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

Rectified Pessimistic-Optimistic Learning for Stochastic Continuum-armed Bandit with Constraints

This paper studies the problem of stochastic continuum-armed bandit with constraints (SCBwC), where we optimize a black-box reward function $f(x)$ subject to a black-box constraint function $g(x)\leq 0$ over a continuous space $\mathcal X$. We model reward and constraint functions via Gaussian processes (GPs) and propose a Rectified Pessimistic-Optimistic Learning framework (RPOL), a penalty-based method incorporating optimistic and pessimistic GP bandit learning for reward and constraint functions, respectively. We consider the metric of cumulative constraint violation $\sum_{t=1}^T(g(x_t))^{+},$ which is strictly stronger than the traditional long-term constraint violation $\sum_{t=1}^Tg(x_t).$ The rectified design for the penalty update and the pessimistic learning for the constraint function in RPOL guarantee the cumulative constraint violation is minimal. RPOL can achieve sublinear regret and cumulative constraint violation for SCBwC and its variants (e.g., under delayed feedback and non-stationary environment). These theoretical results match their unconstrained counterparts. Our experiments justify RPOL outperforms several existing baseline algorithms

Accurate Estimation of Transport Coefficients Using Model-free Time Correlation Functions in Equilibrium Simulations

Transport coefficients, such as the diffusion coefficient and shear viscosity, are important material properties that are calculated in computer simulations. In this study, the criterion for the best estimation of viscosity, as an example of transport coefficients, is determined by using the Green-Kubo formula without any artificial models. The related algorithm is given by the estimation of the viscosities of polyethylene oxide solutions by using a molecular dynamics simulation for testing. The algorithm can be used in the simulations of complex systems with a long tail of correlations typically found in macromolecular and biological simulation systems.Comment: 8 pages, 5 figures, 1 tabl