The rising computational demand of modern workloads has renewed interest in energy-efficient paradigms such as neuromorphic and analog computing. A fundamental operation in these systems is matrix-vector multiplication (MVM), ubiquitous in signal processing and machine learning. Here, we demonstrate MVM using inverse-designed metastructures that exploit heat conduction as the signal carrier. The proposed approach is based on a generalization of effective thermal conductivity to systems with multiple input and output ports: The input signal is encoded as a set of applied temperatures, while the output is represented by the power collected at designated terminals. The metastructures are obtained via density-based topology optimization, enabled by a differentiable thermal transport solver and automatic differentiation, achieving an accuracy $>99\%$ in most cases across a pool of matrices with dimensions $2\times2$ and $3\times3$. We apply this methodology -- termed thermal analog computing -- to realize matrices relevant to practical tasks, including the discrete Fourier transform and convolutional filters. These findings open new avenues for analog information processing in thermally active environments, including temperature-gradient sensing in microelectronics and thermal control systems.

This work investigates amplitude-dependent nonlinear corrections to the dissipative conductivity in superconductors, using the Keldysh-Usadel theory of nonequilibrium superconductivity, which captures the nonequilibrium dynamics of both quasiparticles and the pair potential. Our rigorous formulation naturally incorporates both the direct nonlinear action of the photon field and indirect contributions mediated by nonequilibrium variations in the pair potential, namely, the Eliashberg effect and the Higgs mode. The third-harmonic current, often regarded as a hallmark of the Higgs mode in disordered superconductors, arises from both the direct photon action and the Higgs mode. Our numerical results are in excellent agreement with previous studies. In contrast, the first-harmonic current, and consequently the dissipative conductivity, receives contributions from all three mechanisms: the direct photon action, the Higgs mode, and the Eliashberg effect. It is shown that the nonlinear correction to dissipative conductivity in dirty-limit superconductors can serve as a fingerprint of the Higgs mode, appearing as a resonance peak at a frequency near the superconducting gap Δ . In addition, our results provide microscopic insight into amplitude-dependent dissipation at frequencies well below Δ , which is particularly relevant for applied superconducting devices. In particular, the long-standing issue concerning the frequency dependence of the amplitude-dependent quality factor is explained as originating from the direct nonlinear action of the photon field, rather than from contributions by the Higgs mode and the Eliashberg effect. Our practical and explicit expression for the nonlinear conductivity formula makes our results accessible to a broad range of researchers.

We determine the macroscopic features of thermal transport in heterogeneous conductors by generalizing an exact, source-driven homogenization method originally developed for waves. The formulation accommodates random or periodic media of finite or infinite extent, with or without pores. Our homogenization shows that the effective heat flux and entropy are spatiotemporally nonlocal functions of both the effective temperature and its gradient, and that the emergent bianisotropic cross-couplings form an adjoint pair when the microscopic relations are self-adjoint. A spatially local approximation highlights how the homogenized diffusion equation can become hyperbolic due to temporal nonlocality, and that the medium’s thermal impedance can become direction dependent, as captured by the bianisotropic terms. In addition, we develop a retrieval method for one-dimensional deterministic composites, whose results reinforce our conclusions.

Acoustic metalenses that enable wide-incident-angle and high-efficiency focusing are in high demand for diverse applications, from underwater imaging to biomedical diagnostics. In this work, we introduce a design paradigm for an acoustic metalenses based on a quadratic phase profile, which can incorporate a synergistic combination of a central metasurface and a peripheral metagrating. By our integrating grating diffraction theory with phase engineering and applying an intelligent optimization algorithm, our design achieves high-efficiency, ultrawide-angle focusing of underwater sound across a continuous angular range from 0\ifmmode^\circ\else\textdegree\fi{} to \ifmmode\pm\else\textpm\fi{}85\ifmmode^\circ\else\textdegree\fi{}, with an average efficiency of 31.72%. Thanks to its wavelength-scale thickness and distinct design principle, this metalens provides a compact platform suitable for integration into advanced acoustic systems with complex functional requirements.

Tunable-barrier dynamic quantum dots are known to generate very accurate single-electron-based currents and can be used as a source of single-electron wave packets for use in quantum metrology, sensing, or information processing. To realize their full technological potential, it is desirable to maximize their frequency of operation to increase the current; however, it has been observed that the mechanism of electron transfer across the quantum dot consistently breaks down for gigahertz frequencies, and this remains unexplained. Here, we present an analysis technique, combined with detailed modeling, to present a mechanism of high-frequency breakdown in this class of quantum dots as a rapidly imparted momentum impulse. Such understanding aids future design and operation protocols, allowing their use in high-frequency and real-time quantum measurements and technologies.