Tremendous progress in experimental quantum optics in recent decades has enabled the advent of quantum technologies, one of which is quantum communication. Aimed at novel methods for more secure or more efficient information transfer, quantum communication has developed into an active field of research and proceeds toward full-scale implementations and industrialization. Continuous-variable methods of multiphoton quantum state preparation, manipulation, and coherent detection, as well as the respective theoretical tools of phase-space quantum optics, offer the possibility of making quantum communication efficient, applicable, and accessible, thus boosting the development of the field. The methodology, techniques, and protocols of continuous-variable quantum communication are reviewed, from the first theoretical ideas through milestone implementations and recent developments. The review covers quantum key distribution as well as other quantum communication schemes that are suggested on the basis of continuous-variable states and measurements.

Continuous gravitational waves from rapidly rotating neutron stars are on the new frontiers of gravitational-wave astrophysics and have strong connections to electromagnetic astronomy, nuclear astrophysics, and condensed matter physics. This Colloquium surveys prospects for the detection of continuous gravitational waves from various neutron star populations, especially when aided by electromagnetic observations. Although there are caveats, current theories and observations suggest that the first detections are likely with planned improvements to current detectors, and that many are likely with next-generation detectors such as Cosmic Explorer and the Einstein Telescope. This Colloquium also surveys what can be learned from these signals, each of which will contain more cycles than all the compact binary mergers ever detected. Since continuous gravitational-wave emission mechanisms depend on aspects of neutron star physics, such as crustal elasticity, that are not well constrained by current astronomical observations and physical experiments, their detection can tell us a great deal that is new about extreme matter. Even more can be learned by combining gravitational-wave observations with data from the Square Kilometre Array, the Next Generation Very Large Array, the Five-hundred-meter Aperture Spherical Telescope, and other electromagnetic detectors operating in the next-generation era.

Three important driving forces for creating qualitatively new phases in quantum materials are the topology of the materials’ electronic band structures, frustration in the electrons’ motion or magnetic interactions, and strong correlations between their charge, spin, and orbital degrees of freedom. In few material systems do all of these aspects come together to contribute on an equal footing to stabilize new electronic states with unprecedented properties; however, the search for such systems can be guided by models of configurational motifs or key sublattices that can host such physics. One of the most fascinating structural motifs for realizing this rich interplay of frustration, electronic topology, and electron correlation effects is the kagome lattice. This review provides an overview of the theoretical underpinnings driving the physics of kagome lattices and a subsequent discussion on experimental progress in realizing novel states enabled by kagome networks in crystalline materials. Different material classes are discussed, with an emphasis on the phenomenologies of their electronic states and how they map to interactions arising from their kagome lattices.

A key problem in atmospheric physics is to quantitatively understand the processes controlling the formation of precipitation. In clouds consisting of only liquid water (no ice), there is a bottleneck between the initial activation and growth of cloud droplets by vapor condensation and the subsequent growth to form drizzle or rain through the collision and coalescence of cloud droplets. The precipitation bottleneck problem is the context for this Colloquium. Convection-cloud chambers are experimental tools that allow aerosol-cloud-precipitation interactions to be investigated under controlled laboratory conditions. The Colloquium explores the governing physics for cloudy Rayleigh-Bénard convection, detailing the thermodynamic, turbulence, and microphysical processes that underlie cloud formation and evolution. Mean-field and stochastic mathematical models are presented to capture the effects of turbulence, water-vapor supersaturation, and droplet growth. Mechanisms that promote broadening of the droplet size distribution are emphasized because they are expected to contribute to overcoming the condensation-to-coalescence bottleneck problem. Connections between laboratory experiments and atmospheric cloud processes are made using computational models that allow chamber observations to be scaled up to real-world conditions. Simulations of cloudy Rayleigh-Bénard convection are compared with measurements to validate the representation of microphysical processes, including fluctuations in supersaturation and droplet growth. Additional topics, such as the study of mixed-phase clouds, aerosol-cloud interactions, and the role of turbulent entrainment, are explored, emphasizing the versatility of the convection-cloud chamber. The Colloquium concludes with a discussion of future directions, including the development of convection-cloud chambers with larger vertical extents, mixed-phase capabilities, and applications to planetary atmospheres.

