Gravitational waves are a unique probe of the early Universe, as the Universe is transparent to gravitational radiation right back to the end of inflation. This review summarizes detection prospects and the wide scope of primordial events that could lead to a detectable stochastic gravitational wave background. Any such background would shed light on what lies beyond the standard model, sometimes at remarkably high scales. The range of strategies for detecting a stochastic gravitational wave background is overviewed before the review delves into three major primordial events that can source such a background. Finally, the landscape of other sources of primordial backgrounds is summarized.

Over the past two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished. This environment includes codes to obtain Wannier functions and interfaces with first-principles simulation software, as well as an increasing number of related postprocessing packages. Wannier functions can be obtained for isolated or extended systems (both crystalline and disordered) and can be used to understand chemical bonding; to characterize electric polarization, magnetization, and topology; and as an optimal basis set, providing accurate interpolations in reciprocal space or large-scale Hamiltonians in real space. This review summarizes the current landscape of techniques, materials properties, and simulation codes based on Wannier functions that have been made accessible to the research community and that are now well integrated into what is referred to as a Wannier-function software ecosystem. To begin, the theory and practicalities of Wannier functions, starting with their broad domains of applicability to advanced minimization methods using alternative approaches beyond maximal localization, are introduced. The concept of a Wannier ecosystem and its interactions and interoperability with many quantum simulations engines and postprocessing packages are then defined. The review focuses on some of the key properties and capabilities that are empowered by such an ecosystem (from band interpolations and large-scale simulations to electronic transport, Berryology, topology, electron-phonon couplings, dynamical mean-field theory, embedding, and Koopmans functionals) and concludes with the current status of interoperability and automation. The review aims at highlighting the basic theory and concepts behind codes while providing mentions of more in-depth references. It also elucidates the relationships and connections between codes and, where relevant, the different motivations and objectives behind their development strategies. Finally, an outlook on future developments is provided and comments are made on the goals of biodiversity and sustainability for the entire software ecosystem.

The physics of isolated plasma potential structures sustained by a deficit of phase-space density on trapped orbits, commonly known as electron or ion holes, is reviewed. The principles of their equilibria are explained and illustrated, and contrasted with solitons. A review of literature mostly from prior to 2016 highlights the key historical developments of the field. Progress since, especially in hole acceleration, stability, and multidimensional effects, is summarized in more detail.

Semidefinite programs are convex optimization problems involving a linear objective function and a domain of positive-semidefinite matrices. Over the past two decades, they have become an indispensable tool in quantum information science. Many otherwise intractable fundamental and applied problems can be successfully approached by means of relaxation to a semidefinite program. This methodology is reviewed here in the context of quantum correlations. The manner in which the core idea of semidefinite relaxations can be adapted is discussed for a variety of research topics in quantum correlations, including nonlocality, quantum communication, quantum networks, entanglement, and quantum cryptography.

Cosmological gravitational particle production (CGPP) is the creation of particles in an expanding universe due solely to their gravitational interaction. These particles can play an important role in the cosmic history through their connection to various cosmological relics including dark matter, gravitational-wave radiation, dark radiation, and the baryon asymmetry. This review explains the phenomenon of CGPP as a consequence of quantum fields in a time-dependent background, catalogs known results for the spectra and cosmological abundance of gravitationally produced particles of various spins, and explores the phenomenological consequences and observational signatures of CGPP.

Over the past 15 years, the numerical conformal bootstrap has become an indispensable tool for studying strongly coupled conformal field theories in various dimensions. Reviewed here are the main developments in the field in the five years since the publication of the previous comprehensive review [D. Poland, S. Rychkov, and A. Vichi, Rev. Mod. Phys. 91, 015002 (2019)]. Developments in the software (SDPB 2.0, scalar_blocks, blocks_3d, autoboot, hyperion, and simpleboot) and on the algorithmic side (Delaunay triangulation, cutting surface, tiptop, navigator function, and skydive) are described. Also chronicled are the main physics applications that have been obtained using new technologies.

