Space- and ground-based observatories are discovering exoplanetary systems and new worlds without bound. Understanding the composition, evolution, and implications of these compact objects requires one to unlock the nature of their interiors, where conditions reach millions (hundreds of gigapascals) to billions (hundreds of terapascals) of atmospheres in pressure owing to the crushing influence of gravity. These conditions span from chemical pressures, $\sim 100\mathrm{GPa}={10}^6\text{atm}$, where external forces overwhelm chemical forces, to atomic pressures, $\sim 30\mathrm{TPa}=3\times {10}^8\text{atm}$, which disrupts the shell structure of atoms, to the incipient threshold of thermonuclear fusion at $\sim 30\mathrm{PPa}=3\times {10}^{11}\text{atm}$, which is roughly the upper bound interior pressure for giant planets. Understanding matter at such conditions is just now becoming possible with today’s high-energy-density facilities, both high-energy lasers and pulsed-power facilities. Many discoveries have already reshaped our understanding and intuition of extreme matter including the dramatic density-temperature dependence for hydrogen metallization, the phase separation of helium and hydrogen in the deep interior conditions of Jupiter and Saturn, the superionic phases of water and ammonia at the deep interior conditions of Uranus and Neptune, the formation and persistence of diamond upon compression of hydrocarbons, and the melting of ${\mathrm{SiO}}_2$ to a conducting-polymeric soup making the formation of magma oceans in terrestrial systems possible. This Colloquium describes a suite of laser-induced dynamic compression experiments that are currently underway to characterize the properties of matter under these uncharted extreme conditions together with some unexpected discoveries and planetary implications.

In 2021 the Nobel Prize in Physics was awarded in part to Syukuro Manabe, a climate physicist, “for the physical modeling of Earth’s climate, quantifying variability and reliably predicting global warming.” The Colloquium introduces the audience of Reviews of Modern Physics to climate as a complex system, Manabe’s research, and his legacy of using a hierarchy of climate models across a range of physical complexity to simulate and understand global warming. The Colloquium reviews Manabe’s work with his colleagues from the late 1960s to the early 1990s. During this time Manabe and his colleagues developed a hierarchy of climate models across a range of physical complexity and used them to simulate and understand the temperature response to increased carbon dioxide (${\mathrm{CO}}_2$) concentration in the atmosphere. The Colloquium discusses Manabe’s approach of (1) applying physical constraints to large-spatial scales while making simplifying assumptions about small-scale physics, (2) predicting the temperature response to increased ${\mathrm{CO}}_2$ as physical complexity was added through dimensionality, and (3) understanding the emergent temperature responses by connecting them to the underlying physics that was added. It highlights that this approach was key to reliably predicting—before they were observed—global-mean surface warming, upper-level cooling, that the Arctic is warming the most, that land is warming more than the ocean, and delayed Southern Ocean warming. Furthermore, Manabe and his colleagues showed how uncertainty due to assumptions about small-scale physics could be quantified by holding physical processes (water vapor, clouds, etc.) fixed, allowing for a clear understanding of their impact. Manabe’s legacy is more important than ever as we enter a unique time in climate science where additional signals have emerged from the noise in observations, including both successful predictions and discrepancies. Furthermore, complex new tools have emerged, such as machine learning emulators and kilometer-scale climate models, that benefit from Manabe’s reductionist, hierarchical approach.

Quantum geometry, which describes the geometry of quantum wave functions, plays a crucial role across a wide range of physics, including quantum information, subatomic physics, and cosmology. In particular, the quantum geometry of Bloch wave functions has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components: the quantum metric (the real part) and the Berry curvature (the imaginary part). While Berry curvature gained prominence through its manifestation in the intrinsic anomalous Hall effect, recent advances have revealed equally significant effects arising from the quantum metric. This includes its signatures in nonlinear transport, superfluid density of flat-band superconductors, and nonlinear optical responses. These advances underscore how quantum geometry is reshaping our understanding of condensed matter systems, with far-reaching implications for future technologies. This review surveys recent progress in the field, focusing on both foundational concepts and emergent phenomena in transport and optics—with a particular emphasis on the pivotal role of the quantum metric.

