We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet–Magnus expansion. The high-order errors in the engineered Floquet Hamiltonian are mitigated by adding high-order driving potentials perturbatively. We introduce a transformation method that allows us to obtain an analytical expression of the leading-order correction drive for engineering a target Hamiltonian with discrete rotational and chiral symmetries in phase space. We also provide a numerically efficient procedure to calculate high-order correction drives and apply it to engineer the target Hamiltonian with degenerate eigenstates of multi-component cat states that are important for fault-tolerant hardware-efficiency bosonic quantum computation.

Liquid–liquid crystalline phase separation (LLCPS) is the process by which an initially homogenous single-phase solution composed of a solvent-most frequently water- and a solute-typically rigid or semiflexible macromolecules, polymers, supramolecular aggregates, or filamentous colloids-demixes into two (or more) distinct phases in which one phase is depleted by the solute and features properties of isotropic solutions, whereas the other is enriched by the solute and exhibits liquid crystalline anisotropic properties. Differently from the more common liquid–liquid phase separation (LLPS) of flexible macromolecules, which is a trade-off between entropy and enthalpy, LLCPS is mostly an entropy-controlled process in which the morphology, composition and properties of the new phases depend primarily on kinetics and thermodynamic factors and, unexpectedly, on the history followed to reach a specific point in the phase diagram. This review aims to comprehensively discuss the process of LLCPS from experimental, theoretical, and simulation standpoints. We discuss the main systems and experimental approaches followed over the past decades to induce and control LLCPS, then we delve into the main theoretical and modeling approaches available to rationalize this process, and finally, we expand on how numerical simulations can significantly enrich the understanding of LLCPS. A final section touches on possible applications and the significance of LLCPS beyond pure physics, that is, in the broader context of biology, nanotechnology, and everyday life.

The fill factor ($\mathrm{F F}$) is a critical parameter for solar cell efficiency, but its analytical description is challenging due to the interplay between recombination and charge extraction processes. A significant factor contributing to $\mathrm{F F}$ losses, beyond recombination, that has not received much attention is the influence of charge transport. In most state-of-the-art organic solar cells, the primary limitations of the $\mathrm{F F}$ do not just arise from non-radiative recombination, but also from low conductivity of the organic semiconductors. A closer look reveals that even in the highest efficiency cells, performance losses due to transport resistance are significant. This finding highlights the need for refined models to predict the $\mathrm{F F}$ accurately. Here, we extend the analytical model for transport resistance to a more general case by incorporating energetic disorder. We introduce a straightforward set of equations to predict the $\mathrm{F F}$ of a solar cell, enabling the differentiation of losses attributed to recombination and transport resistance. Our analytical model is validated with a large set of experimental current–voltage and light intensity-dependent open-circuit voltage data for a wide range of temperatures. Based on our findings, we provide valuable insights into strategies for mitigating $\mathrm{F F}$ losses, guiding the development of more efficient solar cell designs and optimisation strategies.

We review recent progress regarding the double scaled Sachdev–Ye–Kitaev model and other p-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in AdS₂. More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative q-deformed AdS₂. We conclude with discussion of related universality classes, and survey some of the current research directions.

The smoothed particle hydrodynamics (SPH) method is expanding and is being applied to more and more fields, particularly in engineering. The majority of current SPH developments deal with free-surface and multiphase flows, especially for situations where geometrically complex interface configurations are involved. The present review article covers the last 25 years of development of the method to simulate such flows, discussing the related specific features of the method. A path is drawn to link the milestone articles on the topic, and the main related theoretical and numerical issues are investigated. In particular, several SPH schemes have been derived over the years, based on different assumptions. The main ones are presented and discussed in this review underlining the different contexts and the ways in which they were derived, resulting in similarities and differences. In addition, a summary is provided of the recent corrections proposed to increase the accuracy, stability and robustness of SPH schemes in the context of free-surface and multiphase flows. Future perspectives of development are identified, placing the method within the panorama of Computational Fluid Dynamics.

