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Nucleation and growth is studied in a system undergoing diffusion-controlled condensation under gradual changes in parameters, such as cooling. It is demonstrated that when Gibbs-Thompson effect becomes negligible, the system falls into a universal regime. i.e. the final droplet size distribution remains invariant under certain rescaling of system parameters. An approximate yet very accurate analytic form is obtained for the size distribution function in this regime., Comment: 4 pages, 2 figures

Even a century after the formulation of Quantum Mechanics (QM), the wave function collapse (WFC) remains a contentious aspect of the theory. Environment-induced decoherence has offered a partial resolution by illustrating how unitary evolution in an open quantum system can lead to effective WFC within its components. However, this approach by itself does not lead to a fully self-consistent reformulation of QM. We introduce a modified set of QM postulates, which exclude both WFC and Born's probability rule. They are replaced with the Maximum Entropy Principle, a weaker postulate that specifies conditional probabilities for mutually compatible observations. Within this formulation, both WFC and Born's rule become emerging properties., Comment: 6 pages, 1 figure

Bond-orientational order in DNA-assembled nanoparticle lattices is explored with the help of recently introduced Symmetry-specific Bond Order Parameters (SymBOPs). This approach provides a more sensitive analysis of local order than traditional scalar Bond Order Parameters, facilitating the identification of coherent domains at the single bond level. The present study expands the method initially developed for assemblies of anisotropic particles to the isotropic ones or cases where particle orientation information is unavailable. The SymBOP analysis was applied to experiments on DNA-frame-based assembly of nanoparticle lattices. It proved highly sensitive in identifying coherent crystalline domains with different orientations, as well as detecting topological defects, such as dislocations. Furthermore, the analysis distinguishes individual sublattices within a single crystalline domain, such as pair of interpenetrating FCC lattices within a cubic diamond. The results underscore the versatility and robustness of SymBOPs in characterizing ordering phenomena, making them valuable tools for investigating structural properties in various systems., Comment: 12 pages, 12 figures

The expanded phthalocyanine (EPc) single-layer sheets with double transition metals (labeled as TM2EPc, TM = Sc-Zn) are predicted to be a new class of two-dimensional (2D) metal-organic materials with a series of favorable functional properties by means of systematic first-principle calculations and molecular dynamics simulations. The strong coordination between metal and EPc substrate accounts for the excellent structural stability. Chemical bonding analysis has demonstrated the absence of TM-TM bonding. Each metal center is isolated, but connected to the organic framework by four 2c-2e TM-N {\sigma}-bonds to form an extended 2D network. Unexpectedly, it is found that the V2EPc is an antiferromagnetic metal with Dirac cone, while Cr2EPc exhibits ferromagnetic Dirac half-metallicity, which is not common in 2D materials. Excitingly, the ferromagnetic Cr2EPc and antiferromagnetic Mn2- and Fe2-EPc have high magnetic transition temperatures of 223, 217, and 325 K, respectively, which are crucial for the practical applications of spintronics. Cr2EPc can maintain the Dirac half-metallicity under -6 % ~ 2 % biaxial strains, and Fe2EPc can transform from semiconductor to half-metal by applying -6 % ~ -10 % compressive strains. Additionally, the TM2EPc monolayers exhibit a full response to visible light and some materials have strong absorption in the ultraviolet and infrared regions in addition to visible light, showing extraordinary solar light-harvesting ability. Notably, the designed type-II heterojunctions Fe2EPc/SnC, Co2EPc/GeS, and Ni2EPc/2H-WSe2 have high power conversion efficiency (PCE > 15%), especially the PCE of Ni2EPc/2H-WSe2 reaches 25.19%, which has great potential in solar cell applications. All these desired properties render 2D TM2EPc monolayers promising candidates for future applications in nanoelectronics, spintronics,optoelectronics, and photovoltaic devices.

Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term orderly and predictable within the commensurate spin-orbit resonances, while at eccentricity approaching unity, chaos completely takes over. Here, we present the full 3D rotational equations of motion around all three principle axes for triaxial minor planets and two independent methods of numerical solution based on Euler rotations and quaternion algebra. The domains of chaotic rotation are numerically investigated over the entire range of eccentricity with a combination of trial integrations of Euler's equations of motion and the GALI($k$) method. We quantify the dependence of the order--chaos boundaries on shape by changing a prolateness parameter, and find that the main 1:1 spin-orbit resonance disappears for specific moderately prolate shapes already at eccentricities as low as 0.3. The island of short-term stability around the main 1:1 resonance shrinks with increasing eccentricity at a fixed low degree of prolateness and completely vanishes at approximately 0.8. This island is also encroached by chaos on longer time scales indicating longer Lyapunov exponents. Trajectories in the close vicinity of the 3:2 spin-orbit resonance become chaotic at smaller eccentricities, but separated enclaves of orderly rotation emerge at eccentricities as high as 0.8. Initial perturbations of rotational velocity in latitude away from the exact equilibrium result in a spectrum of free libration, nutation, and polar wander, which is not well matched by the linearized analysis omitting the inertial terms., Comment: Accepted in MNRAS

