Quantum asymptotic phase reveals signatures of quantum synchronization

We propose a fully quantum-mechanical definition of the asymptotic phase for quantum nonlinear oscillators. The asymptotic phase function of the system is introduced in terms of the eigenoperator of the adjoint Liouville superoperator associated with the fundamental frequency. This quantum asymptotic phase yields appropriate phase values of the system even in the strong quantum regime, while reproducing the conventional asymptotic phase in the semiclassical regime. We analyze a quantum van der Pol oscillator with Kerr effect and show that several dominant eigenoperators with different fundamental frequencies exist in the strong quantum regime. Using the quantum asymptotic phase functions with respective fundamental frequencies, we reveal that the multiple phase locking of the system with a harmonic drive at several different frequencies, an explicit quantum signature observed only in the strong quantum regime, can be interpreted as synchronization on a torus rather than a simple limit cycle.Comment: 9 pages, 4 figures + Supplemental Material (6 pages 1 figure

Phase dynamics of noise-induced coherent oscillations in excitable systems

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase reduction of the hybrid system to derive an effective, dimensionality-reduced phase equation. We apply the reduced phase model to a periodically forced excitable system and two-coupled excitable systems, both undergoing noise-induced oscillations. The reduced phase model can quantitatively predict the entrainment of a single system to the periodic force and the mutual synchronization of two coupled systems, including the phase slipping behavior due to noise, as verified by Monte Carlo simulations. The derived phase model gives a simple and efficient description of noise-induced oscillations and can be applied to the analysis of more general cases

NANOS2 promotes male germ cell development independent of meiosis suppression

AbstractNANOS2 is an RNA-binding protein essential for fetal male germ cell development. While we have shown that the function of NANOS2 is vital for suppressing meiosis in embryonic XY germ cells, it is still unknown whether NANOS2 plays other roles in the sexual differentiation of male germ cells. In this study, we addressed the issue by generating Nanos2/Stra8 double knockout (dKO) mice, whereby meiosis was prohibited in the double-mutant male germ cells. We found that the expression of male-specific genes, which was decreased in the Nanos2 mutant, was hardly recovered in the dKO embryo, suggesting that NANOS2 plays a role in male gene expression other than suppression of meiosis. To investigate the molecular events that may be controlled by NANOS2, we conducted a series of microarray analyses to search putative targets of NANOS2 that fulfilled 2 criteria: (1) increased expression in the Nanos2 mutant and (2) the mRNA associated with NANOS2. Interestingly, the genes predominantly expressed in undifferentiated primordial germ cells (PGCs) were significantly selected, implying the involvement of NANOS2 in the termination of the characteristics of PGCs. Furthermore, we showed that NANOS2 is required for the maintenance of mitotic quiescence, but not for the initiation of the quiescence in fetal male germ cells. These results suggest that NANOS2 is not merely a suppressor of meiosis, but instead plays pivotal roles in the sexual differentiation of male germ cells