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Nonadiabatic quantum–classical mapping approaches have significantly gained in popularity over the past several decades because they have acceptable accuracy while remaining numerically tractable even for large system sizes. In the recent few years, several novel mapping approaches have been developed that display higher accuracy than the traditional Ehrenfest method, linearized semiclassical initial value representation (LSC-IVR), and Poisson bracket mapping equation (PBME) approaches. While various benchmarks have already demonstrated the advantages and limitations of those methods, unified theoretical justifications of their short-time accuracy are still demanded. In this article, we systematically examine the intra-electron correlation, as a statistical measure of electronic phase space, which has been first formally proposed for mapping approaches in the context of the generalized discrete truncated Wigner approximation and which is a key ingredient for the improvement in short-time accuracy of such mapping approaches. We rigorously establish the connection between short-time accuracy and intra-electron correlation for various widely used models. We find that LSC-IVR, PBME, and Ehrenfest methods fail to correctly reproduce the intra-electron correlation. While some of the traceless Meyer–Miller–Stock–Thoss (MMST) approaches, partially linearized density matrix (PLDM) approach, and spin partially linearized density matrix (spin-PLDM) approach are able to sample the intra-electron correlation correctly, the spin linearized semiclassical (spin-LSC) approach, which is a specific example of the classical mapping model, and the other traceless MMST approaches sample the intra-correlation faithfully only for two-level systems. Our theoretical analysis provides insights into the short-time accuracy of semiclassical methods and presents mathematical justifications for previous numerical benchmarks. [ABSTRACT FROM AUTHOR]

The Born–Oppenheimer framework stipulates that chemistry and physics occur on potential energy surfaces VBO(X) parameterized by a nuclear coordinate X, which are built by diagonalizing a BO Hamiltonian H ̂ B O (X). However, such a framework cannot recover many measurable chemical and physical features, including vibrational circular dichroism spectra. In this article, we show that a phase-space electronic Hamiltonian H ̂ P S (X , P) , parameterized by both nuclear position X and momentum P, with a similar computational cost as solving H ̂ B O (X) , can recover not just experimental vibrational circular dichroism signals but also a meaningful electronic current density that explains the features of the vibrational circular dichroism rotational strengths. Combined with earlier demonstrations that such Hamiltonians can also recover qualitatively correct electronic momenta with electronic densities that approximately satisfy a continuity equation, the data would suggest that, if one looks closely enough, chemistry in fact occurs on potential energy surfaces parameterized by both X and P, EPS(X, P). While the dynamical implications of such a phase-space electronic Hamiltonian are not yet known, we hypothesize that, by offering classical trajectories that explicitly offer nonzero electronic momentum while also conserving the total angular momentum (unlike Born–Oppenheimer theory), this new phase-space electronic structure Hamiltonian may well explain some fraction of the chiral-induced spin selectivity effect. [ABSTRACT FROM AUTHOR]

The introduction of machine learned potentials (MLPs) has greatly expanded the space available for studying Nuclear Quantum Effects computationally with ab initio path integral (PI) accuracy, with the MLPs' promise of an accuracy comparable to that of ab initio at a fraction of the cost. One of the challenges in development of MLPs is the need for a large and diverse training set calculated by ab initio methods. This dataset should ideally cover the entire phase space, while not searching this space using ab initio methods, as this would be counterproductive and generally intractable with respect to computational time. In this paper, we present the self-learning PI hybrid Monte Carlo Method using a mixed ab initio and ML potential (SL-PIHMC-MIX), where the mixed potential allows for the study of larger systems and the extension of the original SL-HMC method [Nagai et al., Phys. Rev. B 102, 041124 (2020)] to PI methods and larger systems. While the MLPs generated by this method can be directly applied to run long-time ML-PIMD simulations, we demonstrate that using PIHMC-MIX with the trained MLPs allows for an exact reproduction of the structure obtained from ab initio PIMD. Specifically, we find that the PIHMC-MIX simulations require only 5000 evaluations of the 32-bead structure, compared to the 100 000 evaluations needed for the ab initio PIMD result. [ABSTRACT FROM AUTHOR]

