The dominant neutrino fluxes at Earth from different sources are reviewed and the grand unified neutrino spectrum ranging from meV to PeV energies is presented. For each energy band and source, both theoretical expectations and experimental data are discussed. This compact review serves as a reference to those interested in neutrino astronomy, fundamental particle physics, dark-matter detection, high-energy astrophysics, geophysics, and other related topics.

Quantum crystallization of ${}^4\mathrm{He}$ is a first-order phase transition from a superfluid liquid and can proceed extremely quickly at particularly low temperatures. The entropy difference between the two quantum phases, the quantum crystal and superfluid liquid, is small and atoms are carried to the crystal surface via a dissipationless superflow. A limiting process of the transition near absolute zero temperature is quasiparticle scattering off the crystal surface, which is less frequent at lower temperatures. It is known that interfacial phenomena, such as crystallization wave propagations and total reflection of ultrasound, occur on ${}^4\mathrm{He}$ crystal surfaces as a result of the rapid crystallization. The rapid crystallization allows the fundamental physics of crystal shape and growth to be examined in a measurable timescale in laboratories, which otherwise cannot be observed in classical crystals. This Colloquium describes far from equilibrium phenomena of significantly deformed ${}^4\mathrm{He}$ quantum crystals when they are subjected to original driving forces, which are small and usually believed to be irrelevant for ordinary classical crystals. Using driving forces such as gravity, superflow, wettability, acoustic waves, container oscillations, and frictional forces, ${}^4\mathrm{He}$ crystals are placed under highly nonequilibrium conditions, showing various kinds of extraordinary crystallization and relaxation processes in a superfluid liquid. Rapid crystal shape deformations sometimes influence the surrounding superfluid field in return, resulting in instabilities of the flat crystal surface. Direct visualizations by a high-speed video camera are made, providing an unambiguous observation of the dynamics far from equilibrium of ${}^4\mathrm{He}$ quantum crystals at extremely low temperatures.

Recent progress in taking the large dimension limit of Einstein’s equations is reviewed. Most of the analysis is classical and concerns situations where there is a black hole horizon, although various extensions that include quantum gravitational effects are discussed. The review consists of two main parts: the first is a discussion of general aspects of black holes and effective membrane theories in this large dimension limit, and the second is a series of applications of this limit to interesting physical problems. The first part includes a discussion of quasinormal modes that leads naturally into a description of effective hydrodynamiclike equations that describe the near-horizon geometry. There are two main approaches to these effective theories, a fully covariant approach and a partially gauge-fixed one, which are discussed in relation to each other. In the second part the applications are divided up into three main categories: the Gregory-Laflamme instability, black hole collisions and mergers, and the anti–de Sitter/conformal field theory correspondence ($\mathrm{AdS}/\mathrm{CFT}$). $\mathrm{AdS}/\mathrm{CFT}$ posits an equivalence between a gravitational theory and a strongly interacting field theory, allowing the spectrum of applications to be extended to problems in hydrodynamics, condensed matter physics, and nuclear physics. The final, shorter part of the review describes further promising directions where there have been, as yet, few published research articles.

This review is an introduction to causal properties of general relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The review is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand.

Parton distribution functions (PDFs) describe the structure of hadrons as composed of quarks and gluons. They are needed to make predictions for short-distance processes in high-energy collisions and are determined by fitting to cross-section data. Definitions of the PDFs and their relations to high-energy cross sections are reviewed. The focus is on the PDFs in protons, but PDFs in nuclei are also discussed. The standard statistical treatment needed to fit the PDFs to data using the Hessian method is reviewed in some detail. Tests are discussed that critically examine whether the needed assumptions are indeed valid. Also presented are some ideas of what one can do in case tests indicate that the assumptions fail.

