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The development of sustainable energy economies is blocked by the lack of stable electrical energy sources with high power and energy densities. Next‐generation supercapacitors utilizing 2D layered double hydroxides (LDHs) promise to fill this need in hybrid and standalone architectures; however, despite their high power and energy densities, LDH supercapacitors have poor stability. New methods for creating robust LDH electrodes are necessary to prevent this degradation. Herein, the recently developed annular microreactor is used to synthesize defect‐rich NiCoLDH nanocrystals. A simple, solvent‐based method is used to rationally generate binder‐free, superstructured thin films on Ni foam electrodes. Control over crystallite size, thinness, and orientation improves contact with the conductive substrate, increases reactivity, and improves structural stability. Optimized electrodes are fabricated with specific capacitances from 3000 to 5000 F g−1 at charging rates as high as 1000 A g−1, a performance that is retained after 20 000 cycles. This is twice as stable at 5000 times the current density of the most stable reported Ni‐based supercapacitor. Ultimately, this study addresses key concerns in electrode development, introduces new approaches through reactor technology and solvent‐mediated assembly, and opens new ground for more fundamental inquiries into the mechanisms of electron transport in 2D systems.

Identity‐based encryption (IBE), introduced by Shamir, eliminates the need for public‐key infrastructure. The sender can simply encrypt a message by using the recipient's identity (such as email or IP address) without needing to look up the public key. In particular, when ciphertexts of an IBE do not reveal recipient's identity, this scheme is known as an anonymous IBE scheme. Recently, Blazy et al. (ARES '19) analysed the trade‐off between public safety and unconditional privacy in anonymous IBE and introduced a new notion that incorporates traceability into anonymous IBE, called anonymous IBE with traceable identities (AIBET). However, their construction is based on the discrete logarithm assumption, which is insecure in the quantum era. In this paper, we first formalize the consistency of tracing key of the AIBET scheme to ensure that a ciphertext cannot be traced with the use of wrong tracing keys. Subsequently, we present a generic formulation concept that can be used to transform structure‐specific lattice‐based anonymous IBE schemes into an AIBET. Finally, we apply this concept to Katsumata and Yamada's compact anonymous IBE scheme (Asiacrypt '16) to obtain the first quantum‐resistant AIBET scheme that is adaptively secure under the ring learning with errors assumption without random oracle.

In this paper, we prove two identities involving quantum derivatives, quantum integrals, and certain parameters. Using the newly proved identities, we prove new inequalities of Simpson's and Newton's type for quantum differentiable convex functions under certain assumptions. Moreover, we discuss the special cases of our main results and obtain some new and existing Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities. National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11971241] National Natural Science Foundation of China, Grant/Award Number: 11971241 WOS:000710085000001 2-s2.0-85117687946

The measurement problem concerns an apparent conflict between the two fundamental principles of quantum mechanics, namely the Schrodinger equation and the measurement postulate. These principles describe inconsistent behavior for quantum systems in so-called "measurement contexts." Many theorists have thought that the measurement problem can only be resolved by proposing a mechanistic explanation of (genuine or apparent) wavefunction collapse that avoids explicit reference to "measurement." However, I argue here that the measurement problem dissolves if we accept Humeanism about laws of nature. On a Humean metaphysics, there is no conflict between the two principles, nor is there any inherent problem with the concept of "measurement" figuring into the account of collapse.

Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of quantum computing will help to solve many complex and computationally intractable problems in several areas such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm have brought quantum computing much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era - the next logical step being the quantum advantage whereby quantum computers solve a real-world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. Quantum computing is a highly topical and fast-moving field of research with significant ongoing progress in all facets. This article presents a comprehensive review of quantum computing literature, and taxonomy of quantum computing. Further, the proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post-quantum cryptography and quantum computer hardware development to document the current state-of-the-art in the respective areas. We finish the article by highlighting various open challenges and promising future directions for research.

Feshbach resonances in D + HD(v = 1, j = 0) reaction are studied by using the time-independent quantum method. The integral cross section (ICS) results present three Feshbach resonance peaks, which are different from H + HD(v = 1, j = 0) reaction dominated by only one peak. These resonances are attributed to coupling with adiabatic effective potentials of D + HD(v = 1, j = 1) reaction, and the most obvious peak is contributed by J = 1 at 83.16 cm-1 collision energy. For J = 0 and 2, the resonances are related with the same L partial wave and present a double-peak structure in total ICS. The characteristics of product angular distribution show that the resonance of J = 1 is long-lived, while the lifetimes are relatively shorter for the resonance of J = 0 and 2.