The shock response of fully-dense and porous crystalline tellurium dioxide (TeO 2) to the high-pressure and high-temperature fluid regime was investigated within the framework of density functional theory with Mermin's generalization to finite temperatures. The principal and porous shock Hugoniot curves were predicted from canonical ab initio molecular dynamics (AIMD) simulations, with the phase space sampled along isotherms up to 80 000 K, for densities ranging from ρ = 3 to 17 g/cm 3. The polymorphs investigated are α - Te O 2 paratellurite (P 4 1 2 1 2), Te O 2 cotunnite (P n m a), and Te O 2 post-cotunnite (P 2 1 / m). Based on the discontinuity found in the calculated U s − u p slope of TeO 2 post-cotunnite at a shock velocity of U s ≃ 8.35 km/s and a particle velocity of u p ≃ 3.64 km/s, the shock melting temperature and pressure are predicted to be ≃ 6500 K and ≃ 170 GPa. Results from the AIMD simulations are in line with the static compression data of Te O 2 paratellurite and cotunnite, and with the recent shock Hugoniot data for single-crystal α - Te O 2 for pressures up to 85 GPa, obtained using the inclined-mirror method and the velocity interferometer system for any reflector combined with powder gun and two-stage light-gas gun. [ABSTRACT FROM AUTHOR]

Transition state theory (TST) provides a framework to estimate the rate of chemical reactions. Despite its great success with many reaction systems, the underlying assumptions such as local equilibrium and nonrecrossing do not necessarily hold in all cases. Although dynamical systems theory can provide the mathematical foundation of reaction tubes existing in phase space that enables us to predict the fate of reactions free from the assumptions of TST, numerical demonstrations for large systems have been yet one of the challenges. Here, we propose a dimensionality reduction algorithm to demonstrate structures in phase space (called reactive islands) that predict reactivity in systems with many degrees of freedom. The core of this method is the application of supervised principal component analysis, where a coordinate transformation is performed to preserve the dynamical information on reactivity (i.e., to which potential basin the system moves from a region of interest) as much as possible. The reactive island structures are expected to be reflected in the transformed, low-dimensional phase space. As an illustrative example, the algorithm is scrutinized using a modified Hénon–Heiles Hamiltonian system extended to many degrees of freedom, which has three channels leading to three different products from one stable potential basin. It is shown that our algorithm can predict the reactivity in the transformed, low-dimensional coordinate system better than a naïve coordinate system and that the reactivity distribution in the transformed low-dimensional space is considered to reflect the underlying reactive islands. [ABSTRACT FROM AUTHOR]

The generation of cold molecules is an important topic in the field of cold atoms and molecules and has received relevant advanced research attention in ultracold chemistry, quantum computation, and quantum metrology. With a high atomic phase space density, optical dipole traps have been widely used to prepare, trap, and study cold molecules. In this work, Rb2 molecules were photoassociated in a magneto-optical trap to obtain a precise rovibrational spectrum, which provided accurate numerical references for the realization of multiple frequency photoassociation. By meeting the harsh requirements of photoassociation in optical dipole traps, the cold molecule photoassociation process was well explored, and different photoassociation resonances were simultaneously addressed in a single optical dipole trap. This method can be universally extended to simultaneously photoassociate cold molecules with different internal states or atomic species in a single optical dipole trap, thus advancing generous cold molecule studies such as cold molecule collision dynamics. [ABSTRACT FROM AUTHOR]

This paper conducts a detailed study on the thermal transport and thermoelectric properties of Li 2 Rb(Cs)Bi and analyzes the optical phonon frequency shift caused by considering anharmonicity. We mainly focus on studying the microscopic mechanism of the difference in lattice thermal conductivity (κ L) of the two materials. By calculating the group velocity, scattering rate, scattering phase space and scattering sub-process, it is concluded that κ L is mainly dominated by the acoustic branch. Due to its small group velocity and large scattering rate, Li 2 CsBi has a low κ L , which is 0.60 W m − 1 K − 1 at 300 K. Research results show that n-type Li 2 CsBi has a higher ZT value of about 2.1 at T = 900 K, while p-type Li 2 RbBi has a higher ZT value of about 1.5 at the same temperature. These results provide an important theoretical basis for the application of Li 2 Rb(Cs)Bi in the field of thermoelectric conversion. [ABSTRACT FROM AUTHOR]

We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman–Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects. [ABSTRACT FROM AUTHOR]

The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In Paper I, focusing on adiabatic single surface processes, we derive the well-known double Herman–Kluk (DHK) approximation for real-time correlation functions in Wigner phase space and connect it to the linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important "system" degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the "bath") at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators and the decoherence of vibrational probability density of a model I2 Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign problem and employs reduced dimensional prefactors bringing calculations of complex system–bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes. [ABSTRACT FROM AUTHOR]