Opinion dynamics, the study of how individual beliefs and collective public opinion evolve, is a fertile domain for applying the framework of statistical physics to complex social phenomena. Like physical systems, societies exhibit macroscopic regularities arising from numerous localized interactions, leading to an outcome such as consensus or fragmentation. Opinion dynamics has grown from a fringe interest to an active field of physics, attracting interdisciplinary methods from computer science, economics, and sociology. This review covers the ongoing rapid progress in the field, driven by an unprecedented surge in available large-scale behavioral data, bridging the inherently interdisciplinary literature. The review begins with essential concepts and definitions, encompassing the nature of opinions and their microscopic and macroscopic dynamics. This foundation leads to an overview of empirical research, from lab experiments to large-scale data analysis, which informs and validates models of opinion dynamics. Models are then categorized by the macroscopic phenomena they describe (for example, consensus, polarization, and echo chambers) and the microscopic mechanisms of opinion change they encode (for example, homophily and assimilation). The review covers common analytical and computational tools for studying these models, such as stochastic processes, exact and approximate treatments, simulation techniques, and optimization methods. Finally, the review explores emerging frontiers, including the ongoing effort to establish a closer connection between empirical data and models and the recent developments in building artificial intelligence agents as test beds for novel social phenomena. By systematizing terminology across disciplines and emphasizing analogies with traditional physics, the review highlights connections between theoretical models, concepts in social psychology, and observable societal phenomena. This review aims to consolidate current knowledge, provide a robust theoretical foundation, and shape future research directions in opinion dynamics.

The current status of security proofs for practical decoy-state quantum key distribution is reviewed using the Bennett-Brassard 1984 protocol, with a focus on optical implementations with weak coherent pulses and threshold photodetectors. The primary aim of this review is to highlight gaps in the existing literature. Such gaps may arise, for instance, from mismatches between detailed protocol specifications and proof-technique elements, reliance on earlier results based on different assumptions, or protocol choices that overlook real-world requirements. While substantial progress has been made, this overview draws attention to the details that still demand careful attention.

This review provides a comprehensive survey of theoretical and experimental studies of the properties of polarons formed by mobile impurities that strongly interact with quantum many-body systems. A unified perspective is presented on the universal concepts and theoretical techniques used to characterize polarons in two distinct platforms, ultracold atomic gases and atomically thin transition-metal dichalcogenides, which are linked by many deep parallels. The review discusses polarons in both fermionic and bosonic environments, highlighting their similarities and differences, including the intricate interplay between few- and many-body physics. Various kinds of polarons with long-range interactions or in magnetic backgrounds are discussed, and the theoretical and experimental progress toward understanding interactions between polarons is described. The review outlines how polaron physics, regarded as the low-density limit of quantum mixtures, provides fundamental insights regarding the phase diagram of complex condensed matter systems. Furthermore, how polarons may serve as sensors of complex many-body physics is described. The review highlights open problems, identifies new research directions, and provides a comprehensive framework for this rapidly evolving research field.

Recent advances in molecular cooling have enabled the realization of strongly dipolar Bose-Einstein condensates (BECs) of molecules, and BECs of many different molecular species may become experimentally accessible in the near future. Here the unique properties of such BECs and the new insights they may offer into dipolar quantum fluids and many-body physics are explored. The Colloquium examines which parameter regimes can realistically be achieved using currently available experimental techniques, discusses how to implement these techniques, and outlines which molecular species are particularly well suited to exploring exotic new states of matter. The Colloquium further determines how state-of-the-art beyond-mean-field theories, originally developed for weakly dipolar magnetic gases, can be pushed to their limits and beyond, and what other long-standing questions in the field of dipolar physics may realistically come into reach using molecular systems.

Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of $\mathrm{\mu }\mathrm{eV}$. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. Their dynamical and thermodynamic properties are discussed in one, two, and three dimensions, and recent investigations into their out-of-equilibrium behavior are reviewed. An outlook on future directions for exploring novel condensed-matter phenomena with trapped-ion crystals, as well as for exploiting these features for scientific and technical applications, is provided.

