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NATO ASI series. Series B : Physics

A Physical Characterization of the Ground State of the Spin-Boson Interaction

Elisabetta Paladino

Published Jan 1, 1997• 0 citations
Publisher
DOI
10.1007/978-1-4615-5835-4_64

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In this work we study the yrast states of sd\mathit{sd}sd-boson systems in the presence of random interactions. It is found that the yrast states with spin-zero ground states among the random ensemble exhibit strong correlations, characterized by anharmonic vibration, sss-boson or ddd-boson condensation, as well as vibrational and rotational motions. We study these correlations explicitly based on their wave functions and the features of two-body interactions in the random ensemble.
A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{z}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}}_{z}$ for the eigenstates of the system, regardless of the trapping potential. The low-energy states of the repulsively interacting two-boson system are characterized. In the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is a direct energy-level crossing in the ground state of the system between states of different Jz{J}_{z}Jz​, the third component of the total angular momentum, that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.