Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems
| dc.creator | Mostafazadeh, Ali | |
| dc.date | 1996-08-20 | |
| dc.date.accessioned | 2026-07-07T10:59:07Z | |
| dc.date.available | 2026-07-07T10:59:07Z | |
| dc.description | Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually solving the full eigenvalue problem for the instantaneous Hamiltonian. The parameter space of such systems which has the structure of $\xC P^2$ is explicitly constructed. The results of this article are applicable for arbitrary multipole interaction Hamiltonians $H=Q^{i_1,\cdots i_n}J_{i_1}\cdots J_{i_n}$ and their linear combinations for spin $j=1$ systems. In particular it is shown that the nuclear quadrupole Hamiltonian $H=Q^{ij}J_iJ_j$ does actually lead to non-Abelian geometric phases for $j=1$. This system, being bosonic, is time-reversal-invariant. Therefore it cannot support Abelian adiabatic geometrical phases. | |
| dc.description | Plain LaTeX, 17 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9608031 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9608031 | |
| dc.identifier | J.Phys.A30:7525-7535,1997 | |
| dc.identifier | doi:10.1088/0305-4470/30/21/023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/187340 | |
| dc.subject | Quantum Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems | |
| dc.type | text |