As the study of active matter has developed into one of the most rapidly growing subfields of condensed matter physics, more and more kinds of physical systems have been included in this framework. While the word ‘active’ is often thought of as referring to self-propelled particles, it is also applied to a large variety of other systems. Developing novel forms of active matter, as attempted, for example, in the framework of quantum active matter, requires a clear idea of what active matter is. Active matter is defined here based on commonly employed criteria as a system that is driven out of equilibrium by a local energy influx and that generates motion and/or forces whose direction is not determined by external fields. The limits of such a definition and to what extent a unified definition of ‘active matter’ is still possible are also critically discussed. Moreover, we discuss the definition of an ‘active field theory,’ where ‘active’ is used as an attribute of a theoretical model rather than of a physical system. We show that the usage of the term ‘active’ requires agreement on a description that neglects certain degrees of freedom. The meaning of this word is discussed both in general terms and via the specific examples of chemically driven particles, particles with nonreciprocal interactions, intracellular phase separation, and quantum active matter.

The confinement of the electromagnetic near field at the atomically sharp apex of a scanning tunneling microscope (STM) tip enables the investigation of light-matter interactions with atomic-scale resolution. This marks a paradigm shift in the exploration of optical properties, reaching down to the scale of individual molecules. The combination of the optical response with the electronic transport properties of molecules in these STM junctions enables the acquisition of fluorescence spectral information from the molecules, including their intensity, spectral shifts, and broadenings, with exquisite spatial precision. Here an overview of recent developments in STM-induced luminescence is provided, together with the main concepts underlying the light-emission process. The review discusses in detail the electrical excitation mechanism and the interactions of the probed molecules with electromagnetic fields localized at the tip apex, examines recent progress in the field, including optically driven processes, and provides perspectives for future directions in hyperresolution microscopy.

The center of the Galaxy is a prominent source in x-rays and gamma rays. The study of its high-energy (HE) emission is crucial to understanding the physical phenomena taking place in this dense and extreme environment, where the closest supermassive black hole (SMBH) to us, Sagittarius ${\mathrm{A}}^{\star }$, is lurking nearly invisible today in most of the energy spectrum. These phenomena are probably common to other galactic nuclei and may explain the feedback processes between nuclear regions and galaxies, which are so important for the overall evolution of the Universe. The Galactic Center HE emission is complex and consists of both thermal and nonthermal radiation produced by compact and extended sources, surrounded by more diffuse components. All these objects and media are interacting with each other in the narrow and dense Central Molecular Zone (CMZ). Some of them also show relevant extensions toward the Galactic poles, indicating energetic outflows that seem to link the center to the recently observed large Galactic polar structures. In spite of the fundamental advances obtained over the past 25 years with the most sensitive x-ray and gamma-ray observatories, several questions remain open to investigation. The main observational results and the open issues on the high-energy diagnostics of the Galactic nuclear activity are reviewed, with a focus on processes that take place in the CMZ, and, in particular, a discussion on the role of present and past SMBH activities in powering this region and possibly the entire Galaxy.

Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems serves as motivation for investigating the feasibility of solving linear system problems using quantum computers. This review surveys the main advances in quantum linear system algorithms, together with some applications. The main ideas behind certain algorithms for the quantum linear system problem are summarized and analyzed. The analysis begins by examining the Harrow-Hassidim-Lloyd (HHL) solver. The review first notes its limitations and reliance on computationally expensive quantum methods then highlights subsequent research efforts that have aimed to address these limitations and optimize run-time efficiency and precision via various paradigms. A particular focus is placed on the post-HHL enhancements that have paved the way toward optimal lower bounds with respect to error tolerance and condition number. In the process a taxonomy that categorizes these studies is proposed. Furthermore, by contextualizing these developments within the broader landscape of quantum computing, the review explores the foundational work that has inspired and informed their development, as well as subsequent refinements. Some of the open problems regarding the optimal linear solver efficiency are highlighted. Finally, the potential applications of these algorithms in differential equations, machine learning, and many-body physics are discussed.

