Configuration Space Research Articles

Renormalization group flows from the Hessian geometry of quantum effective actions

We explore a geometric perspective on quantum field theory by considering the configuration space spanned by the correlation functions. Employing n-particle irreducible effective actions constructed via Legendre transforms of the Schwinger functional, this configuration space can be associated with a Hessian manifold. This allows for various properties and uses of the n-particle irreducible effective actions to be re-cast in geometrical terms. In the 2PI case, interpreting the two-point source as a regulator, this approach can be readily connected to the functional renormalization group. Renormalization group flows are then understood in terms of geodesics on this Hessian manifold.

Optimizing canopy spacing configuration enhances foxtail millet grain yield and water productivity by improving stalk lodging resistance in the North China Plain

Optimizing canopy spacing configuration can enhance resources utilization, supporting robust growth and dry matter production, while mitigating the risk of lodging and improving crop yield and quality. However, research specifically addressing optimal canopy spacing configurations for foxtail millet remains limited. Over a two-year period, a field experiment in the North China Plain assessed the impacts of four-row spacing configurations (T0: 40 + 40 cm; T1: 30 + 50 cm; T2: 20 + 60 cm; T3: 10 + 70 cm), to investigate the effects of row spacing configuration on lodging resistance, canopy spatial configuration, stem characteristics, yield, and water productivity (WP) of foxtail millet, aiming to elucidate the underlying regulatory mechanisms. Row spacing configurations significantly influenced lodging resistance, yield, and WP. Under T1, improvements were observed in stem morphology and mechanical properties, particularly in the 2nd-6th basal internodes (I2-I6). The light interception rate in T1 at wide rows in the middle canopy (30–90 cm aboveground) increased by 97.89 %, compared to T0. Partial least squares-structural equation modeling revealed that improved light interception in wide rows in the middle canopy contributed to a rise in diameter and dry plumpness of I2. This, in turn, promoted greater breaking resistance of I2 and tensile resistance, ultimately reducing the lodging likelihood. Simultaneously, the decrease in lodging resulted in higher yield and WP at yield level of foxtail millet. Therefore, T1 demonstrated the lowest lodging rate (67.34 %–91.92 % lower than T0), and the highest yield and WP at yield level (4.10 %–8.03 % and 20.79 %–22.46 % higher than T0). Optimizing canopy spacing configuration is essential for cultivating high-yielding and water-efficient foxtail millet populations. The results indicated that the 30 + 50 cm row spacing configuration improves light distribution in the middle canopy, enhancing lodging resistance and consequently increasing both yield and WP. This research offers a theoretical foundation for foxtail millet breeding and agronomic practices to achieve lower lodging rate, higher yields, and enhanced WP in the North China Plain.

Effect of Different Planting Density in Cocoa (Theobroma cacao l.) on Leaf Macro and Micronutrient Levels Grown under Coconut Ecosystem

An experiment investigating the impact of different cocoa densities on leaf macro and micronutrient levels within a coconut ecosystem was conducted at the Coconut Farm of the Horticultural College and Research Institute, Tamil Nadu Agricultural University, Coimbatore. The study employed a Randomized Block Design (RBD) comprising eight treatments, each replicated three times. Notably, among the various spacing configurations, T1 (3m x 1.2m) exhibited the highest levels of leaf nitrogen (1.86%), phosphorus (0.084%), potassium (1.39%), and boron (91.33 ppm) content. This suggests that under Tamil Nadu conditions, high-density planting in the T1 treatment not only resulted in elevated nutrient levels but also correlated with a notable increase in revenue. These findings underscore the potential benefits of adopting high-density planting practices in cocoa cultivation within coconut ecosystems. Further research is warranted to explore the long-term implications of spacing configurations and nutrient interactions on crop productivity and profitability.

A fast and smooth one-electron approach for investigating charge transfer states and D1-D0 crossings for systems with odd numbers of electrons.

We propose an efficient version of ensemble Hartree-Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions-even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for abinitio non-adiabatic dynamics in the near future.

WFOT: A Wave Function Overlap Tool between Single- and Multi-Reference Electronic Structure Methods for Spectroscopy Simulation.

We report the development of a novel diagnostic tool, named wave function overlap tool (WFOT), designed to evaluate the overlap between wave functions computed at single-reference [i.e., time-dependent density functional theory or configuration interaction singles (CIS)] and multireference (i.e., CASSCF/CASPT2) electronic structure levels of theory. It relies on truncating the single- and multireference WFs to CIS-like expansions spanning the same configurational space and maximizing the molecular orbital overlap by means of a unitary transformation. To demonstrate the functionality of the tool, we calculate the transient spectrum of acetylacetone by evaluating excited state absorption signals with multireference quality on top of single-reference on-the-fly dynamics simulations. Semiautomatic spectra generation is facilitated by interfacing the tool with the COBRAMM package, which also allows one to use WFOT with several quantum chemistry codes such as Gaussian, NWChem, and OpenMolcas. Other exciting possibilities for the utilization of the code beyond the simulation of transient absorption spectroscopy are eventually discussed.

