Attempt to Describe Phase Slips by Means of an Adiabatic Approximation

As a plausibility test for the feasibility of extension of the quasiclassical Keldysh–Usadel technique to slowly varying situations, we assess the influence of the time-derivative term in the time-dependent Ginzburg–Landau equation. We consider cases in which the superconducting state in a nanowire varies slowly, either because the voltage applied on it is small, or because most of phase drift takes place next to the boundaries. An approximation without this time derivative can describe the superconducting state away from phase slips, but is unable to predict the value or the existence of a critical voltage at which evolution becomes non-stationary.

Phase Drift in Networks of Coupled Colpitts Oscillators

In modern times, satellite-based global positioning and navigation systems, such as the GPS, include precise time-keeping devices, e.g. atomic clocks, which are crucial for navigation and for a wide range of economic and industrial applications. However, precise timing might not be available when the environment renders satellite equipment inoperable. In response to this critical need, we have been carrying out, over the past three years, theory and preliminary experiments [Buono et al., 2018a; Buono et al., 2018b; Palacios et al., 2020], towards developing a novel and inexpensive precision timing device that can function independently of GPS availability. The fundamental idea is to exploit collective behavior generated by networks of coupled nonlinear oscillators. Common sense may suggest that synchronized oscillations may lead to higher accuracy. Previous works show, however, that it is not synchronization but rather, traveling wave patterns, in which consecutive oscillators are out of phase by a constant amount, that can better reduce the negative effects of noise and material imperfections which cause phase drift. In this work we advance the state-of-art in the network-based concept by studying, mainly computationally, collective behavior in networks of Colpitts oscillators. These type of oscillators are chosen because they offer a wide range of advantages (such as the ability to tune up the oscillations over a broad frequency range). The results highlight the regions of parameter space, including coupling strength, where traveling wave patterns have the largest basins of attraction and the ability to reduce phase drift by a [Formula: see text] scaling law, where [Formula: see text] is the number of oscillators in the network. The results should also provide guidelines for follow-up design and fabrication tasks of a network-based technology for precision timing.

A Wireless Covert Channel Based on Dirty Constellation with Phase Drift

Modern telecommunications systems require the use of various transmission techniques, which are either open or hidden. The open transmission system uses various security techniques against its unauthorized reception, and cryptographic solutions ensure the highest security. In the case of hidden transmissions, steganographic techniques are used, which are based on the so-called covert channels. In this case, the transparency and stealth of the transmission ensure its security against being picked up by an unauthorized user. These covert channels can be implemented in multimedia content, network protocols, or physical layer transmissions. This paper focuses on wireless covert channels. We present a novel method of steganographic transmission which is based on phase drift in phase-shift keying or quadrature amplitude modulation (QAM) and is included in the so-called dirty constellation techniques. The proposed approach is based on the drift correction modulation method, which was previously used in the watermarking of audio-signals. The developed solution is characterized by a variable bit rate, which can be adapted to the used modulation type and transmission conditions occurring in radio channels. In the paper, we present the method of generating and receiving hidden information, simulation research, and practical implementation of the proposed solution using the software-defined radio platform for selected QAM.

On the Scaling Law of Phase Drift in Coupled Nonlinear Oscillators for Precision Timing

Computational and experimental works reveal that the coupling of similar crystal oscillators leads to a variety of collective patterns, mainly various forms of discrete rotating waves and synchronization patterns, which have the potential for developing precision timing devices through phase drift reduction. Among all observed patterns, the standard traveling wave, in which consecutive crystals oscillate out of phase by [Formula: see text], where [Formula: see text] is the network size, leads to optimal phase drift error that scales down as [Formula: see text] as opposed to [Formula: see text] for an uncoupled ensemble. In this manuscript, we provide an analytical proof of the scaling laws, for uncoupled and coupled symmetric networks, and show that [Formula: see text] is the fundamental limit of phase-error reduction that one can obtain with a symmetric network of nonlinear oscillators of any type, not just crystals.