Quantum Dynamics of Mesoscopic Driven Duffing Oscillators

We investigate the nonlinear dynamics of a mesoscopic driven Duffing oscillator in a quantum regime. In terms of Wigner function, we identify the nature of state near the bifurcation point, and analyze the transient process which reveals two distinct stages of quenching and escape. The rate process in the escape stage allows us to extract the transition rate, which displays perfect scaling behavior with the driving distance to the bifurcation point. We numerically determine the scaling exponent, compare it with existing result, and propose open questions to be resolved.Comment: 4 pages, 4 figures; revised version accepted for publication in EP

Dark Energy and Fate of the Universe

We explore the ultimate fate of the Universe by using a divergence-free parametrization for dark energy $w(z)=w_0+w_a({\ln (2+z)\over 1+z}-\ln2)$. Unlike the CPL parametrization, this parametrization has well behaved, bounded behavior for both high redshifts and negative redshifts, and thus can genuinely cover many theoretical dark energy models. After constraining the parameter space of this parametrization by using the current cosmological observations, we find that, at the 95.4% confidence level, our Universe can still exist at least 16.7 Gyr before it ends in a big rip. Moreover, for the phantom energy dominated Universe, we find that a gravitationally bound system will be destroyed at a time $t \simeq P\sqrt{2|1+3w(-1)|}/[6\pi |1+w(-1)|]$, where $P$ is the period of a circular orbit around this system, before the big rip.Comment: 5 pages, 3 figures; typos corrected, publication version, Sci China-Phys Mech Astron, doi: 10.1007/s11433-012-4748-