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.

Over the past three decades, atomic-scale microscopy techniques (atom-probe tomography, scanning tunneling microscopy, and transmission electron microscopy) have played a significant role in the understanding of order- and disorder-related phenomena in compound semiconductors. The possibility of imaging and quantifying disorder in the direct space within a small and selected field of view, with atomic-scale spatial resolution, and the possibility of retrieving information on composition opened new perspectives and led to a new level of understanding in semiconductor physics. On the basis of results from the domain of III-V semiconductors, this review sketches a synoptic picture of the application of microscopy to the study of order and disorder and aims to establish a clear reference of methods for research facing order- and disorder-related issues in new semiconductor materials.

Novel interactions beyond the four known fundamental forces in nature (electromagnetic, gravitational, strong, and weak interactions) may arise due to “new physics” beyond the standard model, manifesting as a “fifth force.” This review focuses on spin-dependent fifth forces mediated by exotic bosons such as spin-0 axions and axionlike particles and spin-1 $Z^{\prime }$ bosons, dark photons, and paraphotons. Many of these exotic bosons are candidates to explain the nature of dark matter and dark energy, and their interactions may violate fundamental symmetries. Spin-dependent interactions between fermions mediated by the exchange of exotic bosons have been investigated in a variety of experiments, particularly at the low-energy frontier. Experimental methods and tools used to search for exotic spin-dependent interactions, such as atomic comagnetometers, torsion balances, nitrogen-vacancy spin sensors, and precision atomic and molecular spectroscopy, are described. A complete set of interaction potentials, derived based on quantum field theory with minimal assumptions and characterized in terms of reduced coupling constants, are presented. A summary of existing experimental and observational constraints on exotic spin-dependent interactions is given, in the process illustrating the current research landscape and promising directions of further research.

Universality is a powerful concept that enables qualitative and quantitative predictions to be made in systems with extensively many degrees of freedom. It finds realizations in almost all branches of physics, including in the realm of nonequilibrium systems. The focus of this review is on universality’s manifestations within a specific class of nonequilibrium stationary states: driven open quantum matter. Progress in this field is fueled by a number of increasingly prominent platforms ranging from light-driven quantum materials over synthetic quantum systems like cold atomic gases to the functional devices of the noisy intermediate-scale quantum era. These systems share the characteristic that, on the microscopic scale, they obey the laws of quantum mechanics, while detailed balance underlying thermodynamic equilibrium is broken owing to the simultaneous presence of Hamiltonian unitary dynamics and nonunitary drive and dissipation. The challenge is then to connect this microscopic physics to macroscopic observables and to identify universal collective phenomena that uniquely witness the breaking of equilibrium conditions, thus having no equilibrium counterparts. In the framework of a Lindblad-Keldysh field theory, on the one hand, this review discusses the principles delimiting thermodynamic equilibrium from driven open stationary states, and, on the other hand, it is shown how unifying concepts such as symmetries, the purity of states, and scaling arguments are implemented. Then presented are instances of universal behavior structured into three classes: new realizations of paradigmatic nonequilibrium phenomena, including a survey of first experimental realizations; novel instances of nonequilibrium universality found in these systems made of quantum ingredients; and genuinely quantum phenomena out of equilibrium, including in fermionic systems. Perspectives for future research on driven open quantum matter are also discussed.

The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially interesting in the quantum-mechanical domain. In this Colloquium several ideas are reviewed that indicate how multilevel quantum systems, also known as qudits, can be used for efficient realization of quantum algorithms, which are represented via standard qubit circuits. The focus in the Colloquium is on techniques for leveraging qudits for simplifying decomposition of multiqubit gates and for compressing quantum information by encoding multiple qubits in a single qudit. As discussed in the Colloquium, these approaches can be efficiently combined. This allows a reduction in the number of entangling (two-body) operations and the number of quantum information carriers used compared to straightforward qubit realizations. These theoretical schemes can be implemented with quantum computing platforms of various natures, such as trapped ions, neutral atoms, superconducting junctions, quantum light, spin systems, and molecules. The Colloquium concludes by summarizing a set of open problems whose resolution will be an important further step toward employing universal qudit-based processors for running qubit algorithms.

