The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has been challenging due to incompatibilities of the underlying theories—general relativity and quantum field theory. While quantum field theory utilizes compact, finite-dimensional symmetries associated with the internal degrees of freedom of quantum fields, general relativity is based on noncompact, infinite-dimensional external space-time symmetries. The present work aims at deriving the gauge theory of gravity using compact, finite-dimensional symmetries in a way that resembles the formulation of the fundamental interactions of the Standard Model. For our eight-spinor representation of the Lagrangian, we define a quantity, called the space-time dimension field, which enables extracting four-dimensional space-time quantities from the eight-dimensional spinors. Four U(1) symmetries of the components of the space-time dimension field are used to derive a gauge theory, called unified gravity. The stress-energy-momentum tensor source term of gravity follows directly from these symmetries. The metric tensor enters in unified gravity through geometric conditions. We show how the teleparallel equivalent of general relativity in the Weitzenböck gauge is obtained from unified gravity by a gravity-gauge-field-dependent geometric condition. Unified gravity also enables a gravity-gauge-field-independent geometric condition that leads to an exact description of gravity in the Minkowski metric. This differs from the use of metric in general relativity, where the metric depends on the gravitational field by definition. Based on the Minkowski metric, unified gravity allows us to describe gravity within a single coherent mathematical framework together with the quantum fields of all fundamental interactions of the Standard Model. We present the Feynman rules for unified gravity and study the renormalizability and radiative corrections of the theory at one-loop order. The equivalence principle is formulated by requiring that the renormalized values of the inertial and gravitational masses are equal. In contrast to previous gauge theories of gravity, all infinities that are encountered in the calculations of loop diagrams can be absorbed by the redefinition of the small number of parameters of the theory in the same way as in the gauge theories of the Standard Model. This result and our observation that unified gravity fulfills the Becchi–Rouet–Stora–Tyutin (BRST) symmetry and its coupling constant is dimensionless suggest that unified gravity can provide the basis for a complete, renormalizable theory of quantum gravity.

The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarize not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-20th century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource.

It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, this review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the Einstein, Podolsky and Rosen (EPR) experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory and, arguably, quantum from classical physics.

Basic quantum information ideas are next outlined, including qubits and data compression, quantum gates, the `no cloning' property and teleportation. Quantum cryptography is briefly sketched. The universal quantum computer (QC) is described, based on the Church-Turing principle and a network model of computation. Algorithms for such a computer are discussed, especially those for finding the period of a function, and searching a random list. Such algorithms prove that a QC of sufficiently precise construction is not only fundamentally different from any computer which can only manipulate classical information, but can compute a small class of functions with greater efficiency. This implies that some important computational tasks are impossible for any device apart from a QC.

To build a universal QC is well beyond the abilities of current technology. However, the principles of quantum information physics can be tested on smaller devices. The current experimental situation is reviewed, with emphasis on the linear ion trap, high-Q optical cavities, and nuclear magnetic resonance methods. These allow coherent control in a Hilbert space of eight dimensions (three qubits) and should be extendable up to a thousand or more dimensions (10 qubits). Among other things, these systems will allow the feasibility of quantum computing to be assessed. In fact such experiments are so difficult that it seemed likely until recently that a practically useful QC (requiring, say, 1000 qubits) was actually ruled out by considerations of experimental imprecision and the unavoidable coupling between any system and its environment. However, a further fundamental part of quantum information physics provides a solution to this impasse. This is quantum error correction (QEC).

An introduction to QEC is provided. The evolution of the QC is restricted to a carefully chosen subspace of its Hilbert space. Errors are almost certain to cause a departure from this subspace. QEC provides a means to detect and undo such departures without upsetting the quantum computation. This achieves the apparently impossible, since the computation preserves quantum coherence even though during its course all the qubits in the computer will have relaxed spontaneously many times.

The review concludes with an outline of the main features of quantum information physics and avenues for future research.

