A Memristor Model with Piecewise Window Function

In this paper, we present a memristor model with piecewise window function, which is continuously differentiable and consists of three nonlinear pieces. By introducing two parameters, the shape of this window function can be flexibly adjusted to model different types of memristors. Using this model, one can easily obtain an expression of memristance depending on charge, from which the numerical value of memristance can be readily calculated for any given charge, and eliminate the error occurring in the simulation of some existing window function models

Engineering fast and stable splitting of matter waves

When attempting to split coherent cold atom clouds or a Bose-Einstein condensate (BEC) by bifurcation of the trap into a double well, slow adiabatic following is unstable with respect to any slight asymmetry, and the wave "collapses" to the lower well, whereas a generic fast chopping splits the wave but it also excites it. Shortcuts to adiabaticity engineered to speed up the adiabatic process through non-adiabatic transients, provide instead quiet and robust fast splitting. The non-linearity of the BEC makes the proposed shortcut even more stable

Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection

Explicit formulas for the rotation frequency and the long-wavenumber diffusion coefficients of global spirals with $m$ arms in Rayleigh-Benard convection are obtained. Global spirals and parallel rolls share exactly the same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals seem not to have a characteristic frequency $\omega_m$ or a typical size $R_m$, but their product $\omega_m R_m$ is a constant under given experimental conditions. The ratio $R_i/R_j$ of the radii of any two dislocations ($R_i$, $R_j$) inside a multi-armed spiral is also predicted to be constant. Some of these results have been tested by our numerical work.Comment: To appear in Phys. Rev. E as Rapid Communication

Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors

We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat $\pi$ pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols.Comment: 7 pages, 2 figure

Measuring the quality factor of a microwave cavity using superconduting qubit devices

We propose a method to create superpositions of two macroscopic quantum states of a single-mode microwave cavity field interacting with a superconducting charge qubit. The decoherence of such superpositions can be determined by measuring either the Wigner function of the cavity field or the charge qubit states. Then the quality factor Q of the cavity can be inferred from the decoherence of the superposed states. The proposed method is experimentally realizable within current technology even when the $Q$ value is relatively low, and the interaction between the qubit and the cavity field is weak.Comment: 8 page

Multiple Schr\"odinger pictures and dynamics in shortcuts to adiabaticity

A Schr\"odinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes and dynamics. In contrast to this standard scenario, other relations are also possible, such as a common interaction-picture dynamical equation corresponding to several Schr\"odinger equations that represent different physics. This may enable us to design alternative and feasible experimental routes for operations that are a priori difficult or impossible to perform. The power of this concept is exemplified by engineering Hamiltonians that improve the performance or make realizable several shortcuts to adiabaticity