This review consolidates experimental, theoretical, and simulation work examining the behavior of high-field devices and the fundamental process of vacuum arc initiation, commonly referred to as breakdown. Detailed experimental observations and results relating to a wide range of aspects of high-field devices, including conditioning, field and temperature dependence of the breakdown rate, and the ability to sustain high electric fields as a function of device geometry and materials, are presented. The different observations are then addressed theoretically and with simulation, capturing the sequence of processes that lead to vacuum breakdown and explaining the major observed experimental dependencies. The core of the work described in this review was carried out by a broad multidisciplinary collaboration in an over a decade-long program to develop high-gradient, $100\mathrm{MV}/\mathrm{m}$–range, accelerating structures for the Compact Linear Collider project, a possible future linear-collider high-energy physics facility. Connections are made to the broader linear-collider, high-field, and breakdown communities.

Magnetism has played a central role in the long and rich history of modern condensed matter physics, with many foundational insights originating from theoretical studies of two-dimensional (2D) spin systems. The discovery of 2D van der Waals (vdW) magnets has revolutionized this area by providing real, atomically thin magnetic systems for experimental investigation. Since the first experimental reports of antiferromagnetic vdW insulators in 2016—followed by studies on ferromagnetic vdW systems in 2017—the field has witnessed rapid and expansive growth, with more than two dozen vdW magnetic materials now identified, including both ferromagnets and antiferromagnets. This review presents a comprehensive overview of the major scientific and technological developments in this rapidly evolving field. These developments include experimental realizations of various 2D spin Hamiltonians, as well as unexpected phenomena such as magnetic excitons, Floquet-engineered states, and light-induced metastable magnetic phases. In parallel, 2D vdW magnets have shown significant promise in spintronics and related applications, offering a new platform for engineering quantum functionalities. This review traces the historical development of the field, synthesizes key milestones, and highlights its broader impact across condensed matter physics and materials science. The review concludes by outlining several promising directions for future research, charting a path forward in this vibrant and still rapidly growing area.

Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects (non-Markovianity), system-environment hybridization, and the necessity for accuracy beyond the Born-Markov approximation form particular challenges. Approaches to meet these challenges, originating from different fields such as hierarchical equations of motion, Lindblad-pseudomode formulas, chain-mapping approaches, quantum Brownian motion master equations, stochastic unravelings, and refined quantum master equations, have been introduced. This diversity, while indicative of the field’s relevance, has inadvertently led to a fragmentation that hinders cohesive advances and their effective cross-community application to current problems for complex systems. How are different approaches related to each other? What are their strengths and limitations? A systematic overview and a concise discussion are presented addressing these questions. This Colloquium makes use of a unified framework that conveniently allows different schemes to be linked and in turn may also catalyze further progress. In line with the state of the art, this framework is formulated not in a fully reduced space of the system but in an extended state space that, in a minimal fashion, includes effective reservoir modes. It offers a comprehensive understanding of existing methods, elucidating their physical interpretations, interconnections, and applicability.

The mechanical action of various kinds of waves has been recognized for several centuries. The first tide of scientific interest in wave-induced forces and torques emerged at the turn of the 20th century, with the development of wave theories and the concepts of wave momentum and angular momentum. A second surge occurred in the past several decades, driven by technological breakthroughs: the invention of lasers and the controlled generation of structured wave fields. This resulted in major discoveries, including optical trapping and manipulation of small particles, from atomic to micro sizes, as well as acoustic manipulation of larger particles, including biological cells and samples. Currently, radiation forces and torques underpin numerous applications: optical and acoustic tweezers, acoustofluidic sorting of biological cells, optomechanical systems operating in both classical and quantum regimes, solar sails, quantum simulators, volumetric displays, etc. This review presents a unifying perspective on optical and acoustic forces and torques acting on various particles, addressing both their theoretical foundations and their key applications. The approach used here relies on the universal connection between the local energy, momentum, and spin densities of wave fields and the principal forces and torques exerted on small particles. Moreover, important cases of nontrivial (for example, lateral and pulling) forces and complex (for example, chiral and anisotropic) particles are described. Also highlighted are significant experimental achievements involving optical and acoustic manipulation in structured wave fields. The aim of this review is to illuminate the common fundamental origins and close interconnections between the mechanical actions of optical and acoustic fields, thereby fostering a deeper understanding and advancing the development of optomechanical and acoustomechanical applications.