A search for resonances in top quark pair ($\mathrm{t}\overline{\mathrm{t}}$) production in final states with two charged leptons and multiple jets is presented, based on proton–proton collision data collected by the CMS experiment at the CERN LHC at $\sqrt{s} = 13\,\textrm{TeV}$, corresponding to 138 fb⁻¹. The analysis explores the invariant mass of the $\mathrm{t}\overline{\mathrm{t}}$ system and two angular observables that provide direct access to the correlation of top quark and antiquark spins. A significant excess of events is observed near the kinematic $\mathrm{t}\overline{\mathrm{t}}$ threshold compared to the non-resonant production predicted by fixed-order perturbative quantum chromodynamics (pQCD). The observed enhancement is consistent with the production of a color-singlet pseudoscalar (${}^1\mathrm{S}_0^{[1]}$) quasi-bound toponium state, as predicted by non-relativistic quantum chromodynamics. Using a simplified model for ${}^1\mathrm{S}_0^{[1]}$ toponium, the cross section of the excess above the pQCD prediction is measured to be $8.8\,^{+1.2}_{-1.4}\,\textrm{pb}$.

Entangled states of photons form the backbone of many quantum technologies. Due to the lack of effective photon–photon interactions, the generation of these states is typically probabilistic. In the prevailing but fundamentally limited generation technique, known as postselection, the target photons are measured destructively in the generation process. By contrast, in the alternative approach—heralded state generation—the successful creation of a desired state is verified by the detection of ancillary photons. Heralded state generation is superior to postselection in several critical ways: it enables free usage of the prepared states, allows for the success probability to be arbitrarily increased via multiplexing, and provides a scalable route to quantum information processing using photons. Here, we review theoretical proposals and experimental realisations of heralded entangled photonic state generation, as well as the impact of realistic experimental errors. We then discuss the wide-ranging applications of these states for quantum technologies, including resource states in linear optical quantum computing, entanglement swapping for repeater networks, fundamental physics, and quantum metrology.

Quantum spin liquids may be considered ‘quantum disordered’ ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

Two-dimensional (2D) magnetic materials exhibit a wide array of fascinating magnetic properties, making them highly attractive for spintronic applications such as high-density nonvolatile memories and multifunctional nano-devices. Recently, chromium tellurides (CrTe_x) have attracted significant attention due to their metallic band structure, strong magnetic anisotropy, and tunable exchange couplings. The unique tunability of magnetic properties in a metallic ground state makes CrTe_x a promising platform for generating, controlling, and manipulating spin currents. This review summarizes recent advances in large-scale 2D magnetic CrTe_x epitaxial thin films, emphasizing synthesis techniques that produce high-quality, large-area films. It explores the role of self-intercalation and heterostructure engineering in tailoring the magnetic and structural properties of these materials. We also review the band structure, magnetic characteristics, and spin dynamics of CrTe_x, with a particular emphasis on thickness-dependent band dispersion, magnetic anisotropy, and the emergence of skyrmions. Moreover, this review highlights the applications of CrTe_x in spintronics, covering the anomalous Hall effect, topological Hall effect, spin valves, and spin–orbit torque devices. The goal of this review is to furnish readers with a comprehensive overview of the intriguing properties of CrTe_x compounds and to inspire further innovative studies on the vast potential of 2D magnetic materials for next-generation spintronic and quantum devices.

Over the past four decades, additive manufacturing (AM), particularly three-dimensional (3D) printing, has emerged as a transformative force in chemical and biosensing technologies, revolutionizing prototyping and production across laboratories and industries. Recent advancements in 3D printing techniques and materials have accelerated the development of novel sensors for diverse applications, offering unparalleled advantages such as rapid prototyping, customization, and cost efficiency. Unlike traditional fabrication methods, 3D printing creates intricate, high-precision structures while reducing multi-step processes, making it ideal for biosensing applications. Its interdisciplinary potential spans physics, chemistry, engineering, biology, and medicine, positioning it as a transformative tool in biomedical applications, including biosensing. Despite its remarkable promises, some challenges such as limited multi-material integration, standardization hurdles, resolution constraints, biocompatibility concerns, and scalability issues persist. Addressing these gaps through interdisciplinary collaboration could unlock the full potential of AM-enabled sensing devices. This review critically evaluates the evolution and latest progress in AM technologies, including fused deposition modeling, stereolithography, and inkjet printing for designing sensitive, customizable, and affordable biosensing platforms and devices. Additionally, this article explores recent innovations in 3D-printed chemical and biological sensors, analyzing their performance in detecting various analytes. A comprehensive summary of cutting-edge developments is provided, alongside an examination of future directions for refining and inventing 3D printing techniques in biosensing applications. Finally, the review highlights current challenges and opportunities in 3D-printed sensing devices, emphasizing the need for material optimization, improved printing resolution, and enhanced device functionality. By overcoming these barriers, 3D printing can serve as a cornerstone for next-generation diagnostic platforms, driving innovation in chemical and biosensing technologies. This review underscores AM’s transformative role as a catalyst for future breakthroughs in the field.