Complex systems are composed of many particles or agents that move and interact with one another. In most real-world applications, these systems involve a varying number of particles or agents that change owing to interactions with the environment or their internal dynamics. The underlying mathematical framework to model these systems must incorporate the spatial transport of particles or agents and their interactions, as well as changes to their copy numbers, all of which can be formulated in terms of stochastic reaction-diffusion processes. However, the standard probabilistic representation of these processes can be overly complex because of the combinatorial aspects arising from the nonlinear interactions and varying particle numbers. This review addresses the main field theory representations of stochastic reaction-diffusion systems, which handle these issues “under the hood.” To begin, the focus is on bringing techniques familiar to theoretical physicists—such as second quantization, Fock space, path integrals, and quantum field theory—back into the classical domain of reaction-diffusion systems. It is demonstrated how various field theory representations, which have evolved historically, can be unified under a single basis-independent representation. Existing quantum-based methods and notation are then extended to work directly on the level of the unifying representation, and it is illustrated how they can be used to consistently obtain previous known results in a more straightforward manner, such as through numerical discretizations and relations between model parameters at multiple scales. Throughout, the review contextualizes how these representations mirror well-known models of chemical physics depending on their spatial resolution, as well as the corresponding macroscopic (large copy-number) limits. The framework presented here may find applications in a diverse set of scientific fields, including physical chemistry, theoretical ecology, epidemiology, game theory, and socioeconomic models of complex systems, specifically in the modeling and multiscale simulation of complex systems with varying numbers of particles or agents. The presentation is done in a self-contained educational and unifying manner such that it can be followed by researchers across several fields.

Current, ground-based gravitational wave detectors were designed to detect gravitational waves from two primary sources: compact-binary coalescences and core collapse supernovae. Gravitational waves from the former have been detected, but we await the first detection of gravitational waves from the latter. Current theory indicates that the majority of core collapse supernovae are neutrino driven. In rare cases involving significant progenitor rotation, large initial magnetic fields, and the alignment of the two, they may be driven by magnetohydrodynamic stresses. This Colloquium focuses on neutrino-driven core collapse supernovae. Significant progress has been made in the past decade in core collapse supernova theory, culminating in sophisticated three-dimensional simulations and the delineation of key components of the central engine. With that, predictions of gravitational wave emission from core collapse supernovae have become sophisticated as well, and connections between components of the emission and their dynamical sources can now be made. As a result, a core collapse supernova gravitational wave detection promises to provide a view deep into the central engine that can be used to validate models and confirm (or fail to confirm) predictions. Core collapse supernovae are rarer and weaker sources of gravitational waves than compact-binary coalescences. Paralleling modeling efforts, significant effort has been necessarily expended to develop customized and optimized gravitational wave detection strategies and algorithms specifically designed for core collapse supernovae. These strategies rely on the multimessenger detection of gravitational waves, neutrinos, especially the electron-neutrino burst, and electromagnetic counterparts associated with, for example, shock breakout. Moreover, collaboration between core collapse supernova modelers and gravitational wave astronomers, given researchers’ deeper understanding of core collapse supernova gravitational wave sources and the increasingly sophisticated data analysis algorithms available, has significantly advanced core collapse supernova parameter estimation. In the event of a detection, the extraction of critical information about the remnant proto–neutron star, such as its mass, and potentially about the high-density, neutron-rich nuclear equation of state, specifically, the nucleon-nucleon interaction, may be possible as a result. Models, detection strategies, and parameter estimation are advancing. A detection in current interferometers would advance core collapse supernova science by leaps and bounds, and next generation interferometers promise even more.

The past two decades have witnessed tremendous progress in understanding the properties of neutron stars, their maximum mass and radii, and the properties of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations have provided novel constraints on neutron-star structure that are intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is broad and the system spans many orders of magnitude in density. Theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities are reviewed, and the related consequent properties of neutron stars are discussed. How the equation of state at low densities can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments is described. Neutron-star observations, with a particular emphasis on information provided by gravitational-wave signals and electromagnetic observations, are reviewed. Finally, future challenges and opportunities in the field are discussed.

Owing to its fundamental principles, quantum theory holds the promise to enhance the security of modern cryptography, from message encryption to anonymous communication, digital signatures, online banking, leader election, one-time passwords, and delegated computation. While quantum key distribution (QKD) has already enabled secure key exchange over hundreds of kilometers, a myriad of other quantum-cryptographic primitives are being developed to secure future applications against quantum adversaries. This review surveys the theoretical and experimental developments in quantum cryptography beyond QKD over the decades, along with advances in secure quantum computation. It provides an intuitive classification of the main quantum primitives and their security levels, summarizes their possibilities and limits, and discusses their implementation with current photonic technology.