This review addresses experiments on elasticity, plasticity, and flow of solid ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$, focusing on dislocations and other defects that are responsible for the unusual mechanical behavior of such quantum crystals. Helium’s zero point motion prevents it from freezing unless pressure is applied and makes the solid extremely compressible, with elastic constants orders of magnitude smaller than those of conventional solids. Tunneling allows defects to remain mobile at low temperatures, so dislocations have much larger effects on mechanical properties than in conventional solids. At temperatures below 400 mK, dislocations in hexagonal-close-packed (hcp) ${}^4\mathrm{He}$ are essentially undamped and, in the absence of pinning by ${}^3\mathrm{He}$ impurities, glide freely in the basal plane. In this regime, dislocation motion reduces the shear modulus by as much as 90%, an effect that has been referred to as “giant plasticity” although it is reversible and so might be better described as “softening.” In this low temperature regime, macroscopic plastic deformation occurs via sudden dislocation avalanches with a wide range of time and length scales. At higher temperatures, dislocation motion is damped, introducing dissipation in elastic measurements, and thermally activated defect motion makes helium crystals extremely ductile, flowing under millibar stresses near melting. During the last decade, most of the properties of the dislocations that are responsible for the elastic effects described in this review have been accurately measured: their orientation, density, and length distributions, the nature of their networks, and their binding to isotopic impurities. Despite this detailed understanding of mobile dislocations, there remain open questions. Much less is known about defects’ roles in the elastic and plastic behavior of hcp and bcc ${}^3\mathrm{He}$ crystals and even in hcp ${}^4\mathrm{He}$, and almost nothing is known about other types of dislocations that are immobile and thus do not affect elastic properties. These might be responsible for recently observed superfluidlike mass flow in ${}^4\mathrm{He}$ at low temperatures, although it is now clear that the apparent mass decoupling seen in torsional oscillator experiments with solid ${}^4\mathrm{He}$ was due to the elastic effects described in this review, not to supersolidity.

The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or the reduced phase-space probability density function of a classical open system, the Hamiltonian of mean force not only characterizes the reduced state but also contains full information about the thermodynamics of the considered open system. The resulting thermodynamic potentials all assume the form as the difference of the potentials for the total system and the bare environment in the absence of the system. In contrast to work as a mechanical notion, one faces several problems with the definition of heat, which turns out to be largely ambiguous in the case of strong coupling between system and environment. The general theory of the thermodynamics of open systems, in particular, in view of strong coupling, is reviewed and illustrated it with several examples. The vagueness of heat is discussed in the context of the ambiguities in the definitions of a fluctuating internal energy and other fluctuating thermodynamic potentials.

This article is an extended version of a talk given at the March 2019 meeting of the American Physical Society, in connection with the award to the author of the 2019 APS Medal for Exceptional Achievement in Research. The article will summarize some of the author’s work in areas linked to topological aspects of classical and quantum physics. Topics include quantum Hall effects, as well as the theory of melting in to dimensions and effects of vortex motion in a thin superconductor or a superfluid film.

The Sun is our nearest star; it is also the most important star that determines life on Earth. A large variety of phenomena observed on the Sun’s surface, with potential impact on Earth, is thought to arise from turbulent convection in Sun’s interior, this being the dominant mode of heat transport within the outer envelope at $r\gtrsim 0.715R_{\odot }$. However, convection in the Sun differs in most of its aspects from convection processes known on Earth, certainly those under controlled laboratory conditions, thus seriously challenging existing physical models of convective turbulence and boundary conditions in the Sun. Solar convection is a multiscale-multiphysics phenomenon including the transport of mass, momentum, and heat in the presence of rotation, dynamo action, radiation fluxes, and partial changes in chemical composition. Standard variables of state such as pressure, mass density, and temperature vary over several orders of magnitude within the convection region, thus introducing immense stratification. Although the Sun has been explored intensely, observational evidence on the structure and intensity of turbulent convection processes remains indirect and essentially limited to observations of the granular convection patterns at the surface and helioseismologic data that probe the propagation of sound waves in the interior. In this Colloquium characteristic scales and dimensionless parameters are discussed, particularly from the perspective of laboratory convection, a research field that has progressed significantly in the last few decades. The estimates and calculations of solar conditions given here are based mostly on the standard solar model S of Christensen-Dalsgaard et al., which is a mean field model of solar convection. Light is shed on existing results to gain a deeper understanding of dynamical aspects of solar convection.