The simplicity of hard spheres as a model system is deceptive. Although the particles interact solely through volume exclusion, that nevertheless suffices for a wealth of static and dynamical phenomena to emerge, making the model an important target for achieving a comprehensive understanding of matter. In addition, while real colloidal suspensions are typically governed by complex interactions, Pusey and Van Megen [Nature 320, 340 (1986)] demonstrated that suitably tuned suspensions result in hard-sphere-like behavior, thus bringing a valuable experimental complement to the renowned theoretical model. Colloidal hard spheres are thus both a material in their own right and a platform upon which phenomena exhibited by simple materials can be explored in great detail. The various purposes enable a particular synergy between experiment, theory, and computer simulation. The extensive body of work on colloidal hard spheres, which ranges from their equilibrium properties, such as phase behavior, interfaces, and confinement, to some of the nonequilibrium phenomena they exhibit, such as sedimentation, glass formation, and nucleation, is reviewed here.

It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a $\mathcal{PT}$-symmetric Hamiltonian can also define a physically acceptable quantum-mechanical system even if the Hamiltonian is not Hermitian. The study of $\mathcal{PT}$-symmetric quantum systems is a young and extremely active research area in both theoretical and experimental physics. The purpose of this review is to provide established scientists as well as graduate students with a compact, easy-to-read introduction to this field that will enable them to understand more advanced publications and to begin their own theoretical or experimental research activity. The ideas and techniques of $\mathcal{PT}$ symmetry have been applied in the context of many different branches of physics. This review introduces the concepts of $\mathcal{PT}$ symmetry by focusing on elementary one-dimensional $\mathcal{PT}$-symmetric quantum and classical mechanics and relies, in particular, on oscillator models to illustrate and explain the basic properties of $\mathcal{PT}$-symmetric quantum theory.

Liquid argon detectors are ubiquitous in particle, astroparticle, and applied physics. They reached an unprecedented level of maturity thanks to more than 20 years of research and development and the operation of large-scale facilities at CERN, Fermilab, and the Gran Sasso laboratories. This review discusses such an impressive advance, from the grounding of the experimental technique up to cutting-edge applications. The review commences by describing the physical and chemical properties of liquid argon as an active and target medium for particle detection, together with advantages and limitations compared with other liquefied noble gases. The opportunities and challenges of liquid argon detectors operated as calorimeters, scintillators, and time projection chambers are examined. The core applications of liquid argon detectors at colliders (ATLAS), accelerator neutrino beams (SBN and DUNE), and underground laboratories (DarkSide, DEAP, and ICARUS) for the observation of rare events are then delved into. The review concludes by looking at unconventional developments (pixelization, combined light-charge readout, Xe-doped devices, and all-optical readout) and applications in medical and applied physics to extend this technology’s scope toward novel research fields.

Cell growth and gene expression, two essential elements of all living systems, have long been the focus of biophysical interrogation. Advances in experimental single-cell methods have invigorated theoretical studies into these processes. However, until recently there was little dialogue between the two areas of study. In particular, most theoretical models for gene regulation assumed gene activity to be oblivious to the progression of the cell cycle between birth and division. But in fact there are numerous ways in which the periodic character of all cellular observables can modulate gene expression. The molecular factors required for transcription and translation [ribonucleic acid (RNA) polymerase, transcription factors, and ribosomes] increase in number during the cell cycle but are also diluted due to the continuous increase in cell volume. The replication of the genome changes the dosage of those same cellular players but also provides competing targets for regulatory binding. Finally, cell division reduces their number again, and so forth. Stochasticity is inherent to all of these biological processes, manifested in fluctuations in the synthesis and degradation of new cellular components as well as the random partitioning of molecules at each cell division event. The notion of gene expression as stationary is thus difficult to justify. In this review, the emerging paradigm of cell-cycle coupled gene expression is surveyed, with an emphasis on the global expression patterns rather than gene-specific regulation. Recent experimental reports where cell growth and gene expression were simultaneously measured in individual cells are discussed, providing first glimpses into the coupling between the two and prompting several questions. How do the levels of gene expression products (messenger RNA and protein) scale with the cell volume and cell-cycle progression? What are the molecular origins of the observed scaling laws, and when do they break down to yield noncanonical behavior? What are the consequences of cell-cycle dependence for the heterogeneity (“noise”) in gene expression within a cell population? While the experimental findings differ among genes, organisms, and environmental conditions, several theoretical models have emerged that attempt to reconcile these differences and form a unifying framework for understanding gene expression in growing cells.