Stars are slowly developing objects; the lifetimes of the different burning phases are determined by the strength of nuclear reactions, which in turn are defined by the quantum structure of the associated nuclei at the threshold and the respective reaction mechanisms. Stars, from the nuclear physics perspective, are cold environments where only a few of the key nuclear reactions have been measured at the actual stellar plasma temperatures. This is also the case for more dynamic astrophysical phenomena from the big bang to stellar explosions. Most of the nuclear reaction rates are therefore based on theoretical extrapolations. A number of discrepancies between these predictions and the associated stellar signatures have been observed, and many may be due to low-energy or near-threshold quantum effects. These effects need to be understood in order to reliably model nuclear reaction processes, not only for stars but also for low-temperature plasma environments such as controlled magnetic or inertial confinement fusion systems, which operate in similar temperature regimes. This review summarizes the various theoretical techniques presently used for deriving reaction rates and discusses possible quantum effects that may impact the reaction cross section near the reaction threshold. These resemble enhanced single-particle and cluster structures near threshold and associated interference effects. New experimental techniques such as deep-underground accelerators or the study of transfer reactions to mimic the quantum-mechanical transition strength, the so-called Trojan horse method, provide ways to directly or indirectly probe the reaction features that determine the reaction rates at stellar energies. This is demonstrated on a number of key nuclear reactions for different nucleosynthesis environments. Finally, current inconsistencies between experimental predictions and observations are discussed.

Bounds on properties are useful in guiding design of heterogeneous materials and in understanding the distinction between effects that are physically reasonable and those that are not. Several bounds on physical properties can be exceeded by an appropriate choice of material. The reason is that the “proofs” of bounds contain either unstated assumptions about the material or assumptions that are couched in language that appears to be that of incontrovertible mathematics but that actually entails assumptions about the material. If those assumptions are relaxed, limits or bounds can be exceeded, as is demonstrated by analysis and experiments. For example, heat capacity, compressibility, electrical capacitance, and refractive index can be negative. Thermal expansion in composites can be larger or smaller than that of any constituent and can be negative. Materials and systems are known that are non-Hermitian or nonreciprocal. Currently, active fields of endeavor have arisen from such conceptual sources. Research efforts have led to the development of new materials and new classes of materials.

We report the 2022 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council (CODATA). The recommended values can also be found at https://physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through December 31, 2022. A discussion of the major improvements as well as inconsistencies within the data is given.

The study of gas bubble dynamics in liquids is justified by the numerous applications and natural phenomena where this two-phase flow is encountered. Gas bubbles move as forces are applied to them; their dynamics are full of nuances that need to be addressed carefully. Since the mass of gas bubbles is practically negligible, in comparison to that of the surrounding liquid, their reaction to the fluid is controlled by the added mass acceleration and is thus impacted by all the forces arising from the fluid action. Furthermore, since their surface can be deformed by the same forces acting on them, their shape may change, leading to changes in their resistance to move and the drag force and therefore affecting their speed and their interaction with the surrounding flow, which is often turbulent. The liquid rheology, as well as its surfactant content, can also affect the bubble shape and motion. Understanding these issues, in addition to the effect of interactions with other bubbles, walls, and nonuniform flows, provides sufficient elements to model and predict bubble behavior through the solution of dynamic equations. In this review the key aspects of noncondensable gas bubble dynamics are covered. Classical references on the subject are surveyed, and an overview of the main findings in the past 20 years is provided. The review concludes with a scope and suggestions for future research directions, with special attention paid to the dynamics of bubbles in turbulence, in non-Newtonian fluid, and/or in the presence of electrolytes.