A few decades ago, quantum optics stood out as a new domain of physics by exhibiting states of light with no classical equivalent. The first investigations concerned single photons, squeezed states, twin beams, and Einstein-Podolsky-Rosen states, which involve only one or two modes of the electromagnetic field. The study of the properties of quantum light then evolved in the direction of more and more complex and rich situations, involving many modes of the spatial, temporal, frequency, or polarization type. Actually, each mode of the electromagnetic field can be considered as an individual quantum degree of freedom. It is then possible, using the techniques of nonlinear optics, to couple different modes and thus build in a controlled way a quantum network [H. Jeff Kimble, Nature (London) 453, 1023 (2008)] in which the nodes are optical modes, and that is endowed with a strong multipartite entanglement. In addition, such networks can be easily reconfigurable and are subject only to weak decoherence. They indeed open many promising perspectives for optical communications and computation. Because of the linearity of Maxwell equations a linear superposition of two modes is another mode. This means that a “modal superposition principle” exists hand in hand with the regular quantum state superposition principle. The purpose of this review is to show the interest of considering these two aspects of multimode quantum light in a global way. Indeed, using different sets of modes allows one to consider the same quantum state under different perspectives: a given state can be entangled in one basis and factorized in another. It is shown that there exist some properties that are invariant over a change in the choice of the basis of modes. The method of finding the minimal set of modes that are needed to describe a given multimode quantum state is also presented. It is then shown how to produce, characterize, tailor, and use multimode quantum light while also considering the effect of loss and amplification on such light and the modal aspects of the two-photon coincidences. Switching to applications to quantum technologies, this review shows that it is possible to find not only quantum states that are likely to improve parameter estimation but also the optimal modes in which these states “live.” Finally, details on how to use such quantum modal networks for measurement-based quantum computation are presented.

Fluid flows hosting electrical phenomena are the subject of a fascinating and highly interdisciplinary scientific field. In recent years, the extraordinary success of electrospinning and solution-blowing technologies for the generation of polymer nanofibers has motivated vibrant research aiming at rationalizing the behavior of viscoelastic jets under applied electric fields or other stretching fields including gas streams. Theoretical models unveiled many original aspects in the underpinning physics of polymer solutions in jets and provided useful information to improve experimental platforms. This review examines advances in the theoretical description and numerical simulation of polymer solution jets in electrospinning and solution blowing. Instability phenomena of electrical and hydrodynamic origin, which play a crucial role in the relevant flow physics, are highlighted. Specifications leading to accurate and computationally viable models are formulated. Electrohydrodynamic modeling, theories on jet bending instability, recent advances in Lagrangian approaches to describe the jet flow, including strategies for dynamic refinement of simulations, and effects of strong elongational flow on polymer networks are reviewed. Finally, the current challenges and future perspectives in the field are outlined and discussed, including the task of correlating the physics of the jet flows with the properties of relevant materials, as well as the development of multiscale techniques for modeling viscoelastic jets.

This review covers the work of the three decades since the first spectroscopic identification of the ${\mathrm{H}}_3^{+}$ molecular ion outside of the laboratory in 1988, in the auroral atmosphere of the giant planet Jupiter. These decades have seen the astronomy related to this simple molecular ion expand to such an extent that a summary and evaluation of some 450 refereed articles is provided in the review. This enormous body of work has revealed surprises and illuminated the extensive role played by ${\mathrm{H}}_3^{+}$ in astrophysical environments in our Solar System and beyond. At the same time the physical chemistry and chemical physics of the molecule that has been revealed and studied during this time has proved to be fascinating and enabled high-resolution spectroscopy to benchmark its achievements against equally high-precision calculations. This review includes a brief look at some of the key foundational articles from before the original 1988 Jupiter detection (including the original 1911 ion discharge tube detection by J. J. Thomson and the key laboratory spectroscopy and quantum mechanics calculations on ${\mathrm{H}}_3^{+}$ structure and spectrum). The review explains the original detection and its serendipitous nature and looks at the astronomy that followed, all the way up to the latest results from NASA’s Juno mission. Also covered are the major advances in our understanding of the interstellar medium (known as ISM) that have resulted from the detection of ${\mathrm{H}}_3^{+}$ absorption lines there in 1996. The review closes by examining claims for the ion’s presence in other astrophysical environments and its potential role in the atmospheres of exoplanets and brown dwarfs.

