular plane to the direction of the spatial grid points [Lagrange mesh and harmonic oscillator (LMHO)]. By using the LMHO, the calculations of the HFB and TDHFB are carried out in the typical nuclei of 20O{}^{20}\mathrm{O}20O and 34Mg{}^{34}\mathrm{Mg}34Mg as an illustration of the feasibility of the TDHFB formulation with the LMHO. The strength functions of the quadrupole vibrations (K=0K=0K=0) are obtained and are compared with the ones calculated with the 3DHO.