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of high-quality single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost macroscopic dimensions, while the advent of special-purpose massive computers—by the Janus Collaboration—enables dynamical simulations that approach experimental timescales and length scales. This review provides an account of the quantitative convergence of these two avenues of research, with precise experimental measurements of the expected scaling laws and numerical reproduction of classic experimental results, such as memory and rejuvenation. The review opens with an examination of the defining spin-glass properties—randomness and frustration—and their experimental consequences. These apparently simple characteristics are shown to generate rich and complex physics. Models are introduced that enable quantitative dynamical descriptions, either analytically or through simulations. The many theoretical pictures of the low-temperature phase are reviewed. After a summary of the main numerical results in equilibrium, paying particular attention to the concept of temperature chaos, this review examines off-equilibrium dynamics in the absence of a magnetic field and shows how it can be related to the structure of the equilibrium spin-glass phase through the fluctuation-dissipation relations. The nonlinear response at a given temperature is then developed, including experiments and scaling in the vicinity of the spin-glass transition temperature $T_{\mathrm{g}}$. The consequences of temperature change—including temperature chaos, rejuvenation, and memory—are reviewed. The interpretation of these phenomena requires several length scales relevant to dynamics to be identified, which, in turn, generates new insights. Finally, issues for future investigations are introduced, including what is to be “nailed down” theoretically, why the Ising Edwards-Anderson model is so successful at modeling spin-glass dynamics, and experiments yet to be undertaken.

The cosmological principle, which states that the Universe is homogeneous and isotropic (when averaged on large scales), is the foundational assumption of Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies such as the current standard $\mathrm{\Lambda }$-cold-dark-matter ($\mathrm{\Lambda }\mathrm{CDM}$) model. This simplification yields an exact solution to the Einstein field equations that relates space and time through a single time-dependent scale factor, which defines cosmological observables such as the Hubble parameter and the cosmological redshift. The validity of the cosmological principle, which underpins modern cosmology, can now be rigorously tested with the advent of large, nearly all-sky catalogs of radio galaxies and quasars. Surprisingly, the dipole anisotropy in the large-scale distribution of matter is found to be inconsistent with the expectation from kinematic aberration and Doppler-boosting effects in a perturbed FLRW universe, which is the standard interpretation of the observed dipole in the cosmic microwave background (CMB). Although the matter dipole agrees in direction with that of the CMB dipole, it is anomalously larger, demonstrating either that the rest frames in which matter and radiation appear isotropic are not the same or that there is an unexpected intrinsic anisotropy in at least one of them. This discrepancy now exceeds $5\sigma$ in significance. Recent findings are reviewed, as are the potential biases, systematic issues, and alternate interpretations that have been suggested to help alleviate the tension. The Colloquium’s conclusion is that the cosmic dipole anomaly poses a serious challenge to FLRW cosmology, and the standard $\mathrm{\Lambda }\mathrm{CDM}$ model in particular, as an adequate description of our Universe.

Self-interacting dark matter (SIDM) arises generically in scenarios for physics beyond the standard model that have dark sectors with light mediators or strong dynamics. The self-interactions allow energy and momentum transport through halos, altering their structure and dynamics relative to those produced by collisionless dark matter. SIDM models provide a promising way to explain the diversity of galactic rotation curves, and they form a predictive and versatile framework for interpreting astrophysical phenomena related to dark matter. This review provides a comprehensive explanation of the physical effects of dark matter self-interactions in objects ranging from galactic satellites (dark and luminous) to clusters of galaxies and the large-scale structure. The second major part describes the methods used to constrain SIDM models, including current constraints, with the aim of advancing tests with upcoming galaxy surveys. This part also provides a detailed review of the unresolved small-scale structure-formation issues and concrete ways to test simple SIDM models. The review is rounded off by a discussion of the theoretical motivation for self-interactions, degeneracies with baryonic and gravitational effects, extensions to the single-component elastic-interaction SIDM framework, and future observational and theoretical prospects.