Brownian Dynamics is used to study self-assembly in a hybrid system of istotropic particles (IPs), combined with anisotropic building blocks that represent special "designer particles". Those are modeled as spherical patchy particles (PPs) with binding only allowed between their patches and IPs. In this study, two types of PPs are considered: Octahedral PPs (Oh-PPs) and Square PPs (Sq-PPs), with octahedral and square arrangements of patches, respectively. The self-assembly is additionally facilitated by the simulated annealing procedure. The resultant structures are characterized by a combination of local correlations in cubatic ordering, and a symmetry-specific variation of bond orientation order parameters (SymBOPs). By varying the PP/IP size ratio, we detected a sharp crossover between two distinct morphologies, in both types of systems. High symmetry phases, NaCl crystal for Oh-PP and square lattice for Sq-PP, are observed for larger size ratios. For smaller ones, the dominant morphologies are significantly different, e.g., Oh-PPs form a compact amorphous structure with predominantly Face-to-Face orientation of neighboring PPs. Unusually for a morphology without a long range order, it is still possible to identify well organized coherent clusters of this structure, thanks to the adoption of our SymBOP-based characterization., Comment: 9 pages, 14 figures

A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries. Two classes of tensor order parameters are associated with polyhedral nematic, and bond orientational order, respectively. For the latter, a variation of classical bond order parameters is introduced that takes advantage of the symmetry of constituent particles, and/or expected crystalline phases. These Symmetrized Bond Order Parameters (SymBOPs) can be averaged over an entire system, or assigned locally to an individual bond. By combining that with bond percolation procedure, one is able to identify coherent domains within a self-assembled structure. As a demonstration of the proposed framework, we apply it to a simulated hybrid system that combines isotropic and patchy particles with octahedral symmetry. Not only does the methodology allow one to identify individual crystalline domains, but it also detects coherent clusters of a peculiar compact amorphous structure that is not space-filling and lacks any long-range order., Comment: 8 pages, 4 figures

Using a realistic molecular catalyst system, we conduct scaling studies of ab initio molecular dynamics simulations using the CP2K code on both Intel Xeon CPU and NVIDIA V100 GPU architectures. We explore using process placement and affinity to gain additional performance improvements. We also use statistical methods to understand performance changes in spite of the variability in runtime for each molecular dynamics timestep. We found ideal conditions for CPU runs included at least four MPI ranks per node, bound evenly across each socket, and fully utilizing processing cores with one OpenMP thread per core, no benefit was shown from reserving cores for the system. The CPU-only simulations scaled at 70% or more of the ideal scaling up to 10 compute nodes, after which the returns began to diminish more quickly. Simulations on a single 40-core node with two NVIDIA V100 GPUs for acceleration achieved over 3.7x speedup compared to the fastest single 36-core node CPU-only version, and showed 13% speedup over the fastest time we achieved across five CPU-only nodes., Comment: 8 pages, 8 figures

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic packings in 2D and 3D, and the result is further expanded to the case of "floppy" particle clusters. The theory is directly applicable to sticky colloids, and in addition, generalizes concepts of granular and glassy configurational entropies for the case of non-jammed systems., Comment: 8 pages, 7 figures

It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, i.e. constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models we demonstrate the emergence of a new long timescale governing the epidemic in broad agreement with empirical data. Our model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multiple waves, which are transiently suppressed due to the dynamic nature of social activity. The existence of the long timescale due to the interplay between epidemic and social dynamics provides a unifying picture of how a fast-paced epidemic typically will transition to the endemic state.

We conducted a joint experimental-theoretical investigation of the high-pressure chemistry of europium polyhydrides at pressures of 86-130 GPa. We discovered several novel magnetic Eu superhydrides stabilized by anharmonic effects: cubic $EuH_{9}$, hexagonal $EuH_{9}$, and an unexpected cubic (Pm-3n) clathrate phase, $Eu_{8}H_{46}$. Monte Carlo simulations indicate that cubic $EuH_{9}$ has antiferromagnetic ordering with T(Neel) up to 24 K, whereas hexagonal $EuH_{9}$ and Pm-3n-$Eu_{8}H_{46}$ possess ferromagnetic ordering with T(Curie) = 137 and 336 K, respectively. The electron-phonon interaction is weak in all studied europium hydrides, and their magnetic ordering excludes s-wave superconductivity, except, perhaps, for distorted pseudohexagonal $EuH_{9}$. The equations of state predicted within the DFT+U approach (the Hubbard corrections were found within linear response theory) are in close agreement with the experimental data. This work shows the great influence of the atomic radius on symmetry-breaking distortions of the crystal structures of superhydrides and on their thermodynamic stability.