Active systems are driven out of equilibrium by exchanging energy and momentum with their environment. This endows them with anomalous mechanical properties that are reviewed in this Colloquium. The case of dry scalar active matter is considered, which encompasses systems whose large-scale behaviors are entirely captured by their density—a scalar field. Arguably the simplest of active-matter systems, they have attracted considerable attention due to their unusual properties when put in contact with boundaries, inclusions, tracers, or disordered potentials. Indeed, studies of the mechanical pressure of active fluids and of the dynamics of passive tracers have shown that active systems impact their environment in nontrivial ways, for example, by propelling and rotating anisotropic inclusions. Conversely, the long-range density and current modulations induced by localized obstacles show how the environment can have a far-reaching impact on active fluids. This is best exemplified by the propensity of bulk and boundary disorder to destroy bulk phase separation in active matter, thereby showing active systems to be much more sensitive to their surroundings than passive ones. This Colloquium aims to provide a unifying perspective on the rich interplay between active systems and their environments.

Ultrahigh dose rate, FLASH radiotherapy has emerged as one of the most promising innovations over the past decade in the field of radiation oncology, with the potential to eradicate radiation resistant primary tumors and improve the therapeutic outcome for cancer patients. FLASH is based on delivering radiation doses at ultrahigh dose rates (UHDR; $>40\mathrm{Gy}/\mathrm{s}$), more than 1000 times faster than irradiation at conventional dose rates (CONV). The experimental evidence demonstrating the differential effect of dose rate modulation on tumors and normal tissue is reviewed. Preclinical data consistently show that the antitumor efficacy of cytotoxic doses is not dependent on dose rate, but in normal tissues UHDR significantly reduces normal tissue toxicities compared to CONV, as observed in vivo. These observations define the FLASH effect. The FLASH effect has been reported to occur when using single or hypofractionated dose regimens in several experimental animal models (mice, rat, zebrafish, pig, and cats) and in multiple organs (lung, skin, gut, and brain) by numerous groups worldwide. Note that the FLASH effect has been demonstrated with electron, photon, and hadron (proton and heavier ion) beams. The current status and future technological development are reviewed, with an emphasis on critical beam parameters, future beam modalities, and prerequisites for safe clinical translation in terms of dosimetry, radioprotection, and treatment planning systems. Mechanistic investigations at the physicochemical and biological levels are presented, as are strategies to support and initiate clinical translation. This comprehensive review provides multidisciplinary radiation scientists with a road map of the technological, physical, chemical, biological, and clinical considerations that have made FLASH topical. These considerations are presented with a realistic and practical backdrop of the limitations and challenges that lie ahead.

The written version of my lecture is a personal reflection on decades of research on electron-light interactions, culminating in their control and observation in real time at the turn of the millennium. Electrons and light attracted my attention when attending the lectures of György Marx on quantum mechanics and Károly Simonyi on electrodynamics during the 1980s in Budapest. This interest was solidified by my mentor, Arnold Schmidt, and deepened by Paul Corkum, during the 1990s in Vienna. They have influenced my path most profoundly. It has been a tremendous privilege to stand on the shoulders of scientists, including many Nobel laureates, who made seminal contributions to our understanding of electrons and light, when walking the path to exploring sub-atomic motions. To eventually exploit them for addressing grand challenges. To the benefit of humankind.

Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this Colloquium, the development, theory, and applications of eigenvector continuation and projection-based emulators are presented. The basic concepts are introduced, the underlying theory and convergence properties are discussed, and recent applications for quantum systems and future prospects are presented.