Quantum spin liquids (QSLs) represent exotic states of matter where quantum spins interact strongly yet evade long-range magnetic order down to absolute zero. Characterized by nonlocal quantum entanglement and the resultant fractionalized excitations, QSLs have emerged as a frontier in condensed matter physics, bolstered by the recent identification of several candidate materials. This field holds profound implications for understanding strong correlations, topological order, and emergent phenomena in quantum materials. Among them, the spin-$1/2$ Kitaev honeycomb model, featuring bond-directional Ising interactions, provides a rare exactly solvable QSL example. Its ground state is a topological QSL with spin degrees of freedom fractionalized into emergent Majorana fermions. Under an applied magnetic field, the Kitaev QSL transitions to a topologically nontrivial chiral spin liquid state with non-Abelian anyons, offering potential resources for topological quantum computation. The non-Abelian character of these anyons in the Kitaev QSL demonstrates a profound connection to certain topological superconductors and even-denominator fractional quantum Hall states. Since the theoretical prediction that the Kitaev model could manifest in spin-orbit-coupled materials such as honeycomb iridates and ruthenates, research has focused on identifying candidate compounds. In particular, experimental evidence suggests spin fractionalization and topological phenomena akin to the Kitaev model in the spin-orbit Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$. However, results and interpretations remain actively debated. This review begins with an exploration of QSLs in other systems, followed by a comprehensive survey of existing studies on Kitaev candidate materials, with a particular focus on $\alpha \text{−}{\mathrm{RuCl}}_3$. Rather than offering conclusive remarks, the review aims to inspire future research by examining several key aspects of the current literature and perspectives.

Perceptions and actions, thoughts and memories result from coordinated activity in hundreds or even thousands of neurons in the brain. It is an old dream of the physics community to provide a statistical mechanics description for these and other emergent phenomena of life. These aspirations appear in a new light because of developments in our ability to measure the electrical activity of the brain, sampling thousands of individual neurons simultaneously over hours or days. The progress that has been made in bringing theory and experiment together is reviewed, with a focus on maximum entropy methods and a phenomenological renormalization group. These approaches have uncovered new, quantitatively reproducible collective behaviors in networks of real neurons and provide examples of rich parameter-free predictions that agree in detail with experiments.

Weak scale supersymmetry (SUSY) is highly appropriate in that it provides a technically natural ’t Hooft solution to the gauge hierarchy problem. However, recent strong limits from superparticle searches at LHC Run 2 may exacerbate the so-called little hierarchy problem, which is a matter of practical naturalness: why is $m_{\mathrm{weak}}\ll m_{\mathrm{soft}}$? Recent LHC and weakly interacting massive particle dark matter search bounds are reviewed, as is their impact on a variety of proposed SUSY models: gravity, gauge, anomaly, mirage, and gaugino mediation, along with dark matter proposals such as well-tempered neutralinos. The naturalness question is addressed. Also discussed is the emergence of the string landscape at the beginning of the 21st century and its impact on expectations for SUSY. Generally, the string landscape statistically prefers large soft SUSY breaking terms but is subject to the anthropic requirement that the derived value of the weak scale for each pocket universe within the greater multiverse lies within the Agrawal-Barr-Donoghue-Seckel window of values. This stringy natural approach implies that $m_h\sim 125\mathrm{GeV}$, more often than not with sparticles beyond or well-beyond present LHC search limits. Detailed reach calculations of the High-Luminosity LHC (HL-LHC) for nonuniversal Higgs mass models, which present perhaps the most plausible realization of SUSY from the string landscape, are reviewed. In contrast to conventional wisdom, from a stringy naturalness point of view, the search for SUSY at LHC has only just begun to explore the interesting regimes of parameter space. How nonuniversal Higgs models could be differentiated from other expressions of natural SUSY, such as natural anomaly mediation and natural mirage mediation at HL-LHC, is commented upon.

Internal conversion is a vital vibronic loss mechanism that competes with all other photophysical mechanisms, and a plethora of information on the subject is available in the literature. However, these data are often difficult to penetrate owing to their complexity. In addition, owing to the sheer number of methods, it is often difficult to understand which method is better for certain systems. This comprehensive review on the state of the art explores the history of internal conversion and provides context to its evolution up to modern quantum chemistry. The most prevalent methods used to study atomic systems, as well as where they rise and they fall, are highlighted. Each method and the corresponding results are noted in a simplified manner, and information is threaded together to elucidate how everything is related. This tapestry illustrating the ups and downs of internal conversion will aid researchers in their study of new and innovative materials and provides a vital comparison of methods not easily gained.

