Collective dynamics of unstable quantum states

Pavel Cejnar, Pavel Stránský, Michal Kloc

Quantum spectra of excited states of numerous collective many-body models show singularities related to stable and unstable stationary points of the corresponding classical dynamics. We show several examples of these singularities and discuss some of their consequences.

V. M. Akulin

H. Hofmann, Dieter Kiderlen

We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the fluctuations are governed by diffusion coefficients D_{μν}. The latter are obtained through a fluctuation dissipation theorem generalized to allow for a treatment of unstable modes. Numerical evaluations of the D_{μν} are presented. We discuss briefly how this picture may be used to describe global motion within a locally harmonic approximation.

Joerg, Evers

Sanu Kumar Gangwar, Rajamanickam Ravisankar, Henrique Fabrelli +2 more

We analyze the impact of spin-orbit and Rabi couplings on the dynamical stability of spin-orbit-coupled spin-1 Bose-Einstein condensates for ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Determining the collective excitation spectrum through Bogoliubov--de Gennes theory, we characterize the dynamical stability regime via modulational instability. For AFM interactions, the eigenspectrum reveals the presence of both stable and unstable avoided crossings (UACs), with the first-excited branch undergoing a double unstable avoided crossing. In contrast, with ferromagnetic interactions, only a single UAC, which occurs between the low-lying and first-excited branches, is observed. Furthermore, the eigenvectors demonstrate the transition from densitylike to spinlike behavior, as the collective excitation shows the transition from the stable to the unstable mode for both the FM and AFM interactions. In the multiband instability state, eigenvectors display spin-density mixed mode, while they show spin-flip nature in the avoided crossing regime. Our analysis suggests that spin-orbit coupling enhances the instability gain, while Rabi coupling plays the opposite role. Finally, we corroborate our analytical findings of stable and unstable regimes through numerical simulations of the dynamical evolution of the condensates by introducing the perturbations upon quenching the trap strength. The dynamical phases show the formation of complex domains with AFM interaction, which may be attributed to the double unstable avoided crossings in such a system.

Elisheva Elbaz