Of quantum physics, quantum chemistry and quantum mechanics, the latter is least useful for both chemical education and the practice of chemistry as a science concerned with the reactions and properties of chemical substances. We show that quantum mechanics must be viewed as a collection of methods, numbering at least thirteen, that one might apply for calculations on a system of an atomic scale. Instead of quantum mechanics we advocate the quantum laws or laws of discreteness, which have simple roots in laws of conservation and which have practical applications in various areas of observations of chemical phenomena. We conclude that quantum mechanics is largely irrelevant for the general practice of chemistry.

In the standard implementation of Borgnakke–Larsen (BL) rotation and translation energy exchange in DSMC not every rotational mode of each molecule is active in every collision. In some collisions, the rotation mode of one molecule is “frozen” (cannot be changed by the collision); in other collisions the rotation mode of both molecules is frozen. Different relaxation rates are obtained by varying the proportion of frozen-rotation collisions. In 1974 Larsen and Borgnakke proposed a “restricted exchange” version of BL in which a portion of the energy of each mode is frozen in each collision; the method seemed physically plausible but did not satisfy the detailed balance condition. In 1978 Pullin proposed a general restricted exchange of BL exchange which did satisfy the detailed balance condition; it was more CPU intensive than the original BL scheme. It was seen as “laborius” and “cumbersome” and it seemed to be incompatible with vibration energy-exchange models. Here a simplified version, a special case, of Pullin's restricted exchange scheme is described. The new method is only 12%–17% more CPU-intensive than standard BL methods and can be used with the standard DSMC quantum vibration exchange model. It is shown that the elimination of frozen-rotation collisions changes the high energy distribution of vibration energy in nonequilibrium conditions which may slightly decrease the nonequilibrium dissociation rate when restricted exchange is used with the quantum-kinetic method for dissociation reactions.

Efficient organic emitters in the deep-red region are rare due to the "energy gap law". Herein, multiple boron (B)- and nitrogen (N)-atoms embedded polycyclic heteroaromatics featuring hybridized π-bonding/ non-bonding molecular orbitals are constructed, providing a way to overcome the above luminescent boundary. The introduction of B-phenyl-B and N-phenyl-N structures enhances the electronic coupling of those para-positioned atoms, forming restricted π-bonds on the phenyl-core for delocalized excited states and thus a narrow energy gap. The mutually ortho-positioned B- and N-atoms also induce a multi-resonance effect on the peripheral skeleton for the non-bonding orbitals, creating shallow potential energy surfaces to eliminate the high-frequency vibrational quenching. The corresponding deep-red emitters with peaks at 662 and 692 nm exhibit narrow full-width at half-maximums of 38 nm, high radiative decay rates of ca. 108 s-1 , ≈100 % photo-luminescence quantum yields and record-high maximum external quantum efficiencies of ca. 28 % in a normal planar organic light-emitting diode structure, simultaneously.

A delicate interplay of covalent and noncovalent interactions gives proteins their unique ability to flexibly play numerous roles in cellular processes. This interplay is inherently quantum mechanical and highly dynamic in nature. To directly interrogate the evolving nature of the electronic structure of proteins, we carry out 100-ps-scale ab initio molecular dynamics simulations of three representative small proteins with range-separated hybrid density functional theory. We quantify the nature and length-scale of the coupling of residue-specific charge probability distributions in these proteins. While some nonpolar residues exhibit expectedly narrow charge distributions, most polar and charged residues exhibit broad, multimodal distributions. Even for nonpolar residues, we observe sequence-specific deviations corresponding to charge accumulation or depletion that would be challenging to capture in a fixed charge force field. We quantify the effect of residue–residue interactions on charge distributions first with linear cross-correlations. We then show how additional insight can be gained from evaluating the mutual information of charge distributions. We show that a significant number of residues couple most strongly with residues that are distant in both sequence and space over a range of secondary structures including a-helical, b-sheet, disulfide bridging, and lasso motifs. The mutual information analysis is necessary to capture coupling between some polar and charged residues. These analyses are expected to be broadly useful in understanding the mechanisms of long-range charge transfer in proteins and for determining what interactions require a quantum mechanical description for predictive simulation of enzyme mechanism and protein function.