The usefulness of solid-state spins in quantum technologies depends on how long they can remain in a coherent superposition of quantum states. This Colloquium discusses how first-principles simulations can predict spin dynamics for different types of solid-state electron spins, helping design novel and improved platforms for quantum computing, networking, and sensing. The Colloquium first outlines the concepts necessary for understanding the noise affecting generic quantum systems. It then delves into recent advances in predicting spin-phonon relaxation of spin-defect qubits. Next discussed are cluster methods as a means of simulating quantum decoherence induced by spin-spin interactions, with an emphasis on the critical role of validation in ensuring the accuracy of these simulations. The manner in which validated cluster methods can be instrumental in interpreting recent experimental results and, more importantly, in predicting the coherence properties of novel spin-based quantum platforms is highlighted, thereby guiding the development of next-generation quantum technologies.

Quantum simulation is making a significant impact on scientific research. The prevailing tendency of the field is to build quantum simulators that get closer to real-world systems of interest, in particular, electronic materials. However, progress in the microscopic design also provides an opportunity for an orthogonal research direction: building quantum many-body systems beyond real-world limitations. This Colloquium takes this perspective: concentrating on synthetic quantum matter in nonstandard lattice geometries, such as fractal lattices and quasicrystals, as well as higher-dimensional or curved spaces, it aims at providing an introduction to the field of quantum simulation aligned with recent trends across various quantum simulation platforms, including atomic, photonic, and electronic devices. Light is shone on the novel phenomena that arise from these geometries: condensed matter physicists may appreciate the variety of different localization properties as well as novel topological phases that are offered by such exotic quantum simulators. But also in the search for quantum models for gravity and cosmology, quantum simulators of curved spaces can provide a useful experimental tool.

Self-alignment describes the property of a polar active unit to align or antialign its orientation toward its velocity. In contrast to mutual alignment, where the headings of multiple active units tend to directly align with each other—as in the Vicsek model—self-alignment impacts the dynamics at the individual level by coupling the rotation and displacements of each active unit. This enriches the dynamics even in the absence of interactions and allows, for example, a single self-propelled particle to orbit in a harmonic potential. At the collective level, self-alignment modifies the nature of the transition to collective motion already in the mean-field description and can lead to other forms of self-organization such as collective actuation in dense or solid elastic assemblies of active units. This has significant implications for the study of dense biological systems, metamaterials, and swarm robotics. Here a number of models are reviewed that were introduced independently to describe the previously overlooked property of self-alignment and some of its experimental realizations are identified. The aim of this review is threefold: (i) to underline the importance of self-alignment in active systems, especially in the context of dense populations of active units and active solids; (ii) to provide a unified mathematical and conceptual framework for the description of self-aligning systems; and (iii) to discuss the common features and specific differences of the existing models of self-alignment. The review concludes by discussing promising research avenues in which the concept of self-alignment could play a significant role.

Quantum theory and general relativity are about one century old. At present, they are considered the best available explanations of physical reality, and they have been corroborated so far by all realized experiments. Nonetheless, the quest to unify them is still ongoing, with several yet untested proposals for a theory of quantum gravity. Here the nascent field of information-theoretic methods applied to designing tests of quantum gravity in the laboratory is reviewed. This field emerges from the extension of quantum-information-theory methodologies beyond the domain of applicability of quantum theory itself to cover gravity. The focus is mainly on the detection of gravitational entanglement between two quantum probes, with this method compared to single-probe schemes. The experimental proposal that originated this field is reviewed, as are its variants and their applications. Their potential implications for the quantum theory of gravity are discussed. The role of general information-theoretic principles in illuminating the search for quantum effects in gravity is also highlighted.