In stars that lie on the main sequence in the Hertzsprung-Russell diagram, like our Sun, hydrogen is fused to helium in a number of nuclear reaction chains and series, such as the proton-proton chain and the carbon-nitrogen-oxygen cycles. Precisely determined thermonuclear rates of these reactions lie at the foundation of the standard solar model. This review, the third decadal evaluation of the nuclear physics of hydrogen-burning stars, is motivated by the great advances made in recent years by solar neutrino observatories, putting experimental knowledge of the proton-proton ($pp$)-chain neutrino fluxes in the few-percent precision range. The basis of the review is a one-week community meeting held in July 2022 in Berkeley, California, and many subsequent digital meetings and exchanges. The relevant reactions of solar and stellar hydrogen burning are reviewed here from both theoretical and experimental perspectives. Recommendations for the state of the art of the astrophysical $S$ factor and its uncertainty are formulated for each of them. Several other topics of paramount importance for the solar model are reviewed as well: recent and future neutrino experiments, electron screening, radiative opacities, and current and upcoming experimental facilities. In addition to reaction-specific recommendations, general recommendations are also formed.

To solve difficult computational tasks, artificial neural networks need to construct appropriate internal representations by adapting the weights on their connections in the direction that improves performance. In the 1980s, there were two promising techniques for computing the gradients required to adapt the weights. One technique was backpropagation, which is now used in almost all artificial intelligence systems. The other was the Boltzmann machine learning algorithm, which is no longer used. After describing two of the major successes of backpropagation, this Nobel Lecture explains the Boltzmann machine learning algorithm, which uses a property of the Boltzmann distribution to compute gradients in an elegant and unexpected way.

The study of nonequilibrium phenomena in interacting lattice systems can provide new perspectives on correlation effects and information on metastable states of matter. Mott insulators are a promising class of systems for nonequilibrium studies since they exhibit exotic phenomena and complex phase diagrams upon doping and because a large Mott gap provides protection against fast thermalization and heating after photoexcitations. One can thus expect the emergence of interesting nonlinear responses, transient states, and photoinduced phases in Mott systems. This review provides a comprehensive overview of the current understanding of photoexcited Mott insulators by discussing excitation protocols, nonlinear optical responses, the underlying mechanisms governing photocarrier dynamics, and the pathways leading to photoinduced metastable states. The review focuses on recent theoretical progress, identifies the relevant underlying concepts, and links them to experimental observations. The review starts with a general discussion of field-induced nonequilibrium setups and an overview of key experiments that revealed characteristic properties of photoexcited Mott states, proceeds with an overview of the theoretical tools that have been developed to investigate these strongly correlated nonequilibrium states, and then analyzes Mott insulators driven out of equilibrium by static electric fields, periodic fields, and short laser pulses. The appearance of nonthermal electronic orders in photoexcited Mott systems, including nonthermal spin and orbital orders, $\eta$-pairing states, and novel types of excitonic orders, is also discussed.

Competing magnetic interactions may stabilize smooth magnetization textures that can be characterized by a topological winding number. Such textures, which are spatially localized within a two-dimensional plane, are commonly known as skyrmions. On the classical level, their significance for fundamental science and their potential for applications, ranging from spintronic devices to unconventional computation platforms, have been intensively investigated in recent years. This Colloquium considers quantum effects associated with skyrmion textures: their theoretical origins, the experimental and material challenges associated with their detection, and the promise of exploiting them for quantum operations. Starting with classical skyrmions, this Colloquium discusses their magnon and electron excitations and shows how hybrid architectures offer new platforms for engineering quantum orders, including topological superconductivity. The focus then moves to the quantization of the skyrmion texture itself and the formulation of long-time skyrmion dynamics in terms of collective coordinates. Discussed next are the quantization of helicity and phenomena of macroscopic quantum tunneling, key concepts that fundamentally distinguish quantum skyrmions from their classical counterparts. Looking ahead, material classes suitable for the realization of skyrmions in quantum spin systems are proposed and device architectures are identified with the promise of achieving quantum operations. The Colloquium closes by addressing the advances in experimental methods that will be prerequisites for resolving the quantum aspects of topological spin patterns, sensing their local dynamical response, and achieving their predicted functionalities in magnetic systems.