Developing phase diagrams for inhomogeneous systems in thermodynamics is difficult, in part, due to the large phase space and the possibility of unstable and metastable solutions arising from first-order phase transitions. Pseudo-arclength continuation (PAC) is a method that allows one to trace out stable and unstable solutions of nonlinear systems. Typically, PAC utilizes the Jacobian in order to implement Newton (or quasi-Newton) steps. In this work, we present a Jacobian-free PAC method that is amenable to the usual workflows in inhomogeneous thermodynamics. We demonstrate our method in systems that have first-order phase transitions, including a novel example of polyelectrolyte complex coacervation in confinement, where multiple surface phase transitions occur and can overlap with one another. [ABSTRACT FROM AUTHOR]

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a fixed time-increment (τ > 0), it was generally believed that there exists a unique Hamiltonian producing a continuous trajectory that coincides at all discrete times (t = nτ with n integers) as long as τ is small enough. However, it is now exactly demonstrated that, for any given discrete symplectic dynamics of a harmonic oscillator, there exist an infinite number of real-valued Hamiltonians for any small value of τ and an infinite number of complex-valued Hamiltonians for any large value of τ. In addition, when the transition matrix is similar to a Jordan normal form with the supradiagonal element of 1 and the two identical diagonal elements of either 1 or −1, only one solution to the Hamiltonian is found for the case with the diagonal elements of 1, but no solution can be found for the other case. [ABSTRACT FROM AUTHOR]

For microscale gaps, DC breakdown voltage is described theoretically and through simulation by accounting for field emission generated electrons and the subsequent ionization of neutral gas and ion-induced secondary electron emission. Here, we extend DC microscale breakdown theory to AC. Particle-in-cell (PIC) simulations show that breakdown voltage V varies linearly with gap distance d independent of frequency and the ion-induced secondary electron coefficient γ S E for d ≲ 4 μ m , where field emission dominates breakdown over ionization and avalanche. For d ≳ 4 μ m and γ S E = 0 , DC breakdown voltage increases linearly with d; for γ S E = 0.05 , DC breakdown voltage decreases to a minimum before beginning to increase at larger gap distances. For AC fields with γ S E = 0.05 , V behaves similarly to the DC case with the decrease corresponding to secondary emission occurring at higher voltages and larger gap distances with increasing frequency. At 10 GHz and γ S E = 0.05 , V resembles that of the DC case with γ S E = 0 up to ∼8 μm, suggesting that increasing the frequency effectively changes the number of ions striking the electrodes and the resulting electrons released. Phase space plots showing electron and ion velocities as a function of position across the gap show that electrons and ions are increasingly trapped within the gap with increasing frequency, reducing the number of ions that can strike the cathode and the subsequent secondary emission. Incorporating the resulting effective secondary emission coefficient for AC microscale gaps yields a simple phenomenologically based modification of the DC microscale gas breakdown equation. [ABSTRACT FROM AUTHOR]

We investigate roaming in the photodissociation of acetaldehyde (CH3CHO), providing insights into the contrasting roaming dynamics observed for this molecule compared to formaldehyde. We carry out trajectory studies for full-dimensional acetaldehyde, supplemented with an analysis of a two-degree-of-freedom restricted model and obtain evidence for two distinct roaming pathways. Trajectories exhibit roaming at both shorter (9–11.5 au) and larger (14.5–22.9 au) maximum CH3–HCO separations, characterized by differing amounts of HCO rotation. No roaming trajectories were found in the intervening gap region. The roaming dynamics near 14.5–22.9 au are well-reproduced by the restricted model and involve passage through a centrifugal barrier, analogous to formaldehyde roaming. However, the shorter-range 9–11.5 au roaming appears unique to acetaldehyde and is likely facilitated by repulsive interactions absent in the simplified models. Phase space analysis reveals that this additional roaming pathway is inaccessible in the reduced dimensionality system. The findings suggest that acetaldehyde's increased propensity for roaming compared to formaldehyde may arise from the presence of multiple distinct roaming mechanisms rather than solely the higher roaming fragment mass. [ABSTRACT FROM AUTHOR]

We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system–bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu–Planck potentials as entropic potentials and the Helmholtz–Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker–Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system–bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions. [ABSTRACT FROM AUTHOR]