In this contribution, we report on a class of emitters based on bridged oxo‐ and/or thioethers revealing striking photoluminescence properties in fluid solution and in the solid state. In total, nine compounds were investigated concerning their photophysical properties, which were interpreted by quantum chemical calculations. To our delight, we discovered compounds possessing nearly identical photoluminescence quantum yields (Φ F) in solution and in the solid state, which has been rarely reported so far. Besides these efforts, we shed light on the influence of polymorphism and solvent polarity on the emission properties. In addition, an in‐depth X‐ray diffractometric analysis was conducted to correlate molecular packing in the crystal with differences in the photophysical properties., A highly emissive system based on bridged aromatic oxo‐ and/or thioethers is implemented. These compounds reveal striking emission properties in the solid state as well as in fluid solutions. Furthermore, solvatochromism as well as polymorphism were observed and the structure‐property relationship within a library of nine different compounds was assessed.

The formal Cu(III) complex [Cu(CF3)4]1− has often served as a paradigmatic example of challenging oxidation state assignment – with many reports proposing conflicting descriptions. Here we report a computational analysis of this compound, employing Energy Decomposition Analysis and Intrinsic Bond Orbital Analysis. We present a quasi-d10 perspective of the metal centre, resulting from ambiguities in d-electron counting. The implications for describing reactions which undergo oxidation state changes, such as the formal reductive elimination from the analogous [Cu(CF3)3(CH2Ph)]1− complex (Paeth et al. J. Am. Chem. Soc. 2019, 141, 3153), are probed. Electron flow analysis finds that the changes in electronic structure may be understood as a quasi-d10 to d10 transition at the metal centre, rendering this process essentially redox neutral. This is reminiscent of a previously studied formal Ni(IV) complex (Steen et al., Angew. Chem. Int. Ed. 2019, 58, 13133–13139), and indicates that our description of electronic structure has implications for the understanding of elementary organometallic reaction steps.

For quantum symmetric pairs $(\textbf {U}, \textbf {U}^\imath )$ of Kac–Moody type, we construct $\imath$-canonical bases for the highest weight integrable $\textbf U$-modules and their tensor products regarded as $\textbf {U}^\imath$-modules, as well as an $\imath$-canonical basis for the modified form of the $\imath$-quantum group $\textbf {U}^\imath$. A key new ingredient is a family of explicit elements called $\imath$-divided powers, which are shown to generate the integral form of $\dot {\textbf {U}}^\imath$. We prove a conjecture of Balagovic–Kolb, removing a major technical assumption in the theory of quantum symmetric pairs. Even for quantum symmetric pairs of finite type, our new approach simplifies and strengthens the integrality of quasi-$K$-matrix and the constructions of $\imath$-canonical bases, by avoiding a case-by-case rank-one analysis and removing the strong constraints on the parameters in a previous work.

The negative impact of rare-earth elements (REEs) on the environment, limited supply and high cost prompt the need for REE-free phosphor-converted white light-emitting diodes (LEDs). Here, we report the gram-scale synthesis of red/green/blue solid-state bandgap fluorescent carbon quantum rings (R/G/B-SBF-CQRs) with high quantum yields up to 30-46 %. This was achieved using cyano-group-bearing p-phenyldiacetonitrile as precursor and forming carbon quantum rings of different diameters through the linkage of curved carbon quantum ribbons of different lengths. The results show the role of cyano groups in inducing the curvature of the carbon quantum ribbons for CQR formation and emission of stable solid-state bandgap fluorescence. R/G/B-SBF-CQRs-phosphor-based LEDs emitted warm white light with low CCT (3576 K), high CRI (96.6), and high luminous efficiency (48.7 lm W-1 ), comparable to REE-phosphor-based LEDs.

No‐wait flow shop scheduling problems (NWFSPs) are widespread in practical applications. The authors propose a quantum‐inspired cuckoo co‐evolutionary algorithm for the NWFSP to minimize the makespan. There are three algorithm components: quantum solution construction, quantum population evolution, and an improved neighbourhood local search. They generate initial solutions, search solutions, and improve solution qualities, respectively. Parameters of the proposed algorithm are calibrated statistically. The proposal with calibrated parameters is compared with three existing algorithms on Reeves and Taillard benchmark instances with middle scales. Experimental results show that the proposal outperforms the compared algorithms.