We present an in-depth analysis of the energy dependence of optical breakdown in water by tightly focused laser pulses, from plasma formation to shock waves and cavitation. Laser pulses of fs to ns durations and UV to IR wavelengths are aberration-free focused through microscope objectives. Photography captures luminescent plasmas with submicrometer resolution, and bubble threshold and size are determined via probe beam scattering. The energy dependence of mechanical effects is quantified through the maximum bubble radius R_max. We find three key scenarios depicting the interaction between multiphoton and avalanche ionization, recombination, and thermal ionization from nanoeffects near threshold to extreme energy densities. They include a previously unknown scenario that emerges with single-longitudinal-mode UV ns pulses from compact lasers. It enables cost-effective creation of nanoeffects, as demonstrated on corneal tissue and glass. High-resolution color photography revealed new insights in the spatiotemporal dynamics of plasma formation, with an interplay of breakdown waves, string formation by local instabilities of avalanche ionization, and radiative energy transport. Plasma volume data from photographs together with absorption measurements show that the average energy density of luminescent fs and ns plasmas is similar, ranging between 10 and 40 kJ cm⁻³. However, small hot regions with up to 400 kJ cm⁻³ are formed in ns breakdown. From the hot regions, energy is spread out via x-ray bremsstrahlung, forming a luminescent halo. Well above threshold, R_max scales with E^1/3 across all scenarios, with 15%–20% conversion of laser energy into bubble energy. With increasing plasma energy density, an ever-larger energy fraction is converted into shock wave energy (75% at 40 kJ cm⁻³). We discuss guidelines for parameter selection in laser surgery and material processing in bulk media as well as for laser ablation and breakdown spectroscopy in liquids. Finally, we suggest roadmaps for future experimental and modeling work, and for broadening applications.

Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase, in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. The last decades of research have brought an unprecedented new variety of tools and indicators to study the breakdown of ergodicity, ranging from spectral and wave function measures, matrix elements of observables, through quantities probing unitary quantum dynamics, to transport and quantum information measures. We give a comprehensive overview of these approaches and attempt to provide a unified understanding of their main features. We emphasize general trends towards ergodicity with increasing length and time scales, which exclude naive single-parameter scaling hypothesis, necessitate the use of more refined scaling procedures, and prevent unambiguous extrapolations of numerical results to the asymptotic limit. Providing a concise description of numerical methods for studying ETH and MBL, we explore various approaches to tackle the question of the MBL phase. Persistent finite size drifts towards ergodicity consistently emerge in quantities derived from eigenvalues and eigenvectors of disordered many-body systems. The drifts are related to continuous inching towards ergodicity and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede the understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength provides premises suggesting the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.

Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. This class of micro- and nano-structured artificial media have attracted great interest during the past 15 years and yielded ground-breaking electromagnetic and photonic phenomena. However, the high losses and strong dispersion associated with the resonant responses and the use of metallic structures, as well as the difficulty in fabricating the micro- and nanoscale 3D structures, have hindered practical applications of metamaterials. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response (e.g. scattering amplitude, phase, and polarization), mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the Pancharatnam–Berry phase and Huygens’ metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in few-layer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. We also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of opportunities and challenges in this rapidly developing research field.

Surface plasmonics (SP) studies the collective oscillations of electrons in materials following excitation by light and related evanescent wave properties under near-field coupling. Due to the advantages of near-field enhancement, wavelength tunability, and overcoming the band gap limitation on the absorption wavelength, SPs is considered promising for broad developments in optoelectronics. Over the past decade, SP phenomena have been used in various technologies, for example photodetectors. This review discusses the physical models, role of waveguides, carrier dynamics and energy transfer modes of plasmons, particularly the structure and working principle of state-of-the-art plasmon photodetectors, with the aim of delving into the underlying mechanisms. In addition, we summarize recent developments in simulation techniques and detection methods in plasmonic photoelectric detection engineering. Finally, we present the latest progress, future prospects and remaining challenges associated with plasmon enhanced photodetection.