This study focuses on conducting an ab initio evolutionary investigation to search for stable polymorphs of iron diborocarbides with the formula FeB 2 C 2. We also examined other forms of C contents, including FeB 3 C and FeBC 3. Our findings reveal that the lowest energetic structure of FeB 2 C 2 is a semimetallic monoclinic phase with a space group (s.g.) of C2/m and a metastable metallic phase of FeB 2 C 2 is an orthorhombic structure with s.g. of Pmmm. In addition, structural and relative properties of FeB 3 C and FeBC 3 are performed and discussed to compare with FeB 2 C 2. All predicted structures are dynamically and elastically stable, verified without negative phonon frequency and Born criteria, respectively. We also analyzed the energetic stability through calculated cohesive and formation energies, which showed that C2/m- FeB 2 C 2 is stable at low pressure. Interestingly, the C2/m and Pmmm phases of FeB 2 C 2 are hard materials with Vickers hardness ( H v) of 22.40 and 27.52 GPa, respectively. Additionally, we examined the electron–phonon coupling of both FeB 2 C 2 phases. Unexpectedly, we found that the semimetallic C2/m- FeB 2 C 2 phase is a superconductor with a significant superconducting temperature ( T c) exceeding 6 K. These findings provide some novel results for the Fe–B–C system and pave the way for investigating other metal borocarbides and related ternary compounds. [ABSTRACT FROM AUTHOR]

Modern electronic structure theory is built around the Born–Oppenheimer approximation and the construction of an electronic Hamiltonian H ̂ e l (X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ′) and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, H ̂ P S (X , P). While classical Born–Oppenheimer dynamics that run along the eigensurfaces of the operator H ̂ e l (X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of H ̂ P S (X , P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general. [ABSTRACT FROM AUTHOR]

Time-Resolved Serial Femtosecond Crystallography (TR-SFX) conducted at X-ray Free Electron Lasers (XFELs) has become a powerful tool for capturing macromolecular structural movies of light-initiated processes. As the capabilities of XFELs advance, we anticipate that a new range of coherent control and structural Raman measurements will become achievable. Shorter optical and x-ray pulse durations and increasingly more exotic pulse regimes are becoming available at free electron lasers. Moreover, with high repetition enabled by the superconducting technology of European XFEL (EuXFEL) and Linac Coherent Light Source (LCLS-II) , it will be possible to improve the signal-to-noise ratio of the light-induced differences, allowing for the observation of vibronic motion on the sub-Angstrom level. To predict and assign this coherent motion, which is measurable with a structural technique, new theoretical approaches must be developed. In this paper, we present a theoretical density matrix approach to model the various population and coherent dynamics of a system, which considers molecular system parameters and excitation conditions. We emphasize the use of the Wigner transform of the time-dependent density matrix, which provides a phase space representation that can be directly compared to the experimental positional displacements measured in a TR-SFX experiment. Here, we extend the results from simple models to include more realistic schemes that include large relaxation terms. We explore a variety of pulse schemes using multiple model systems using realistic parameters. An open-source software package is provided to perform the density matrix simulation and Wigner transformations. The open-source software allows us to define any arbitrary level schemes as well as any arbitrary electric field in the interaction Hamiltonian. [ABSTRACT FROM AUTHOR]

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π, vi = 1, 3, ji = 0, 1) → H + NO+(X1Σ+) has been studied based on the recently constructed diabatic potential energy matrix. It was found that the vibrational excitation of reactant NO inhibits the reactivity, while the rotational excitation of reactant NO has little effect on the reaction probability. These attributes were also observed in the semi-classical trajectory calculations employed in the adiabatic representation. Such an inhibitory effect of the vibrational excitation of reactant NO was owing to lower accessibility of the conical intersection and avoided crossing regions, which are located in the wells with respect to the Π diabat, as evidenced by the analysis of the population of the time-independent wave functions. Calculated vibrational state distributions of the product show that the decrease of the reaction mainly leads to the less formation of low vibrational states (vf < 6), and the product vibrational state distributions are more evenly populated for vi = 1 and 3, suggesting a non-statistical behavior. However, the overall shapes of the product rotational distributions remain unchanged, indicating that the redistribution of energy into the rotation of product NO is sufficient in the charge transfer process between H+ and NO. While the reaction is dominated by the forward and backward scattering in differential cross sections (DCSs), consistent with the complex-forming mechanism, a clear forward bias in the DCSs appears, indicating that the occurrence of the reaction is not sufficiently long to undergo the whole phase space of the interaction configurations. [ABSTRACT FROM AUTHOR]

The effect of ring stiffness and pressure on the glassy dynamics of a thermal assembly of two-dimensional ring polymers is investigated using extensive coarse-grained molecular dynamics simulations. In all cases, dynamical slowing down is observed with increasing pressure, and thereby, a phase space for equilibrium dynamics is identified in the plane of the obtained monomer density and ring stiffness. When the rings are highly flexible, i.e., have low ring stiffness, glassiness sets in via the crowding of crumpled polymers, which take on a globular form. In contrast, at large ring stiffness, when the rings tend to have large asphericity under compaction, we observe the emergence of local domains having orientational ordering at high pressures. Therefore, our simulations highlight how varying the deformability of rings leads to contrasting mechanisms in driving the system toward the glassy regime. [ABSTRACT FROM AUTHOR]

