Thomas M. Antonsen

We theoretically and experimentally establish a connection between linearly chirped pulse propagation properties and the complex generalization of Wigner–Smith time delay for both transmitted and reflected pulses in linear and dispersive reverberant non-Hermitian scattering systems. We demonstrate that the time shift of the chirped pulse depends on both the real and imaginary parts of the complex time delay (CTD) of the scattering system. We also show that the chirped pulse experiences a center frequency shift that is directly proportional to the imaginary component of CTD, similar to that found in Giovannelli et al (2025 Phys. Rev. Lett. 135 043801). Using these insights, we then demonstrate how CTD can be harnessed to systematically tune the propagation properties of a chirped pulse such that a near-zero time shift can be achieved for a wide range of pulse center frequencies in a resonant scattering system. Overall, this work broadens the utility and establishes the physical significance of complex time delays in non-Hermitian settings.

Accurate knowledge of the phase space at beam creation is essential for understanding and predicting beam dynamics to extract or suppress phase space structures without causing avoidable emittance growth. Both first-principles models—which do not account for beam structure—and simulations using ideal phase space distribution may prove unable to capture unique beam structures. Here, we initialize the phase space distribution in first-principles simulations with velocity-space data measured using a pinhole scan. We show that the evolution of internal beam structure is highly sensitive to these initial conditions; tuning them within their experimental measurement error allows for remarkably accurate replication of the experimental beam evolution, including the emergence of a characteristic cruciform shape.

Reservoir computers (RCs) are powerful machine learning architectures for time series prediction. Recently, next generation reservoir computers (NGRCs) have been introduced, offering distinct advantages over RCs, such as reduced computational expense and lower training data requirements. However, NGRCs have their own practical difficulties, including sensitivity to sampling time and type of nonlinearities in the data. Here, we introduce a hybrid RC-NGRC approach for time series forecasting of dynamical systems. We show that our hybrid approach can produce accurate short-term predictions and capture the long-term statistics of chaotic dynamical systems in situations where the RC and NGRC components alone are insufficient, e.g., due to constraints from limited computational resources, sub-optimal hyperparameters, sparsely sampled training data, etc. Under these conditions, we show for multiple model chaotic systems that the hybrid RC-NGRC method with a small reservoir can achieve prediction performance approaching that of a traditional RC with a much larger reservoir, illustrating that the hybrid approach can offer significant gains in computational efficiency over traditional RCs while simultaneously addressing some of the limitations of NGRCs. Our results suggest that the hybrid RC-NGRC approach may be particularly beneficial in cases when computational efficiency is a high priority and an NGRC alone is not adequate.

We present the theoretical framework required to describe the statistics of microwave networks that serve to model quantum graphs. The networks are described by impedance and admittance matrices relating the voltages and currents at the network's ports. As we show, these matrices can be calculated in a number of ways. Normal modes of the network are characterized by a discrete set of wave numbers corresponding to the propagation constants on the network's bonds for which the determinant of the admittance matrix vanishes. The distribution of the spacings between adjacent eigenmode wave numbers is found to depend on the nature of the way bonds are connected at nodes. The critical quantity is the reflection coefficient presented at a node to a wave on a bond. As the reflection coefficient increases, the spacing distribution changes from one characteristic of the spacing of eigenvalues of a Gaussian orthogonal ensemble matrix to a Poisson distribution. The effect of loss is studied, and the scaling of the variance of the impedance values on network size, degree distribution, and other parameters is characterized. We attempted to find universal scaling relations for the distribution of impedance values for networks of different sizes. Finally, we compare the distribution of impedance values predicted by the model with those measured in a network of cables.