The climate is a forced, dissipative, nonlinear, complex, and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This review covers the observational evidence on climate phenomena and the governing equations of planetary-scale flow and presents the key concept of a hierarchy of models for use in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand, and nonequilibrium statistical physics, on the other hand, are brought together for the first time and shown to complement each other in helping understand and predict the system’s behavior. These complementary points of view permit a self-consistent handling of subgrid-scale phenomena as stochastic processes, as well as a unified handling of natural climate variability and forced climate change, along with a treatment of the crucial issues of climate sensitivity, response, and predictability.

Electronic transport properties of single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions, and by means of scanning tunneling microscopes. In parallel, many theoretical tools have been developed and refined for describing such transport properties and for obtaining numerical predictions. Most prominent among these theoretical tools are those based upon density functional theory. In this review, theory and experiment are critically compared, and this confrontation leads to several important conclusions. The theoretically predicted trends nowadays reproduce the experimental findings well for series of molecules with a single well-defined control parameter, such as the length of the molecules. The quantitative agreement between theory and experiment usually is less convincing, however. Two main sources for the quantitative discrepancies can be identified. Experimentally, the atomic structure of the junction typically realized in the measurement is not well known, so simulations rely on plausible scenarios. In theory, correlation effects can be included only in approximations that are difficult to control for experimentally relevant situations. Therefore, one typically expects qualitative agreement with present modeling tools; in exceptional cases a quantitative agreement has already been achieved. For further progress, benchmark systems are required that are sufficiently well defined by experiment to allow quantitative testing of the approximation schemes underlying the theoretical modeling. Several key experiments can be identified suggesting that the present description may even be qualitatively incomplete in some cases. Such key experimental observations and their current models are also discussed here, leading to several suggestions for extensions of the models toward including dynamic image charges, electron correlations, and polaron formation.

Immediately after the discovery of high temperature superconductivity in the cuprates in 1987, properties in the metallic state above $T_c$ were discovered that violated the reigning paradigm in condensed matter physics: the quasiparticle concept due to Landau. The most discussed of such properties is the linear in temperature resistivity down to asymptotically low temperatures, sometimes called Planckian resistivity, above the region of the highest $T_c$. Similar anomalies have since also been discovered in the heavy-fermion compounds and in the Fe-based superconducting metals, and most recently in twisted bilayer graphene. Innumerable papers in the past three decades have pointed out that the linear in $T$ resistivity and associated properties are a mystery and the most important unsolved problem in condensed matter physics; superconductivity itself is a corollary to the normal state properties. Even in this prolifically investigated field, quantitative experimental results on crucial normal state and superconducting state properties have only recently become available. It is now possible to compare some of the detailed predictions of a theory for the normal and superconductive state in cuprates and in heavy fermions with the experiments. The theory gives the frequency and temperature dependence of various normal state properties and also their measured magnitudes in terms of the same values of two parameters. It also resolves the paradox of $d$-wave symmetry of superconductivity in the cuprates given that the scattering rate of fermions in the normal state is nearly momentum independent. The same parameters that govern the normal state anomalies are also deduced from the quantitative analysis of data in the superconducting state in cuprates. The simplicity of the results depends on the discovery of a new class of quantum-critical fluctuation in which orthogonal topological excitations in space and time determine the spectra, such that the correlations of the critical spectra are a product of a function of space and a function of time with the spatial correlation length proportional to the logarithm of the temporal correlation length. The fermions scattering with such fluctuations form a marginal Fermi liquid.

The nuclear-physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the standard model through symmetries and lattice simulations of quantum chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. The three main nuclear EFTs—chiral, pionless, and halo/cluster—are reviewed, highlighting their similarities, differences, and connections. The structural properties and reactions of nuclei that have been derived from the ab initio solution of the few- and many-body problem built upon EFT input are surveyed.