As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions. [ABSTRACT FROM AUTHOR]

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters based on a local loss function that promotes the fast exploration of phase space. We show that a good correspondence between loss and autocorrelation time can be established, allowing for gradient-based optimization using a fully differentiable set-up. The loss is constructed in such a way that it also allows for gradient-driven learning of a distribution over the number of integration steps. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein commonly used as a test case for simulation methods. Through the application to the harmonic oscillator, we highlight the importance of not using a fixed timestep to avoid a rugged loss surface with many local minima, otherwise trapping the optimization. In the case of alanine dipeptide, by tuning the only free parameter of our loss definition, we find a good correspondence between it and the autocorrelation times, resulting in a > 100 fold speedup in the optimization of simulation parameters compared to a grid search. For this system, we also extend the integrator to allow for atom-dependent timesteps, providing a further reduction of 25% in autocorrelation times. [ABSTRACT FROM AUTHOR]

Preparation of atomic Bose–Einstein condensate (BEC) with tunable interactions in a quasi-one-dimensional (quasi-1D) optical trap is essential for both the observation of bright matter-wave solitons and the quantum simulation based on the discrete atomic momentum states. However, the quasi-1D BEC has been obtained by a complex process, which includes the creation of a three-dimensional BEC and its adiabatic transform into a quasi-1D trap. Here, we report the direct creation of a quasi-1D BEC of 133 Cs atoms by the fast evaporative cooling of ultracold atoms prepared by the degenerated Raman sideband cooling. We produce the pure BEC of up to 5.5 × 10 4 atoms in a quasi-1D optical trap with an evaporative time of 6 s. We demonstrate the anisotropic expansion of the atomic cloud after the release from the quasi-1D trap and study the dependence of both the phase space density and the temperature on the number of atoms in the trap during the evaporative cooling. Our study facilitates the promising applications of quasi-1D interacting atomic gases. [ABSTRACT FROM AUTHOR]

Solid-state batteries use composites of solid ion conductors and active materials as electrode materials. The effective transport of charge carriers and heat thereby strongly determines the overall solid-state battery performance and safety. However, the phase space for optimization of the composition of solid electrolyte, active material, additive is too large to cover experimentally. In this work, a resistor network model is presented that successfully describes the transport phenomena in solid-state battery composites, when benchmarked against experimental data of the electronic, ionic, and thermal conductivity of LiNi0.83Co0.11Mn0.06O2-Li6PS5Cl positive electrode composites. To highlight the broadness of the approach, literature data are examined using the proposed model. As the model is easily accessible and expandable, without the need for high computing power, it offers valuable guidance for experimentalists helping to streamline the tedious process of performing a multitude of experiments to understand and optimize the effective transport of composite electrodes. Effective conductivity is a key performance indicator for solid-state battery electrodes that is influenced by both composition and microstructure. Here, authors present a simple resistor network model to guide the development of composite electrodes towards optimized effective transport. [ABSTRACT FROM AUTHOR]

The increasing global energy demand and reliance on fossil fuels have exacerbated global warming, necessitating sustainable energy solutions. This study aims to explore the possibility of designing n-type and p-type TE materials from the Zr2FeNiSb2 double half-Heusler (DhH) compound using targeted substitutions and compositional tuning. We engineered n-type and p-type compounds by substituting Nb at the Zr site (Zr1.9Nb0.1FeNiSb2) and Sn at the Sb site (Zr2FeNiSb1.9Sn0.1). Microstructural analysis indicated a predominance of the half-Heusler phase with minor Fe-rich secondary phases. To eliminate these secondary phases and establish a direct structure–property correlation, the Fe content was reduced and compensated with increased Ni content. However, increasing Ni tends to decompose the matrix in Zr2Fe0.9Ni1.1Sb2. Further Nb/Sn substitutions stabilized the microstructure without the adverse effects from Fe/Ni tuning. Seebeck coefficient measurements from near RT to 973 K showed that all alloys except Zr2Fe0.9Ni1.1Sb1.9Sn0.1 exhibited n-type behaviour, while this Sn-substituted alloy switched from p-type to n-type upon variation of Fe/Ni ratio. This study also defines the half-Heusler phase composition space, with Fe and Ni varying within ~ 15.64 to 17.39 at% and 15.90 to 18.84 at%, respectively, providing valuable insights for designing DhH-based TE materials. [ABSTRACT FROM AUTHOR]