Thermally driven turbulent flows are omnipresent in nature and technology. A good understanding of the physical principles governing such flows is key for numerous problems in oceanography, climatology, geophysics, and astrophysics for problems involving energy conversion, heating and cooling of buildings and rooms, and process technology. In the physics community, the most popular system to study wall-bounded thermally driven turbulence has been Rayleigh-Bénard flow, i.e., the flow in a box heated from below and cooled from above. The dimensionless control parameters are the Rayleigh number Ra (the dimensionless heating strength), the Prandtl number Pr (the ratio of kinematic viscosity to thermal diffusivity), and the aspect ratio $\mathrm{\Gamma }$ of the container. The key response parameters are the Nusselt number Nu (the dimensionless heat flux from the bottom to the top) and the Reynolds number Re (the dimensionless strength of the turbulent flow). While there is good agreement and understanding of the dependences $\mathrm{N}\mathrm{u}(\mathrm{R}\mathrm{a},\mathrm{P}\mathrm{r},\mathrm{\Gamma })$ up to $\mathrm{R}\mathrm{a}\sim {10}^{11}$ (the “classical regime”), for even larger Ra in the so-called ultimate regime of Rayleigh-Bénard convection the experimental results and their interpretations are more diverse. The transition of the flow to this ultimate regime, which is characterized by strongly enhanced heat transfer, is due to the transition of laminar-type flow in the boundary layers to turbulent-type flow. Understanding this transition is of the utmost importance for extrapolating the heat transfer to large or strongly thermally driven systems. Here the theoretical results on this transition to the ultimate regime are reviewed and an attempt is made to reconcile the various experimental and numerical results. The transition toward the ultimate regime is interpreted as a non-normal–nonlinear and thus subcritical transition. Experimental and numerical strategies are suggested that can help to further illuminate the transition to the ultimate regime and the ultimate regime itself, for which a modified model for the scaling laws in its various subregimes is proposed. Similar transitions in related wall-bounded turbulent flows such as turbulent convection with centrifugal buoyancy and Taylor-Couette turbulence are also discussed.

Recent years have witnessed an explosion of interest in quantum devices for the production, storage, and transfer of energy. This Colloquium concentrates on the field of quantum energy storage by reviewing recent theoretical and experimental progress in quantum batteries. Provided first is a theoretical background discussing the advantages that quantum batteries offer with respect to their classical analogs. The existing quantum many-body battery models are then reviewed and a thorough discussion of important issues related to their “open nature” is presented. The Colloquium concludes with a discussion of promising experimental implementations, preliminary results available in the literature, and perspectives.

Catalysts open up new reaction pathways that can speed up chemical reactions while not consuming the catalyst. A similar phenomenon has been discovered in quantum information science, where physical transformations become possible by utilizing a quantum degree of freedom that returns to its initial state at the end of the process. In this review, a comprehensive overview of the concept of catalysis in quantum information science is presented and its applications in various physical contexts are discussed.

Neutrino masses and mixings produce vacuum oscillations, an established quantum mechanical phenomenon. In matter, the Mikheev-Smirnov-Wolfenstein effect, due to neutrino interactions with the background particles, triggers resonant flavor modification. In dense environments, such as core-collapse supernovae and compact mergers, sizable neutrino-neutrino interactions, shock waves, and turbulence impact the neutrino flavor content under a variety of phenomena. Theoretical approaches of neutrino propagation range from the mean-field approximation to the full quantum kinetic equations. Interesting connections have been uncovered between weakly interacting dense neutrino gases and other many-body systems and domains, from condensed matter and nuclear physics to quantum computing. Besides the intrinsic theoretical interest, establishing how neutrinos change flavor contributes to answering the long-standing open questions of how massive stars explode and of the $r$-process sites. It is also important for future observations of core-collapse supernova neutrinos and of the diffuse supernova neutrino background that should be discovered in the foreseeable future.