We perform a model-independent reconstruction of the cosmic distances using the multi-task Gaussian process framework as well as knot-based spline techniques with Dark Energy Spectroscopic Instrument (DESI)-DR2 baryon acoustic oscillation (BAO) and DES-SN5YR datasets. We calibrate the comoving sound horizon at the baryon drag epoch $r_\mathrm{d}$ to the Planck value, ensuring consistency with early-Universe physics. With the reconstructed cosmic distances and their derivatives, we obtain seven characteristic redshifts in the range $0.3 \unicode{x2A7D} z \unicode{x2A7D} 1.7$. We derive the normalized expansion rate of the Universe E(z) at these redshifts. Our findings reveal a significant deviations of approximately 4–5σ from the Planck 2018 cold dark matter Λcold dark matter predictions, particularly pronounced in the redshift range $z \sim 0.35$–0.55. These anomalies are consistently observed across both reconstruction methods and combined datasets, indicating robust late-time tensions in the expansion rate of the Universe and which are distinct from the existing ‘Hubble Tension’. This could signal new physics beyond the standard cosmological framework at this redshift range. Our findings underscore the role of characteristic redshifts as sensitive indicators of expansion rate anomalies and motivate further scrutiny with forthcoming datasets from DESI-5YR BAO, Euclid, and LSST. These future surveys will tighten constraints and will confirm whether these late-time anomalies arise from new fundamental physics or unresolved systematics in the data.

Relaxation rates are key characteristics of quantum processes, as they determine how quickly a quantum system thermalizes, equilibrates, decoheres, and dissipates. While they play a crucial role in theoretical analyses, relaxation rates are also often directly accessible through experimental measurements. Recently, it was shown that for quantum processes governed by Markovian semigroups, the relaxation rates satisfy a universal constraint: the maximal rate is upper-bounded by the sum of all rates divided by the dimension of the Hilbert space. This bound, initially conjectured a few years ago, was only recently proven using classical Lyapunov theory. In this work, we present a new, purely algebraic proof of this constraint. Remarkably, our approach is not only more direct but also allows for a natural generalization beyond completely positive semigroups. We show that complete positivity can be relaxed to two-positivity without affecting the validity of the constraint. This reveals that the bound is more subtle than previously understood: two-positivity is necessary, but even when further relaxed to Schwarz maps, a slightly weaker—yet still non-trivial—universal constraint still holds. Finally, we explore the connection between these bounds and the number of steady states in quantum processes, uncovering a deeper structure underlying their behavior.

High-energy nuclear collisions have recently emerged as a promising ‘imaging-by-smashing’ approach to reveal the intrinsic shapes of atomic nuclei. Here, I outline a conceptual framework for this technique, explaining how nuclear shapes are encoded during quark–gluon plasma (QGP) formation and evolution, and how they can be decoded from final-state particle distributions. I highlight the method’s potential to advance our understanding of both nuclear structure and QGP physics.

Active particles that translate chemical energy into self-propulsion can maintain a far-from-equilibrium steady state and perform work. The entropy production measures how far from equilibrium such a particle system operates and serves as a proxy for the work performed. Field theory offers a promising route to calculating entropy production, as it allows for many interacting particles to be considered simultaneously. Approximate field theories obtained by coarse-graining or smoothing that draw on additive noise can capture densities and correlations well, but they generally ignore the microscopic particle nature of the constituents, thereby producing spurious results for the entropy production. As an alternative we demonstrate how to use Doi-Peliti field theories, which capture the microscopic dynamics, including reactions and interactions with external and pair potentials. Such field theories are in principle exact, while offering a systematic approximation scheme, in the form of diagrammatics. We demonstrate how to construct them from a Fokker-Planck equation and show how to calculate entropy production of active matter from first principles. This framework is easily extended to include interaction. We use it to derive exact, compact and efficient general expressions for the entropy production for a vast range of interacting conserved particle systems. These expressions are independent of the underlying field theory and can be interpreted as the spatial average of the local entropy production. They are readily applicable to numerical and experimental data. In general, the entropy production due to any pair interaction draws at most on the three point, equal time density; and an n-point interaction on the $(2n-1)$-point density. We illustrate the technique in a number of exact, tractable examples, including some with pair-interaction as well as in a system of many interacting Active Brownian Particles.