The development of red phosphors with good thermal stability, high quantum yield and high color purity is still a big challenge. In this work, a series of novel red phosphors Sr3La2W2O12:xEu3+ (0≤x≤0.18, ∆x = 0.03) were successfully prepared by high‐temperature solid‐phase method. The phosphors reveal a hexagonal phase with the space group of R‐3 m. The phosphor Sr3La2W2O12:Eu3+ produced narrowband red emission from 5D0→7F2 of Eu3+ (616 nm) under excitation at 395 nm, 465 nm, and 533 nm. Importantly, phosphor Sr3La2W2O12:0.09Eu3+ exhibits astonishing quantum efficiency (IQE = 89.60%, EQE = 41.52%), and it demonstrate robust thermal performance with the emission intensity retaining 92.73% at 558 K of that at 298 K. Finally, the prepared red phosphor Sr3La2W2O12:0.09Eu3+ and yellow phosphor YAG:Ce3+ were combined with a blue LED chip (460 nm) to form a WLED device, which presented warm white light with color coordinates of (0.3523, 0.3732), color rendering index of 83.7, and color temperature of 4826 K. [ABSTRACT FROM AUTHOR]

Al3Ni nanowires were fabricated via the selective etching of directionally solidified Al–Ni eutectic alloys. The effects of different growth rates from 2 to 1000 μm/s on the microstructure and morphology of eutectic alloys under a temperature gradient of 10 K/cm were investigated. The mechanism of the cross-sectional morphology transformation of Al3Ni nanofibers was investigated using the dynamic undercooling degree Δ T k . Then, the morphologies of the Al3Ni nanowires at different growth rates and corrosion time were studied using the constant potential corrosion method. Increasing the growth rate increased the roundness of the section and decreased the fiber phase spacing and diameter. At a growth rate of 2 μm/s, both Al and Al3Ni exhibited kinetic undercooling ( Δ T k , Al 3 Ni and Δ T k , Al ), with values below the critical kinetic undercooling ( Δ T k , Al 3 Ni c and Δ T k , Al c ). The Al3Ni fibers underwent faceted growth and developed a thin ribbon structure. At 5 μm/s, the kinetic undercooling of Al3Ni and Al exceeded Δ T k , Al 3 Ni c and Δ T k , Al c , respectively, leading to nonfaceted growth and elliptically shaped Al3Ni fibers. With prolonged corrosion time, the length of the Al3Ni nanowires increased. [ABSTRACT FROM AUTHOR]

We study the limit of geometrical optics in dispersive inhomogeneous media. The short wavelength regime of the wave equation is investigated in the framework of the Wigner quasi-distribution function in the phase-space. The evolution of the field is expressed by a Cauchy problem for the position and direction of the optical rays. The extended time-frequency phase-space formalism furnishes a natural framework to study the fast oscillating limit of fields governed by non local in time pseudo-differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of abstract third-order linear evolution equations in time which can be seen as a generalized fractional Moore-Gibson-Thompson (MGT) equation. Given the classic MGT model, we prove the well-posedness and exponential stability of our model in a suitable phase space. [ABSTRACT FROM AUTHOR]

In this paper, we study nonclassical inflaton, which is minimally coupled to the semi-classical gravity in FRW universe in Coherent Squeezed Vacuum State (CSVS). We have determined the Oscillatory phase of inflaton, power-law expansion, scale factor, density fluctuations, quantum fluctuations and particle production for CSVS. We have obtained an estimated leading solution of scale factor in CSVS and found it proportional to t2/3 and showing similar diversification as demonstrated by Semi-classical Einstein Equation (SCEE) of gravity in matter dominated universe. We have also studied the validity of SCEE in CSVS. We have computed validity of uncertainty relation for FRW Universe by determining the quantum fluctuation for CSVS. Our results show that Quantum fluctuations don’t depend on coherent parameter ϒ as the uncertainty relation doesn’t effect by the displacement of ϒ in phase space. We have also studied the production of particles in CSVS for oscillating massive inflaton in flat FRW universe. [ABSTRACT FROM AUTHOR]