The results reported by Wei et al. [Phys. Rev. Lett. 124, 255502 (2020)] can be confronted with predictive, quantitative theories of negative thermal expansion (NTE) and pressure-induced softening, allowing to corroborate, or invalidate certain approaches. Motivated to corroborate the quantitative predictions of the recent Coulomb Floppy Network (CFN) microscopic theory of vibrational and thermomechanical properties of empty perovskite crystals [Tkachenko and Zaliznyak, arXiv:1908.11643 (2019)], we compared theory prediction for the mean-squared transverse displacement of the F atoms, U$_{perp}$, with that reported in Fig. 5 of Wei et al. and observed a marked discrepancy (an order-of-magnitude larger than the error bar). We then compared these results with the previously published Xray diffraction data of Greve, et al. [JACS 132, 15496 (2010)] and the neutron diffraction data of Wendt, et al. [Science Advances 5 (2019), 10.1126/sciadv.aay2748]. We found the latter two data sets to be in a good agreement with each other, as well as with the prediction of CFN theory. We thus conclude that U$_{perp}$ values reported in Fig. 5 of Wei et al. are substantially incorrect. The purpose of this Comment is twofold: (i) to caution the researchers against using the U$_{perp}$ data of Wei et al. for quantitative comparisons with theory, and (ii) to encourage Wei et al. to reconsider their analysis and obtain a reliable U$_{perp}$ data by better accounting for the beam transmission and attenuation effects., Comment: 1 page, 1 figure

The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem size. Increased depth can both degrade the accuracy of the results and reduce trainability. In this work, we propose a novel approach to reduce ansatz circuit depth. Our approach, called PermVQE, adds an additional optimization loop to VQE that permutes qubits in order to solve for the qubit Hamiltonian that minimizes long-range correlations in the ground state. The choice of permutations is based on mutual information, which is a measure of interaction between electrons in spin-orbitals. Encoding strongly interacting spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state. For representative molecular systems, LiH, H$_2$, (H$_2$)$_2$, H$_4$, and H$_3^+$, we demonstrate for linear qubit connectivity that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. This approach can be extended to any qubit connectivity and can significantly reduce the depth required to reach a desired accuracy in VQE. Moreover, our approach can be applied to other variational quantum algorithms beyond VQE., Comment: 11 pages, 8 figures, 10 pages of Supplemental Material

The emergence of longer information-carrying and functional nucleotide polymers from random short strands was a major stepping stone at the dawn of life. But the formation of those polymers under temperature oscillation required some form of selection. A plausible mechanism is template-based ligation where theoretical work already suggested a reduction in information entropy. Here, we show how nontrivial sequence patterns emerge in a system of random 12mer DNA sequences subject to enzyme-based templated ligation reaction and temperature cycling. The strands acted both as a template and substrates of the reaction and thereby formed longer oligomers. The selection for templating sequences leads to the development of a multiscale ligation landscape. A position-dependent sequence pattern emerged with a segregation into mutually complementary pools of A-rich and T-rich sequences. Even without selection for function, the base pairing of DNA with ligation showed a dynamics resembling Darwinian evolution., Comment: 11 pages, 5 figures, SI attached

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through parameterization. We derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Transient and long-term levels of heterogeneity are estimated by using empirical data from the COVID-19 epidemic as well as from real-life face-to-face contact networks. These results suggest that the hardest-hit areas, such as NYC, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.

We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov Chain Monte Carlo (MCMC) methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its sub-regions in order to account for the wide disparities in population size and density. Without prior information on non-pharmaceutical interventions (NPIs), the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing Stay-at-Home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic., Comment: The manuscript uses data provided by the Illinois Department of Public Health through a Data Use Agreement with Civis Analytics. The source code for the model is freely available online at https://github.com/uiuc-covid19-modeling/pydemic. v3 includes demonstration of modeling for New York City

We develop an approach for fitting the results of modeling of wriggling radial large scale iron pattern along the Galactic disk, derived over young (high massive) Cepheids, with the metallicity distribution, obtained using low mass long living dwarf stars in the close solar vicinity. For this, at the step of computing of the theoretical abundance distribution over low mass stars in the solar vicinity we propose to redefine the initial mass function so as the resulting theoretical stellar distribution over masses would be close to the distribution in the observed sample. By means of the above algorithm and subsequent corrections of the theoretical metallicity distribution function, described in literature, we have achieved fairly well agreement of the theoretical and observed metallicity distribution functions for low mass stars in the local solar vicinity., Comment: 10 pages, 6 figures

