Table of contents

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.

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 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.

A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer's potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize the resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm's number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.

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.

A search for light long-lived particles (LLPs) decaying to displaced jets is presented, using a data sample of proton–proton collisions at a center-of-mass energy of 13.6 TeV, corresponding to an integrated luminosity of 34.7 fb⁻¹, collected with the CMS detector at the CERN LHC in 2022. Novel trigger, reconstruction, and machine-learning techniques were developed for and employed in this search. After all selections, the observations are consistent with the background predictions. Limits are presented on the branching fraction of the Higgs boson to LLPs that subsequently decay to quark pairs or tau lepton pairs. An improvement by up to a factor of 10 is achieved over previous limits for models with LLP masses smaller than 60 GeV and proper decay lengths smaller than 1 m. The first constraints are placed on the fraternal twin Higgs (FTH) and folded supersymmetry (FSUSY) models, where the lower bounds on the top quark partner mass reach up to 350 GeV for the FTH model and 250 GeV for the FSUSY model.

Irradiation of condensed matter with ionizing radiation generally causes direct photoionization as well as secondary processes that often dominate the ionization dynamics. Here, large helium (He) nanodroplets with radius $\gtrsim40\,$nm doped with lithium (Li) atoms are irradiated with extreme ultraviolet (XUV) photons of energy $h\nu\unicode{x2A7E} 44.4$ eV and indirect ionization of the Li dopants is observed in addition to direct photoionization of the He droplets. Specifically, Li ions are efficiently produced by an interatomic Coulombic decay (ICD) process involving metastable He$^*$ atoms and He$_2^*$ excimers which are populated by elastic and inelastic scattering of photoelectrons in the nanodroplets as well as by electron-ion recombination. This type of indirect ICD, observed in large He nanodroplets in nearly the entire XUV range, turns out to be more efficient than Li dopant ionization by ICD following direct resonant photoexcitation at $h\nu = 21.6\,$eV and by charge-transfer ionization. Indirect ICD processes induced by scattering of photoelectrons likely play an important role in other condensed phase systems exposed to ionizing radiation as well, including biological matter.

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.