Optoacoustic (photoacoustic) microscopy resolves optical absorption in cells and tissues, thus offering a complementary contrast mechanism to optical microscopy. Yet, the marked advances in optical microscopy techniques and their widespread use beg the question of the particular need and utility of an additional microscopy modality that resolves optical absorption. Recent advances that point to advantageous features and uses of optoacoustic microscopy in biological and clinical interrogation are presented. How these advances can be manifested as part of hybrid implementations using optical, optoacoustic, and possibly other forms of microscopy to enhance the ability of the microscopic interrogation is reviewed. Further examined are developments in the miniaturized optical detection of ultrasound, which can transform any optical microscope into a hybrid optical-optoacoustic system. In addition, recent progress with label-free molecular sensing and with new classes of novel reporters that expand the visualization capacity of the optoacoustic method are presented. Finally, how hybrid optical-optoacoustic microscopy offers a next step in multimodal interrogations, thereby impacting biological and clinical readings, is discussed.

The buckling of a soft elastic sample under growth or swelling has highlighted a new interest in materials science, morphogenesis, and biology or physiology. Indeed, the change of mass or volume is a common fact of any living species, and on a scale larger than the cell size, a macroscopic view can help to explain many features of common observation. Many morphologies of soft materials result from the accumulation of elastic compressive stress due to growth and thus from the minimization of a nonlinear elastic energy. The similarity between growth and compression of a piece of rubber has revived the instability formalism of nonlinear elastic samples in compression and, in particular, Biot’s instability. Here a modern treatment of this instability is presented in the light of complex analysis, and the richness of possible profiles that an interface can present under buckling, even if one restricts oneself to the two spatial dimensions, is demonstrated. Special attention is given to wrinkles, folds, and cusps, a surprising observation in swelling gels or clays, and a new threshold for crease patterns below the traditional Biot threshold is discovered. The standard techniques of complex analysis, nonlinear bifurcation theory, and path-independent integrals are revisited to highlight the role of physical parameters at the origin of the observed patterns below and above the Biot threshold.

The traditional view from particle physics is that quantum-gravity effects should become detectable only at extremely high energies and small length scales. Owing to the significant technological challenges involved, there has been limited progress in identifying experimentally detectable effects that can be accessed in the foreseeable future. However, in recent decades the size and mass of quantum systems that can be controlled in the laboratory have reached unprecedented scales, enabled by advances in ground-state cooling and quantum-control techniques. Preparations of massive systems in quantum states pave the way for the explorations of a low-energy regime in which gravity can be both sourced and probed by quantum systems. Such approaches constitute an increasingly viable alternative to accelerator-based, laser-interferometric, torsion-balance, and cosmological tests of gravity. In this review an overview of proposals where massive quantum systems act as interfaces between quantum mechanics and gravity is provided. Conceptual difficulties in the theoretical description of quantum systems in the presence of gravity are discussed, tools for modeling massive quantum systems in the laboratory are reviewed, and an overview of the current state-of-the-art experimental landscape is provided. Proposals covered in this review include precision tests of gravity, tests of gravitationally induced wave-function collapse and decoherence, and gravity-mediated entanglement. The review concludes with an outlook and summary of the key questions raised.

Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and an extensive thermodynamics at the macroscopic level are identified. Large deviations theory is then used to build a macroscopic fluctuation theory around this deterministic behavior, which are shown to preserve the fluctuation theorem. For many systems (such as chemical reaction networks, electronic circuits, and Potts models), this theory does not coincide with Langevin-equation approaches (obtained by adding Gaussian white noise to the deterministic dynamics), which if used are thermodynamically inconsistent. Einstein-Onsager theory of Gaussian fluctuations and irreversible thermodynamics are recovered at equilibrium and close to it, respectively. Far from equilibirum the free energy is replaced by the dynamically generated quasipotential (or self-information), which is a Lyapunov function for the macroscopic dynamics. Thermodynamics connects the dissipation along deterministic and escape trajectories to the Freidlin-Wentzell quasipotential, thus constraining the transition rates between attractors induced by rare fluctuations. A coherent perspective on minimum and maximum entropy production principles is also provided. For systems that admit a continuous-space limit, a nonequilibrium fluctuating field theory with its associated thermodynamics is derived. Finally, the macroscopic stochastic dynamics is coarse grained into a Markov jump process describing transitions among deterministic attractors, and the stochastic thermodynamics emerging from it is formulated.