Floppy Networks (FNs) provide valuable insight into the origin of anomalous mechanical and thermal properties in soft matter systems, from polymers, rubber, and biomolecules to glasses and granular materials. Here, we use the very same FN concept to construct a quantitative microscopic theory of empty perovskites, a family of crystals with ReO$_3$ structure, which exhibit a number of unusual properties. One remarkable example is ScF$_3$, which shows a near-zero-temperature structural instability and large negative thermal expansion (NTE). We trace these effects to an FN-like crystalline architecture formed by strong nearest-neighbor bonds, which is stabilized by net electrostatic repulsion that plays a role similar to osmotic pressure in polymeric gels. NTE in these crystalline solids, which we conceptualize as Coulomb Floppy Networks, emerges from the tension effect of Coulomb repulsion combined with the FN's entropic elasticity, and has the same physical origin as in gels and rubber. Our theory provides an accurate, quantitative description of phonons, thermal expansion, compressibility, and structural phase diagram, all in excellent agreement with experiments. The entropic stabilization of critical soft modes, which play only a secondary role in NTE, explains the observed phase diagram. Significant entropic elasticity resolves the puzzle of a marked, $\approx$50\% discrepancy between the experimentally observed bulk modulus and ab initio calculations. The Coulomb FN approach is potentially applicable to other important materials with markedly covalent bonds, from perovskite oxides to iron chalcogenides, whose anomalous vibrational and structural properties are still poorly understood., Comment: Manuscript with appendices, 12 pages, 3 figures

We outline the Minimalistic Measurement Scheme (MMS) compatible with regular unitary evolution of a closed quantum system. Within this approach, a part of the system becomes informationally isolated (restricted) which leads to a natural emergence of the classical domain. This measurement scenario is a simpler alternative to environment-induced decoherence. In its basic version, MMS involves two ancilla qubits, $A$ and $X$, entangled with each other and with the System $S$. Informational or thermodynamic cost of measurement is represented by $X$-qubit being isolated, i.e. becoming unavailable for future interactions with the rest of the system. Conditional upon this isolation, $A$-qubit, that plays the role of an Apparatus, becomes classical and records the outcome of the measurement. The procedure may be used to perform von Neumann-style projective measurements or generalized ones, that corresponds to Positive-Operator Value Measure (POVM). By repeating the same generalized measurement multiple times with different $A$- and $X$-qubits, one asymptotically approaches the wave function collapse in the basis determined by the premeasurement process. We present a simple result for the total information extracted after $N$ such weak measurements. Building upon MMS, we propose a construction that maps a history of a quantum system onto a set of $A$-qubits. It resembles the Consistent History (CH) formulation of Quantum Mechanics (QM), but is distinct from it, and is built entirely within the conventional QM. In particular, consistency postulate of CH formalism is not automatically satisfied, but rather is an emerging property. Namely, each measurement event corresponds to the branching of mutually exclusive classical realities whose probabilities are additive. In a general case, however, the superposition between different histories is determined by the history density matrix., Comment: 8 pages, 4 figures, substantially expanded

TUS (Tracking Ultraviolet Set-up) is the world's first orbital detector of ultra-high-energy cosmic rays (UHECRs). It was launched into orbit on 28th April 2016 as a part of the scientific payload of the Lomonosov satellite. The main aim of the mission was to test the technique of measuring the ultraviolet fluorescence and Cherenkov radiation of extensive air showers generated by primary cosmic rays with energies above ~100 EeV in the Earth atmosphere from space. During its operation for 1.5 years, TUS registered almost 80,000 events with a few of them satisfying conditions anticipated for extensive air showers (EASs) initiated by UHECRs. Here we discuss an event registered on 3rd October 2016. The event was measured in perfect observation conditions as an ultraviolet track in the nocturnal atmosphere of the Earth, with the kinematics and the light curve similar to those expected from an EAS. A reconstruction of parameters of a primary particle gave the zenith angle around 44$^\circ$ but an extreme energy not compatible with the cosmic ray energy spectrum obtained with ground-based experiments. We discuss in details all conditions of registering the event, explain the reconstruction procedure and its limitations and comment on possible sources of the signal, both of anthropogenic and astrophysical origin. We believe this detection represents a significant milestone in the space-based observation of UHECRs because it proves the capability of an orbital telescope to detect light signals with the apparent motion and light shape similar to what are expected from EASs. This is important for the on-going development of the future missions KLYPVE-EUSO and POEMMA, aimed for studying UHECRs from space., Comment: 24 pages; v2: important changes to address comments by the anonymous referee; main conclusions unchanged

We studied the van der Waals interactions of two finite, solid, cylindrical rods at arbitrary angle and position with respect to each other. An analytic interpolative formula for the interaction potential energy is constructed, based on various asymptotic cases. The potential can be readily used for numerical and analytic description of multi-wall carbon nanotubes, metallic nanorods, rod-shaped colloids, or any other similar objects with significant van der Waals interactions.