Chaos and the Quantum Phase Transition in the Dicke Model

We investigate the quantum chaotic properties of the Dicke Hamiltonian; a quantum-optical model which describes a single-mode bosonic field interacting with an ensemble of $N$ two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N \go \infty limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite $N$ and, by analysing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase-transition. Our considerations of the wavefunction indicate that this is connected with a delocalisation of the system and the emergence of macroscopic coherence. We also derive a semi-classical Dicke model, which exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.Comment: 51 pages, 15 figures, late

Dynamic coding for cognitive control in prefrontal cortex

Cognitive flexibility is fundamental to adaptive intelligent behavior. Prefrontal cortex has long been associated with flexible cognitive function, but the neurophysiological principles that enable prefrontal cells to adapt their response properties according to context-dependent rules remain poorly understood. Here, we use time-resolved population-level neural pattern analyses to explore how context is encoded and maintained in primate prefrontal cortex and used in flexible decision making. We show that an instruction cue triggers a rapid series of state transitions before settling into a stable low-activity state. The postcue state is differentially tuned according to the current task-relevant rule. During decision making, the response to a choice stimulus is characterized by an initial stimulus-specific population response but evolves to different final decision-related states depending on the current rule. These results demonstrate how neural tuning profiles in prefrontal cortex adapt to accommodate changes in behavioral context. Highly flexible tuning could be mediated via short-term synaptic plasticity