Recent years have seen significant advances, both theoretical and experimental, in our understanding of quantum many-body dynamics. Given this problem’s high complexity, it is surprising to observe that a substantial amount of this progress can be ascribed to exact analytical results. A key notion in these advances is space-time duality, in which the roles of space and time are exchanged to access relevant dynamical properties of quantum many-body systems. Dual-unitary circuits present a particularly fruitful implementation of this idea. These circuits constitute minimal models in which space and time are treated on an equal footing, yielding exactly solvable yet possibly chaotic evolution. They were the first in which current notions of quantum chaos could be analytically quantified; could allow for a full characterization of the dynamics of thermalization, scrambling, and entanglement (among others); and could be experimentally realized in current quantum simulators. Here dual unitarity and applications of space-time duality are reviewed.

The standard model of particle physics is a well-established theoretical framework, yet several unresolved issues remain that warrant further experimental and theoretical exploration. In the realm of quark physics, these issues include understanding the nature of quark confinement and elucidating the mechanism linking quarks and gluons to strongly interacting particles within the standard model theory, which may offer insights into the underlying physics mechanisms. These inquiries can be addressed through the study of hadrons produced at $e^{+}{e}^{-}$ collisions and decaying to open-charm meson pairs utilizing the capabilities of the BABAR, Belle, BESIII, and CLEO-c experiments, which have yielded valuable insights into nonstandard hadrons in recent decades. This Colloquium examines the contributions of $e^{+}{e}^{-}$ colliders from the BABAR, Belle, BESIII, and CLEO-c experiments to such studies in the past two decades and discusses future prospects for $e^{+}{e}^{-}$ collider experiments.

The projected reliance on nuclear energy worldwide in the coming decades demands a better understanding of the fundamental properties of the understudied late actinide elements from americium through californium. Many in situ high-pressure studies utilizing diamond-anvil cells were performed on metals, alloys, and binary compounds of these highly radioactive elements in the late 1900s and provided valuable insights into their electronic structures. At ambient conditions the $5f$ electrons of the late actinides are radially beneath the Rn core electrons, shielding them and making them unable to participate in bonding interactions. Under pressure, however, metals and alloys of Am–Cf undergo a Mott transition where the initially localized $5f$ electrons transition to an itinerant state and can contribute to bonding interactions. The area of high-pressure studies on Am–Cf has been reinvigorated over the past five years, expanding the scope to coordination complexes of these elements and employing spectroscopic techniques to probe $5f$ electronic structure. Complexes with ligands of various donor atoms have been synthesized and subjected to these high-pressure spectroscopic investigations to probe the influence of the hard-soft nature of the donor atom on the involvement of the $5f$ orbitals in bonding. The effects of donor atom as well as metal center identity on the degree of the $5f$ contribution to bonding are discussed.

The Arecibo Observatory was home to a unique sensitive geospace radar that probed Earth’s ionosphere—the ionized upper atmosphere—by scattering radio waves off free electrons. Thanks to the 305 m spherical dish, the radar at Arecibo was 20–50 times more sensitive than any other radar that has been used for geospace studies. Arecibo was more than one instrument: it was a multi-instrument facility that also included radars, an ionospheric modification facility, lidars, optical sensors, and satellite-based systems. This unique combination of instruments led to profound discoveries in geospace science, which are reviewed here. One major topic is ionospheric plasma physics via the study of plasma lines (a specific feature in the radar echo), which provided new insights, especially during experiments using high-power radio wave transmissions at very-high-frequency bands. Another is the ultraprecise measurements of the F-region electron concentration profiles in the ionosphere that revealed previously hidden photoelectron processes possible only because of the sensitivity of the incoherent scatter radar at the Arecibo Observatory. Nighttime plasma line detection has also offered clues about the coupling between the ionosphere and the magnetosphere. Other topics are discoveries from uniquely positioned radars operating in the same atmospheric volume and studies of atomic metals observed via lidar. A notable example is the highly sensitive lidar study of calcium ions (${\mathrm{Ca}}^{+}$) in the ionosphere.