Current Additive Manufacturing machines have limited techniques to observe process conditions and to decrease process errors. In order to overcome these limitations and increase the level and accuracy of machine intelligence, machine conditions need to be monitored more meticulously. A novel method for the condition monitoring of a 3D‐printer is proposed in this paper. Quantum support vector machine (QSVM) is compiled for recognizing the health condition of the 3D‐printer. The proposed quantum machine learning approach helps in monitoring the health state of the machine and classifies the same as healthy or aberrant. Classical machine learning approaches are inefficient to process the large amount of experimental data in real time. For better decision‐making on such big data, quantum machine learning approaches are deployed which are much more efficient due to their exponential speed and parallel operation on complex sensor data, they show speedups in both the dimensionality and number of experimental data deployed to train the algorithm. The simulation results show that the proposed method has higher accuracy in fault diagnosis than the traditional Support Vector Machine. All the numerical simulations and experiments have been carried out on a real quantum hardware provided by the IBM Quantum computing over the cloud.

A number of synthetic methodologies and applications of carbon quantum dots (CQDs) have been reported since they were first discovered nearly two decades ago. Unlike metal-based or semiconductor-based (e. g., metal chalcogenides) quantum dots (MSQDs), CQDs have the unique feature of being prepared through a variety of synthetic protocols, which are typically understood from considerations of reaction models and photoluminescence mechanisms. Consequently, this brief review article describes quantum dots, in general, and CQDs, in particular, from various viewpoints: (i) their definition, (ii) their photophysical properties, and (iii) the superiority of CQDs over MSQDs. Where possible, comparisons are made between CQDs and MSQDs. First, however, the review begins with a general brief description of quantum dots (QDs) as nanomaterials (sizes≤10 nm), followed by a short description of MSQDs and CQDs. Described subsequently are the various top-down and bottom-up approaches to synthesize CQDs followed by their distinctive photophysical properties (emission spectra; quantum yields, Φs).

Metal-organic framework (MOF) in biomass valorization is a promising technology developed in recent decades. By tailoring both the metal nodes and organic ligands, MOFs exhibit multiple functionalities, which not only extend their applicability in biomass conversion but also increase the complexity of material designs. To address this issue, quantum mechanical simulations have been used to provide mechanistic insights into the catalysis of biomass-derived molecules, which could potentially facilitate the development of novel MOF-based materials for biomass valorization. The aim of this review is to survey recent quantum mechanical simulations on biomass reactions occurring in MOF catalysts, with the emphasis on the studies of the catalytic activity of active sites and the effects of organic ligand and porous structures on the kinetics. Moreover, different model systems and computational methods used for MOF simulations are also surveyed and discussed in this review.

Access to dithiophene‐fused oxadiborepins and the first azadiborepins attained via a modular synthesis route are presented. The new compounds emit intense blue light, some of which demonstrate fluorescence quantum yields close to unity. Cyclic voltammetry (CV) revealed electrochemically reversible one‐electron reduction processes. The weak aromatic character of the novel 1,2,7‐azadiborepin ring is demonstrated with in‐depth theoretical investigations using nucleus‐independent chemical shift (NICS) scans and anisotropy of the induced current density (ACID) calculations., Dithienooxa‐ and ‐azadiborepins are accessible in a modular way from a common precursor. These BNB‐doped polycyclic aromatic hydrocarbons (PAHs) are highly efficient blue‐light emitters with quantum yields up to 96 %. In‐depth theoretical studies reveal that the previously unknown azadiborepin ring system is weakly aromatic.

This paper proves the validity of the joint mean-field and classical limit of the quantum $N$-body dynamics leading to the pressureless Euler-Poisson system for factorized initial data whose first marginal has a monokinetic Wigner measure. The interaction potential is assumed to be the repulsive Coulomb potential. The validity of this derivation is limited to finite time intervals on which the Euler-Poisson system has a smooth solution that is rapidly decaying at infinity. One key ingredient in the proof is an inequality from [S. Serfaty, with an appendix of M. Duerinckx arXiv:1803.08345v3 [math.AP]].

