RUI: Nonlinear and Neural Dynamics in Josephson Networks

*技术摘要*这个个人研究员奖支持超导约瑟夫森结网络中的非线性动力学的实验和计算研究。约瑟夫森结是非线性系统的例子，它可以用可调节的参数制造，以直接的方式测量，并且很容易扩展到大型网络规模。此外，一个长时间测量的大型约瑟夫森结电路包含了基本上不可能在计算机上计算的动力学，但可以通过电学测量观察到。这个项目将采用多方面的方法来研究约瑟夫森结网络的集体涌现行为。首先，它将遵循该领域以前在称为磁通子的类孤子模式和称为离散呼吸子的局域模式方面的工作。接下来，我们将研究无序振子系统的同步问题。最后，将制造和测试一个约瑟夫森结电路，该电路旨在准确地模拟生物神经元的随时间变化的电压。这有一个更长期的目标，即研究一个大型耦合神经网络的紧急行为。*非技术抽象*当今物理学的一个重要方面是努力理解基本的自然规律如何导致复杂的行为。例如，考虑一个气体分子系统。简单的力和动量定律支配着它们的碰撞。由于只有几个分子，这个系统简单而乏味。然而，对于大量的分子，系统可以将自己组织成某种复杂的东西，比如龙卷风。这种新的行为并不是因为基本定律的变化，而是因为系统的组成成分的数量发生了变化，在这种情况下，气体分子。在这项研究中，研究了一种称为约瑟夫森结的简单电路元件。约瑟夫森结由超导金属制成，在非常低的温度下工作。过去的实验观察了单个约瑟夫森结的行为，发现它能够产生有趣的电学行为。然而，由大量约瑟夫森结组成的电路还没有得到充分的研究。就像气体分子的情况一样，当组分的数量增加时，会产生新的集体行为。本项目将研究其中的几种新行为。其中之一，就像龙卷风一样，是电流的漩涡。另一种是集体电压振荡，一种像钟摆一样的来回运动。最后一种行为是电压尖峰，类似于生物神经元的开关放电。对于最后一种行为，一个更长期的目标是建立模仿人脑集体行为的电路，在人脑中，大量神经元连接在一起。这个项目吸收了本科生作为主要研究人员，为他们在科学领域的技术职业做准备。

****Technical abstract**** This individual investigator award supports an experimental and computational study of nonlinear dynamics in networks of superconducting Josephson junctions. Josephson junctions are examples of nonlinear systems which can be fabricated with adjustable parameters, measured in a straightforward fashion, and easily scaled to large network sizes. In addition, a large Josephson junction circuit measured over a long time contains dynamics which would essentially be impossible to calculate on a computer, but which can be observed with electrical measurements. This project will take a multi-faceted approach to studying the collective, emergent behavior of Josephson junction networks. First, it will follow previous work in the field on soliton-like modes called fluxons and localized modes called discrete breathers. Next, studies will be performed on the synchronization of a system of disordered oscillators. Finally, a circuit of Josephson junctions designed to accurately model the time-dependent voltage of a biological neuron will be fabricated and tested. This has a longer-term goal of studying the emergent behavior of a large, coupled neural network. ****Non-technical abstract**** An important aspect of physics today is the effort to understand how the fundamental laws of nature result in complex behavior. For example, consider a system of gas molecules. Simple laws of force and momentum govern their collisions. With only a few molecules, the system is simple and uninteresting. With a large number of molecules, however, the system can organize itself into something complex, like a tornado. This new behavior comes about not because of a change in the fundamental laws, but rather a change in the number of constituents, in this case gas molecules, of the system. In this research, a simple electrical circuit element known as a Josephson junction is studied. Josephson junctions are made from superconducting metals and work at very low temperatures. Past experiments have looked at the behavior of a single Josephson junction and found it capable of interesting electrical behavior. However, circuits composed of large numbers of Josephson junctions have yet to be fully studied. Just like the case of gas molecules, new collective behaviors result when the number of constituents is increased. This project will look at several of these new behaviors. One of these, like a tornado, is a swirl of electrical current. Another is a collective voltage oscillation, a back and forth motion like pendulums swinging together. A final behavior is voltage spiking, similar to the on-off firing of a biological neuron. With this last behavior, a longer term goal is to build circuits which would emulate collective behaviors in the human brain, where large numbers of neurons are connected together. This project incorporates undergraduate students as the primary researchers, preparing them for technical careers in the sciences.