Surface plasmonics (SP) studies the collective oscillations of electrons in materials following excitation by light and related evanescent wave properties under near-field coupling. Due to the advantages of near-field enhancement, wavelength tunability, and overcoming the band gap limitation on the absorption wavelength, SPs is considered promising for broad developments in optoelectronics. Over the past decade, SP phenomena have been used in various technologies, for example photodetectors. This review discusses the physical models, role of waveguides, carrier dynamics and energy transfer modes of plasmons, particularly the structure and working principle of state-of-the-art plasmon photodetectors, with the aim of delving into the underlying mechanisms. In addition, we summarize recent developments in simulation techniques and detection methods in plasmonic photoelectric detection engineering. Finally, we present the latest progress, future prospects and remaining challenges associated with plasmon enhanced photodetection.

High-energy nuclear collisions have recently emerged as a promising ‘imaging-by-smashing’ approach to reveal the intrinsic shapes of atomic nuclei. Here, I outline a conceptual framework for this technique, explaining how nuclear shapes are encoded during quark–gluon plasma (QGP) formation and evolution, and how they can be decoded from final-state particle distributions. I highlight the method’s potential to advance our understanding of both nuclear structure and QGP physics.

Since 2009, magnetic skyrmions have been identified in diverse materials, attracting interest for their small size, intriguing emergent physics and new device concepts. Over the years, the interplay between deformation and dynamics has been an important topic of magnetic textures, with well-known phenomena like Döring mass, domain wall Walker breakdown and vortex oscillations. This topic is being extended to magnetic skyrmions and is critical for their practical applications. While topological invariance is preserved under continuous deformation, magnetic skyrmions display rich and complex deformation modes, including variations in size, shape, and helicity, which significantly impact their dynamics. These deformations challenge both theoretical and experimental efforts but offer opportunities for ‘deformation engineering’ strategies aimed at optimizing device performance and discovering new functionalities. In this review, we summarize the recent research progresses on magnetic skyrmion dynamics under steady and time-varying deformation. It begins with an introduction on the basic concepts of magnetic skyrmions and analytical descriptions of skyrmion deformation. Subsequently, theoretical and experimental methods for the study of magnetic skyrmion dynamics under deformation are introduced. The characteristics and influencing factors of various deformation modes (including steady and time-varying modes) of magnetic skyrmions are discussed. Finally, we discuss the device applications and open questions related to magnetic skyrmions beyond rigid particles.

Entangled states of photons form the backbone of many quantum technologies. Due to the lack of effective photon–photon interactions, the generation of these states is typically probabilistic. In the prevailing but fundamentally limited generation technique, known as postselection, the target photons are measured destructively in the generation process. By contrast, in the alternative approach—heralded state generation—the successful creation of a desired state is verified by the detection of ancillary photons. Heralded state generation is superior to postselection in several critical ways: it enables free usage of the prepared states, allows for the success probability to be arbitrarily increased via multiplexing, and provides a scalable route to quantum information processing using photons. Here, we review theoretical proposals and experimental realisations of heralded entangled photonic state generation, as well as the impact of realistic experimental errors. We then discuss the wide-ranging applications of these states for quantum technologies, including resource states in linear optical quantum computing, entanglement swapping for repeater networks, fundamental physics, and quantum metrology.

The Dean–Kawasaki (DK) equation, which is at the basis of stochastic density functional theory (SDFT), was proposed in the mid-nineties to describe the evolution of the density of interacting Brownian particles, which can represent a large number of systems such as colloidal suspensions, supercooled liquids, polymer melts, biological molecules, active or chemotactic particles, or ions in solution. This theoretical framework, which can be summarized as a mathematical reformulation of the coupled overdamped Langevin equations that govern the dynamics of the particles, has attracted a significant amount of attention during the past thirty years. In this review, I present the context in which this framework was introduced, and I recall the main assumptions and calculation techniques that are employed to derive the DK equation. Then, in the broader context of statistical mechanics, I show how SDFT is connected to other theories, such fluctuating hydrodynamics, macroscopic fluctuation theory, or mode-coupling theory. The mathematical questions that are raised by the DK equation are presented in a non-specialist language. In the last parts of the review, I show how the original result was extended in several directions, I present the different strategies and approximations that have been employed to solve the DK equation, both analytically and numerically. I finally list the different situations where SDFT was employed to describe the fluctuations of Brownian suspensions, from the physics of active matter to the description of charged particles and electrolytes.

Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely unknown. In this work, we employ linear maps and their inverses to derive new sufficient analytical conditions for absolute separability in arbitrary dimensions, providing extremal points of this set and improving its characterization. Additionally, we employ convex geometry optimization to refine the characterization of the set when multiple non-comparable criteria for absolute separability are available. We also address the closely related problem of characterizing the absolute PPT (positive partial transposition) set, which consists of quantum states that remain positive under partial transposition across all unitary transformations. Finally, we extend our results to multipartite states.

Perovskite solar cells (PSCs) have garnered attention for their high efficiency and low production costs. However, long-term operational stability remains a significant challenge due to strain-induced degradation that impacts the structural integrity and performance of the perovskite layer. Strain, arising from factors such as lattice mismatch between layers, thermal expansion during fabrication, and external mechanical forces, can induce structural defects, accelerate ion migration and further reduce the operational lifespan of devices. Research has shown that strategies such as doping, additive engineering, optimization of annealing processes, and interface modification can effectively relieve the residual strain produced in the fabrication process of perovskite film, thereby enhancing the overall performance of the device. Among them, interface engineering has proven to be a key strategy for regulating strain and accordingly enhancing device stability. This article provides a comprehensive overview of recent advances in interface engineering approaches aimed at strain regulation in PSCs. The role of interface design with strain regulation in enhancing crystallinity, reducing defect density, and improving long-term performance is discussed in details, offering insights into future strategies for improving the stability and efficiency of perovskite-based photovoltaic devices.

Traditional three-dimensional perovskite structures encounter significant challenges in achieving high-quality light emission. In contrast, low-dimensional metal halide perovskites (LDMHPs) have emerged as promising alternatives, owing to their exceptional luminescent properties. However, the stability of LDMHPs remains a critical issue, limiting their potential in light-emitting and display applications. This review first examines the luminescence mechanisms and instability factors associated with LDMHPs, then summarizes strategies to enhance the stability, offering insights for further improvement. Additionally, the specific applications of LDMHPs are discussed based on electroluminescence and photoluminescence. Finally, the challenges and future directions are explored for the commercialization of LDMHPs in luminescent or display devices. This review provides valuable guidance for ongoing researches in this field.

Since Berry’s pioneering 1984 work, the separation of geometric and dynamic contributions in the
phase of an evolving wave has become fundamental in wave physics, underpinning diverse phenomena
in quantum mechanics, optics, and condensed matter. Here we extend this geometric-dynamic
decomposition from the wave-evolution phase to a distinct class of wave scattering problems, where
observables (such as frequency, momentum, or position) experience shifts in their expectation values
between the input and output wave sates. We describe this class of problems using a unitary
scattering matrix and the associated generalized Wigner-Smith operator (GWSO), which involves
gradients of the scattering matrix with respect to conjugate variables (time, position, or momentum,
respectively). We show that both the GWSO and the resulting expectation-values shifts admit
gauge-invariant decompositions into dynamic and geometric parts, related respectively to gradients
of the eigenvalues and eigenvectors of the scattering matrix. We illustrate this general theory
through a series of examples, including frequency shifts in polarized-light transmission through a
time-varying waveplate (linked to the Pancharatnam-Berry phase), momentum shifts at spatially
varying metasurfaces, optical forces, beam shifts upon reflection at a dielectric interface, and Wigner
time delays in 1D scattering. This unifying framework illuminates the interplay between geometry
and dynamics in wave scattering and can be readily applied to a broad range of physical systems.

The interplay between the fractional quantum Hall effect and nematicity is intriguing as it links emerging topological order and spontaneous symmetry breaking. Anisotropic fractional quantum Hall states (FQHSs) have indeed been reported in GaAs quantum wells but only in tilted magnetic fields, where the in-plane field explicitly breaks the rotational symmetry. Here we report the observation of FQHSs with highly anisotropic longitudinal resistances in purely perpendicular magnetic fields at even-denominator Landau level fillings ν = 5/2 and 7/2 in ultrahigh-quality GaAs twodimensional hole systems. The coexistence of FQHSs and spontaneous symmetry breaking at half fillings signals the emergence of nematic FQHSs which also likely harbor non-Abelian quasiparticle excitations. By gate tuning the hole density, we observe a phase transition from an anisotropic, developing FQHS to an isotropic composite fermion Fermi sea at ν = 7/2. Our calculations suggest that the mixed orbital components in the partially occupied Landau level play a key role in the competition and interplay between topological and nematic orders.