Evolutionary computation is a powerful optimization method that is well-suited for high-dimensional parameter spaces. In this work, we apply it to an integral task in optical physics, namely, to the problem of programming a deformable mirror to generate laser beams that are partially coherent in space. This involves precise tuning of (on the order of) tens of thousands of phase values in the interval [-π, π) such that they exhibit defined second-order statistical characteristics. We discuss the implementation of two primary methods, the evolution of phase values and of a correlating linear transformation, and provide results based on a Gaussian covariance function. We show that the first-order statistical properties are fixed by the method of choice, which we suggest may be overcome by a multi-objective evolutionary calculation involving symbolic transformations. This is a largely unexplored domain in which stochastic processes, such as genetic algorithms, are superior. Lastly, we discuss the inherently physical limitations that prevent certain types of phase statistics from being realized, even with the genetic algorithm approach.

Electromagnetic wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first-principles, study of this process is usually computationally expensive and the results exhibit extreme sensitivity to scattering details. For this reason, the deterministic approach is often dropped in favor of a statistical one. The random coupling model (RCM) Hemmady et al. [Phys. Rev. Lett. 94, 014102 (2005).] is one such approach that has found great success in providing a statistical characterization for wave chaotic systems in the frequency domain. Here we aim to transform the RCM into the time domain and generalize it to alternative situations. The proposed time-domain RCM (TDRCM) method can treat a wave chaotic system with multiple ports and modes. Two features are now possible with the time-domain approach for chaotic resonators: the incorporation of early time short-orbit transmission path effects between the ports, and the inclusion of arbitrary nonlinear or time-varying port load impedances. We conduct short-pulse time-domain experiments in wave chaotic enclosures, and use the TDRCM to simulate the corresponding experimental setup. We also examine a diode-loaded port and compare experimental results with a numerical TDRCM treatment and find agreement.

Wave energy distribution within enclosures with irregular boundaries is a common phenomenon in many branches of electromagnetics. If the wavelength of the injected wave is small compared with the structure size, the scattering properties of the enclosure will be extremely sensitive to small changes in geometry or wave frequency. In this case, statistical models are sought. The random coupling model (RCM) is one such model that has been explored through experiments and theory. Previous studies were conducted by injecting waves into high Q cavities in a nearly omnidirectional manner. In this article, a directed beam approach is taken, and relatively low Q cavities are considered. The goal is to determine when the so-called “random plane wave hypothesis,” a fundamental basis of the RCM formulation, breaks down. Results show that injecting such directed beams leads to large deviations in the wave statistics for single realizations of the enclosure geometry. The expected statistics are restored to some degree when multiple realizations are considered.

Physicists and engineers frequently encounter situations in which there is a need to evaluate and optimize via numerical simulation the performance of a particular device or system. This leads to calculating a figure of merit (FoM) characterizing the system and its gradient in a high dimensional parameter space. Direct evaluation of the gradient via finite differencing each parameter can become computationally expensive when there are many parameters. In this case a computational savings can be achieved if an "adjoint problem" can be found that produces the desired information without requiring multiple computations. A simple example is the design of a receiving antenna. One wishes to know and optimize the signal received as a function of the incident angle and polarization of incoming waves. It might appear that solution of Maxwell’s field equations would have to be repeated for each possible incident direction and polarization. However, due to the reciprocal property of the governing equations, the desired information is obtained by treating the antenna as a transmitter and calculating the far field radiation pattern. Thus, one computation replaces many. In this talk I will review some problems from the area of plasma physics and charged particle dynamics where adjoint methods have proven useful. Examples include calculation of the plasma current driven by absorption of RF waves in magnetic confinement fusion devices, determination of the sensitivity of stellarator equilibria to changes in magnetic coil locations, optimization of electron beam optics in diodes and accelerator lattices, and optimization of slow wave structures used in microwave and millimeter wave amplifiers.

In this paper, a predictive model is developed to characterize the impact of high-frequency electromagnetic interference (EMI) on the leakage current of CMOS integrated circuits. It is shown that the frequency dependence can be easily described by a transfer function that depends only on a few dominant parasitic elements. The developed analytical model is successfully compared against measurement data from devices fabricated using 180 nm, 130 nm, and 65 nm standard CMOS processes through TSMC. Based on the predictive model, the impact of EMI on leakage current in a CMOS inverter is reduced by increasing the frequency from 10 MHz to 4 GHz.