A large area photo‐diode based homodyne detector for free‐space quantum coherent communication is reported. The detector's performance is studied in terms of the detection bandwidth and electronic noise for shot‐noise limited quantum signal detection. Using large area photo‐diodes increases the signal collection efficiency from turbulent atmospheric channels, in comparison with thetypical fibre‐based free‐space homodyne detectors. Under identical atmospheric turbulence and receiver aperture conditions, over a 700‐km free‐space link at 90° elevation angle, our homodyne detector based on a diameter of 1mm photo‐diode experiences 0dB loss due to turbulence, while a 10‐um fibre‐based detector experiences 13.5dB of signal loss.

Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale and a less accurate quantum theory at the global scale. We introduce the first quantum embedding theory that is also variational, in that it is guaranteed to provide a one-sided bound for the exact ground-state energy. Our method, which we call the variational embedding method, provides a lower bound for this quantity. The method relaxes the representability conditions for quantum marginals to a set of linear and semidefinite constraints that operate at both local and global scales, resulting in a semidefinite program (SDP) to be solved numerically. The accuracy of the method can be systematically improved. The method is versatile and can be applied, in particular, to quantum many-body problems for both quantum spin systems and fermionic systems, such as those arising from electronic structure calculations. We describe how the proper notion of quantum marginal, sufficiently general to accommodate both of these settings, should be phrased in terms of certain algebras of operators. We also investigate the duality theory for our SDPs, which offers valuable perspective on our method as an embedding theory. As a byproduct of this investigation, we describe a formulation for efficiently implementing the variational embedding method via a partial dualization procedure and the solution of quantum analogs of the Kantorovich problem from optimal transport theory.

In this study, we established some new inequalities of Ostrowski type for the functions of two variables by using the concept of newly defined double quantum integrals. We also revealed that the results presented in this paper are the consolidation and generalization of some existing results on the literature of Ostrowski inequalities. WOS:000616064200001 2-s2.0-85100764477

Well defined detection and analysis of nanoparticle-sized samples such as extracellular vesicles or viruses may be important for potential disease diagnostics. However, using conventional flow-cytometry optical methods to evaluate such small particles is quite challenging. The reason is that the particle is smaller than the diffraction limit, making detection difficult. An alternative approach is fluorescence detection via conjugated fluorochromes attached to the nanoparticles; the challenge in this case is the limitation imposed upon detection of a very small number of emitted photons buried in high background photon counts. Emitted fluorescence is described by the well-known equation kf = σa I Q, which describes the emitted fluorescence rate (kf) (photons/s) as the multiplication of molecular absorption cross section(σa), excitation intensity (I), and quantum yield (Q). In addition, the excitation rate is equal to 1/t, which is the inverse of the lifetime of several ns representing the most typical conjugated fluorescent molecules used in flow cytometry. We recently developed a sub-ns photon sensor that is faster than most fluorescence lifetimes, since sub-ns speed is a critically important parameter for the separation of individual emitted photons. Based on our observation of fluorescence and background levels on typical commercial flow cytometers it is evident that a significant component of the background is induced by water-molecular vibrations. Therefore, understanding what constitutes all the components that contribute to the signals we measure in flow cytometry would help in defining what we currently call "background signals." We attempted to define a theoretical model to try to unravel these issues. This model was based on use of a reflective dry surface in the absence of water molecules. Our objective was to determine if it is possible to minimize background and enhance signal, and to provide valuable information on the contributing components of the signals collected. In order to test this model, we tested a single dried particle 50 nm in diameter on a reflective surface with minimum background. While this is clearly not a standard biological system, our results suggest that this quantum approach closely follows established photon base theory. Our goal was to define the parameters for practical nanoparticle-fluorescence analysis while enhancing our knowledge of the contribution of background properties.

Multi-layer π-stacked emitters based on spatially confined donor/acceptor/donor (D/A/D) patterns have been developed to achieve high-efficiency thermally activated delayed fluorescence (TADF). In this case, dual donor moieties and a single acceptor moiety are introduced to form two three-dimensional (3D) emitters, DM-BD1 and DM-BD2, which rely on spatial charge transfer (CT). Owing to the enforced face-to-face D/A/D pattern, effective CT interactions are realized, which lead to high photoluminescence quantum yields (PLQYs) of 94.2 % and 92.8 % for the two molecules, respectively. The resulting emitters exhibit small singlet-triplet energy splitting (ΔEST ) and fast reverse intersystem crossing (RISC) processes. Maximum external quantum efficiencies (EQEs) of 28.0 % and 26.6 % were realized for devices based on DM-BD1 and DM-BD2, respectively, which are higher than those of their D/A-type analogues.