The synthesis of metal oxide nanostructures commonly requires sophisticated scientific apparatus, complex synthesis processes, and time-inefficient processes, or produces undesirable by-products. We have overcome these challenges by developing a low-cost and time-effective synthesis technique that allows considerable control of growth energetics enabling exploration of crystal phases that occupy small regions of phase space. Here, we report on nanostructures of tungsten oxide WO2.76 (W17O47) synthesized in a single-step process, which takes roughly one minute to grow WO2.76 and an additional roughly 30 min for preparation. The nanostructures were synthesized directly onto tungsten filaments by resistive heating of tungsten wire in an oxygen environment. The nanostructures are rod-shaped with an average diameter of 25 ± 9 nm. Their physical properties were investigated through an arsenal of experimental probes including scanning electron microscopy, X-ray diffraction, Raman spectroscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, electrochemical impedance spectroscopy, and cyclic voltammetry. The improved electrochemical performance in comparison to WO3 along with its large dielectric constant suggests that despite WO2.76 being somewhat elusive to researchers, it demonstrates the potential of this compound for functional applications such as supercapacitors and photocatalytic water splitting. [ABSTRACT FROM AUTHOR]

Particle acceleration is a commonly observed phenomenon at dipolarization fronts. Many studies have attempted to determine the acceleration mechanism, with betatron acceleration being a major candidate. In previous work, we attempted to match the observed change in electron energy to the change predicted by betatron acceleration, but found that although this worked in some cases, overall betatron acceleration alone could not describe the observed energy spectrum changes. In this work, we attempted to study whether ion acceleration showed similar behavior and whether a quasi-adiabatic correction would be more accurate. On average the betatron acceleration equation overestimated the observed acceleration and the quasi-adiabatic correction did not account for the difference, although there are limitations to this study due to data fidelity. We then turned to study whether our assumptions about the source population having the same phase space density as the cold pre-existing background population in the plasma sheet are valid. We indirectly studied this by comparing the relative abundances of O + and H e + + as proxies for ionospheric and solar wind populations respectively. We found the betatron acceleration equation method performs slightly better when there is a stronger ionospheric component. This suggests that when more plasma containing O + is present in the dipolarization front, it indicates that the source population is more local and therefore this method of using betatron acceleration is more valid. [ABSTRACT FROM AUTHOR]

We present a characterisation of a blender based on the topological alignment of certain sets in phase space in combination with cone conditions. Importantly, the required conditions can be verified by checking properties of a single iterate of the diffeomorphism, which is achieved by finding finite series of sets that form suitable sequences of alignments. This characterisation is applicable in arbitrary dimension. Moreover, the approach naturally extends to establishing C 1 -persistent heterodimensional cycles. Our setup is flexible and allows for a rigorous, computer-assisted validation based on interval arithmetic. [ABSTRACT FROM AUTHOR]

Coupled map lattices are a popular and computationally simpler model of pattern formation in nonlinear systems. In this work, we investigate three-site interactions with linear multiplicative coupling in one-dimensional coupled logistic maps that cannot be decomposed into pairwise interactions. We observe the transition to synchronization and the transition to long-range order in space. We coarse-grain the phase space in regions and denote them by spin values. We use two quantifiers the flip rate F(t) that quantify departure from expected band-periodicity as an order parameter. We also study a non-Markovian quantity, known as persistence P(t) to study dynamic phase transitions. Following transitions are observed. (a) Transition to two band attractor state: At this transition F(t) as well as P(t) shows a power-law decay in the range of coupling parameters. Here all sites reach one of the bands. The F(t) as well as P(t) decays as power-law with the decay exponent δ1=0.46 and η1=0.28, respectively. (b) The transition from a fluctuating chaotic state to a homogeneous synchronized fixed point: Here both the quantifiers F(t) and P(t) show power-law decay with decay exponent δ2=1 and η2=0.11, respectively. We compare the transitions with the case, where pairwise interactions are also present. The spatiotemporal evolution is analyzed as the coupling parameter is varied. [ABSTRACT FROM AUTHOR]

Accurate financial time series forecasting is an important challenge in the financial field due to varying levels of interaction among multiple financial time series, complicating the extraction of valid information from these variables. This study introduces an effective and efficient multivariable financial time series forecasting model based on phase space reconstruction compensation: Phase Space Reconstruction Compensation Long Short-Term Memory (PSR-LSTM). The PSR-LSTM model leverages the long short-term memory (LSTM) network to analyze short-term data behaviors, reconstructs multiple long-term variables by phase space reconstruction method, and utilizes multivariable trend attention to capture trend information in correlated variables. This trend information is finally used to correct the LSTM network's predictive result. Experimental results demonstrate that the PSR-LSTM outperforms existing multivariable forecasting models by effectively mitigating noise interference while achieving optimal forecasting performance. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the thermodynamic properties of the Schwarzschild–Tangherlini black hole in D-dimension in a generic noncommutativity setting in which geometry and matter are affected. A mass density and radial coordinate (r) are used to carry out this assignment. At this point, the transition on the radial coordinate r is really performed in the same space contrary to the Bopp shift, which requires us to operate in phase space. By contrasting our model with that of earlier research on noncommutative inspired geometry, we are able to see how two-fold deformation affects our black hole’s thermodynamic characteristics. [ABSTRACT FROM AUTHOR]