Liquid–liquid crystalline phase separation (LLCPS) is the process by which an initially homogenous single-phase solution composed of a solvent-most frequently water- and a solute-typically rigid or semiflexible macromolecules, polymers, supramolecular aggregates, or filamentous colloids-demixes into two (or more) distinct phases in which one phase is depleted by the solute and features properties of isotropic solutions, whereas the other is enriched by the solute and exhibits liquid crystalline anisotropic properties. Differently from the more common liquid–liquid phase separation (LLPS) of flexible macromolecules, which is a trade-off between entropy and enthalpy, LLCPS is mostly an entropy-controlled process in which the morphology, composition and properties of the new phases depend primarily on kinetics and thermodynamic factors and, unexpectedly, on the history followed to reach a specific point in the phase diagram. This review aims to comprehensively discuss the process of LLCPS from experimental, theoretical, and simulation standpoints. We discuss the main systems and experimental approaches followed over the past decades to induce and control LLCPS, then we delve into the main theoretical and modeling approaches available to rationalize this process, and finally, we expand on how numerical simulations can significantly enrich the understanding of LLCPS. A final section touches on possible applications and the significance of LLCPS beyond pure physics, that is, in the broader context of biology, nanotechnology, and everyday life.

We review recent progress regarding the double scaled Sachdev–Ye–Kitaev model and other p-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in AdS₂. More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative q-deformed AdS₂. We conclude with discussion of related universality classes, and survey some of the current research directions.

The smoothed particle hydrodynamics (SPH) method is expanding and is being applied to more and more fields, particularly in engineering. The majority of current SPH developments deal with free-surface and multiphase flows, especially for situations where geometrically complex interface configurations are involved. The present review article covers the last 25 years of development of the method to simulate such flows, discussing the related specific features of the method. A path is drawn to link the milestone articles on the topic, and the main related theoretical and numerical issues are investigated. In particular, several SPH schemes have been derived over the years, based on different assumptions. The main ones are presented and discussed in this review underlining the different contexts and the ways in which they were derived, resulting in similarities and differences. In addition, a summary is provided of the recent corrections proposed to increase the accuracy, stability and robustness of SPH schemes in the context of free-surface and multiphase flows. Future perspectives of development are identified, placing the method within the panorama of Computational Fluid Dynamics.

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.

This review aims to comprehensively and systematically analyze the anodic oxidation process to form nanostructured oxide films on the surface of the most technologically relevant Fe-based alloys and steels. A special emphasis is put on detailed analysis of the mechanisms of the anodic formation of Fe-based nanostructured materials. The effect of anodizing parameters including the type of Fe-alloy, electrolyte composition, potential/current regimes, as well as various post-treatment procedures (including annealing treatment) on the growth, morphology, composition, and properties of the resulting oxide films is discussed in detail. Examples of possible applications of the anodic films grown on Fe-alloys in various fields including photocatalysis, energy storage, sensors, biomedicine, and others are also provided. Finally, current trends, challenges, and perspectives in the anodizing of Fe-alloys are addressed.

Two-dimensional (2D) material (graphene, MoS2, MXene, etc.) /group-III nitride (GaN, AlN, and their compounds) hetero-structures have been given special attention, on account of their prospective applications in remarkable performance broadband photodetectors, light-emitting diodes, solar cells, etc. The utilization of advantages of the above two kind materials provides a solution to the dilemma of the degradation of device performance and reliability caused by carrier mobility, lattice mismatch, interface, etc. Therefore, the summary of progress of 2D material/group-III nitride hetero-structures and devices is urgent. In this work, it elaborates on interface interaction and stimulation, growth and device of 2D material/group-III nitride hetero-structures. Initially, it investigates the properties of the hetero-structures, combining the theoretical calculations on interface interaction of the heterojunction with experimental study, particularly emphasizing on interface effects on the hetero-structures performance. Subsequently, the growth of 2D material/group-III nitride hetero-structures are introduced in detail. The problems solved by the advancing synthesis strategies and the formation mechanisms are discussed in particular. Afterwards, based on the 2D material/group-III nitride hetero-structures, devices extending from optoelectronics, electronics, to photocatalyst and sensors, etc., are reviewed. Finally, the prospect of 2D material/group-III nitride hetero-structures and devices is speculated to pave the way for the further promotion.