Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The Exbeta system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the Exepsilon models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the Exbeta system, the ground states of the Exepsilon model always exhibit entanglement. For the Exbeta case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the Exepsilon case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.

Quantum entanglement and fixed-point bifurcations

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.

Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

Restriction of intramuscular neurite branching and extension is lost in agrin and rapsyn-deficient mice

The phrenic nerve enters the diaphragm at approximately embryonic day 12.5 (E12.5) in the mouse. The secondary nerve trunk advances along the centre of the diaphragm muscle and extends tertiary branches primarily towards the lateral side during normal embryonic development. In the present study we quantified the intramuscular neurite branching in the most ventral region of the diaphragm at E15.5 and E18.5 in wild-type mice, agrin knock-out mice (KOAG) and rapsyn knock-out mice (KORAP). KOAG and KORAP have decreased muscle contraction due to their inability to maintain/form acetylcholine receptor (AChR) clusters during embryonic development. Heterozygote mothers were anaesthetised via an overdose of Nembutal (30 mg; Boeringer Ingelheim, Ridgefield, CT, USA) and killed via cervical dislocation. There were increases in the number of branches exiting the medial side of the phrenic nerve trunk in KOAG and KORAP compared to wild-type mice, but not on the lateral side at E15.5 and E18.5. However, the number of bifurcations in the periphery significantly increased on both the medial and lateral sides of the diaphragm at E15.5 and E18.5 in KOAG and KORAP compared to control mice. Furthermore, neurites extended further on both the medial and lateral sides of the diaphragm at E15.5 and E18.5 in KOAG and KORAP compared to wild-type mice. Together these results show that the restriction of neurite extension and bifurcations from the secondary nerve trunk is lost in both KOAG and KORAP allowing us the opportunity to investigate the factors that restrict motoneuron behaviour in mammalian muscles.