This chapter explains the journey of modern magnetism from the beginning of the twentieth century, a remarkable age of scientific breakthroughs that led tithe birth of quantum mechanics and special relativity. A modern understanding of magnetism is based on the concept of spin, which is a purely quantum mechanical property with no classical analogy. To discuss magnetism in a contemporary perspective, therefore, we should start from quantum mechanics. Rather than simply going through formula derivations and jumping into the modern‐yet‐hindsight spin‐based interpretation of microscopic origin of magnetism in matters, instead, the chapter briefly discusses the history of its development. Depending on their responses to the applied magnetic field, these magnetic properties can be roughly categorized into diamagnetism, paramagnet‐ism, ferromagnetism, anti ferromagnetism, and ferrimagnetism. Diamagnetism is present in all materials but is often obscured by paramagnetism or ferromagnetism when unpaired electrons are in presence.

We find a substantial class of pairs of $*$-homomorphisms between graph C*-algebras of the form $C^*(E)\hookrightarrow C^*(G)\twoheadleftarrow C^*(F)$ whose pullback C*-algebra is an AF graph C*-algebra. Our result can be interpreted as a recipe for determining the quantum space obtained by shrinking a quantum subspace. There is a variety of examples from noncommutative topology, such as quantum complex projective spaces (including the standard Podle\'s quantum sphere) or quantum teardrops, that instantiate the result. Furthermore, to go beyond AF graph C*-algebras, we consider extensions of graphs over sinks and prove an analogous theorem for the thus obtained graph C*-algebras., Comment: 17 pages; main results are reformulated and their proofs corrected

Due to low power consumption, tunable wavelength and long lifetime ultraviolet light-emitting diodes (UV LEDs) have found many applications in different fields such as health care, water disinfection, agriculture. In this review, we report different problems that lead to low external quantum efficiency of UV LEDs. We also report various challenges in the growth process of the UV LEDs such as increase in the dislocation density, which affects the optoelectronic performance of the devices. We also report the analysis of the two modes of light polarization, i.e. transverse electric and transverse magnetic in UV LEDs. Moreover, we also summarize various state-of-the-art reported external quantum efficiencies, light output power and peak emission wavelengths in the three UV wavelength regimes, i.e. UV-A, UV-B and UV-C LEDs.

π‐Extended systems are key components for the development of future organic electronic technologies. While conceiving molecules with improved properties is fundamental for the evolution of materials science, keeping control over the 3D arrangement of molecules represents an ever‐expanding challenge. Herein, a synthetic protocol to replace carbon atoms of π‐systems by dissymmetric phosphorus atoms is reported; in particular, it allowed for conceiving new fused phosphapyrene derivatives with improved properties. The presence of dissymmetric phosphorus atoms precluded the formation of excimers. X‐ray diffraction revealed that, meanwhile, strong intermolecular interactions are taking place in the solid state. The phosphapyrenes photoluminesce in the visible region with high quantum yields; importantly, they are CD‐active. In addition, the unique non‐planar features of phosphorus atoms allowed for the control of the 3D arrangement of molecules, rendering lemniscate‐like structures. Based on our discoveries, we envisage the possibility to construct higher‐order, chiral 3D architectures from larger phosphorus‐containing π‐systems., A synthetic method to replace carbon atoms of π‐extended systems by dissymmetric phosphorus centers was developed. It allowed to conceive optically active, luminescent phosphapyrenes whose dissymmetric phosphorus atoms could be employed as cornerstone to keep control over the 3D arrangement of molecules

The manipulation of individual copies of quantum systems is one of the most groundbreaking experimental discoveries in the field of quantum physics. On both an experimental and a theoretical level, it has been shown that the dynamics of a single copy of an open quantum system is a trajectory of a piecewise-deterministic process. To the best of our knowledge, this application field has not been explored by the literature in applied mathematics, from both probabilistic and statistical perspectives. The objective of this chapter is to provide a self-contained presentation of this kind of model, as well as its specificities in terms of observations scheme of the system, and a first attempt to deal with a statistical issue that arises in the quantum world.