In this work, the cosmic solutions, particularly the well-known ΛCDM model, are investigated in the framework of the Gauss–Bonnet (GB) gravity, where the gravitational action incorporates the GB invariant function. We utilize a specialized formulation of the deceleration parameter in terms of the Hubble parameter H, given by q = −1 − Ḣ H2, to solve the field equations. To identify the appropriate model parameters, we align them to the most recent observational datasets, which include 31 data points from the Cosmic Chronometers, Pantheon+, and BAO datasets. The physical characteristics of the cosmographic parameters, such as pressure and energy density, that correlate to the limited values of the model parameters, are examined. The evolution of the deceleration parameter suggests a transition from a decelerated to an accelerated phase of the universe. Additionally, we examine the stability of the assumed model and provide an explanation for late-time acceleration using the energy conditions. The behavior of the equation of state parameter has been analyzed through dynamical variables by constraining various parameters in light of the recent observational data. This study has resulted in a quintessence-like evolution. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of stochastic semilinear parabolic equations subjected to multiplicative noise within singularly perturbed phase spaces. We first establish the existence and smoothness of stable foliations. Then we prove that the long-term behavior of each solution is determined by a solution residing on the pseudo-unstable manifold via a leaf of the stable foliation. Finally, we present the convergence of C 1 invariant foliations as the high dimensional region collapse to low dimensional region. In contrast to the convergence of pseudo-unstable manifolds, we introduce a novel technique to address challenges arising from the singularity of the stable term of hyperbolicity in the proof of convergence of stable manifolds and stable foliations as the space collapses. [ABSTRACT FROM AUTHOR]

We formulate a variant of Fourier restriction for operators in Schatten classes, where the Fourier–Wigner transform of a bounded operator replaces the Fourier transform of a function. The Fourier–Wigner transform is closely related to the group Fourier transform of the Heisenberg group. The first result shows that Fourier–Wigner restriction for Schatten class operators is equivalent to the restriction of the symplectic Fourier transform of functions on phase space. We deduce various Schatten class results for the quantum Fourier extension operator and answer a conjecture by Mishra and Vemuri concerning the Weyl transform of measures in the affirmative. [ABSTRACT FROM AUTHOR]

Planet formation in the Solar system was started when the first planetesimals were formed from the gravitational collapse of pebble clouds. Numerical simulations of this process, especially in the framework of streaming instability, produce various power laws for the initial mass function for planetesimals. While recent advances have shed light on turbulence and its role in particle clustering, a comprehensive theoretical framework linking turbulence characteristics to particle cluster properties and planetesimal mass function remains incomplete. Recently, a kinetic field theory (KFT) for ensembles of point-like classical particles in or out of equilibrium has been applied to cosmic structure formation. This theory encodes the dynamics of a classical particle ensemble by a generating functional specified by the initial probability distribution of particles in phase space and their equations of motion. Here, we apply KFT to planetesimal formation. A model for the initial probability distribution of dust particles in phase space is obtained from a quasi-initial state for a three-dimensional streaming-instability simulation that is a particle distribution with velocities for gas and particles from the Nakagawa relations. The equations of motion are chosen for the simplest case of freely streaming particles. We calculate the non-linearly evolved density power spectrum of dust particles and find that it develops a universal |$k^{-3}$| tail at small scales, suggesting scale-invariant structure formation below a characteristic and time-dependent length-scale. Thus, the KFT analysis indicates that the initial state for streaming instability simulations does not impose a constraint on structure evolution during planetesimal formation. [ABSTRACT FROM AUTHOR]

In this paper, the charged acoustic black hole with a cosmological constant has been assumed. We have taken into account the negative cosmological constant as thermodynamic pressure in the extended phase space. Then we derived the thermodynamic quantities and investigated their behavior. We have studied the critical values of temperature and pressure. By calculating the specific heat capacity, we have analyzed the thermal stability of the charged acoustic black hole. Then we studied the heat engine phenomena of the black hole. We discovered the Carnot engine’s efficiency and the brand-new engine phenomenon of the black hole. [ABSTRACT FROM AUTHOR]

For a simple quantum system weakly interacting with the environment, Wigner's 1932 formulation of quantum physics can be used to derive coupling to the environment using simple algebra. We show that the correct expressions, using coupling terms of "Lindblad form," are forced upon us. This is remarkable given that it took several decades before Lindblad's result was found in 1976. [ABSTRACT FROM AUTHOR]