Input‐output linearization and decoupling of mechanical control systems

AbstractIn this article, we present the problem of simultaneous input‐output feedback linearization and decoupling (noninteracting) for mechanical control systems with outputs. We show that the natural requirement of preserving mechanical structure of the system and of transformations imposes supplementary conditions when compared to the classical solution of the same problem for general control systems. These conditions can be expressed using objects on the configuration space only. We illustrate our results with several examples of mechanical control systems.

Multistable compliant linkages with multiple kinematic paths separated by energy barriers

Multistable morphing structures can reconfigure between different stable states that are separated by energy barriers, and one-degree-of-freedom (1-DOF) mechanisms have many merits, like simple actuation. This paper combines the two and proposes a new family of reconfigurable compliant linkages with many (2−6) 1-DOF kinematic paths that are separated by energy barriers. This new type of design is an extension of multistable structures, where each stable state corresponds to not just one configuration but a 1-DOF configuration space, i.e., a kinematic path. Components of the linkages are made elastically compliant, therefore enabling the switch between two isolated compatible paths with multi-stability. A generation-selection hybrid design algorithm to follow prescribed reconfigurable paths is proposed, and a minimum energy path (MEP) finding method to guide actuation to switch between different kinematic paths is developed. Four design examples with 2–3 reconfigurable paths and their experiments are presented, and the effectiveness of this method is verified. This work provides a fresh perspective to design the single-DOF reconfigurable mechanisms with larger design space, more reconfigurable kinematic paths, and easier reconfiguration actuation.

Free scalar field theory on a Sobolev space over a bounded interval

This paper discusses several functional analytic issues relevant for field theories in the context of the Hamiltonian formulation for a free, massless, scalar field defined on a closed interval of the real line. The fields that we use belong to a Sobolev space with a scalar product. As we show this choice is useful because it leads to an explicit representation of the points in the fibers of the phase space (the cotangent bundle of the configuration space). The dynamical role of the boundary of the spatial manifold where the fields are defined is analyzed.

Glassy Word Problems: Ultraslow Relaxation, Hilbert Space Jamming, and Computational Complexity

We introduce a family of local models of dynamics based on “word problems” from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must “work out” the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic but can be made ergodic by appending a large reservoir of sites in a trivial product state. This finding manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities. In one example, density modulations of wave vector q exhibit almost no relaxation until times O(exp(1/q)), at which point they abruptly collapse. We also comment on extensions of our results to higher dimensions. Published by the American Physical Society 2024

Unveiling the Structure of Oxygen Vacancies in Bulk Ceria and the Physical Mechanisms behind Their Formation.

Understanding the structures of oxygen vacancies in bulk ceria is crucial as they significantly impact the material's catalytic and electronic properties. The complex interaction between oxygen vacancies and Ce3+ ions presents challenges in characterizing ceria's defect chemistry. We introduced a machine learning-assisted cluster-expansion model to predict the energetics of defective configurations accurately within bulk ceria. This model effectively samples configurational spaces, detailing oxygen vacancy structures across different temperatures and concentrations. At lower temperatures, vacancies tend to cluster, mediated by Ce3+ ions and electrostatic repulsion, while at higher temperatures, they distribute uniformly due to configurational entropy. Our analysis also reveals a correlation between thermodynamic stability and the band gap between occupied O 2p and unoccupied Ce 4f orbitals, with wider band gaps indicating higher stability. This work enhances our understanding of defect chemistry in oxide materials and lays the groundwork for further research into how these structural properties affect ceria's performance.

Prediction of two-dimensional carbon nitride materials with semimetal states and flat bands

The search for new two-dimensional (2D) carbon nitride (CN) materials with desirable properties is an important and critical area of research. This study presents a series of 2D CN materials with appealing features such as semimetal or flat bands. By utilizing group theory and graph theory, we perform a random search of the configurational space of 2D CN monolayers, leading to the identification of 721 new CN materials. Extensive density functional theory calculations were then conducted to evaluate their properties. We found that 57 materials exhibit semimetal behavior, while 664 display characteristics of semiconductors and normal metals. Notably, materials such as 51-5-16-C3N-r568 and 55-5-20-C4N-r568 feature topological Dirac semimetals with protected 1D topological boundary states. Moreover, 31 materials possess flat bands near their Fermi level, including two with kagome-like flat bands that induce intrinsic spontaneous magnetization due to partially-occupied flat bands. Our results offer several promising candidates for exploring physical phenomena related to semimetals or flat bands in 2D CN materials.

Effect of Different Spacing Levels on Yield and Yield Contributing Characters in Cocoa (Theobroma cacao L.)

The experiment titled "Effect of different spacing levels on yield and yield contributing characters in cocoa" was conducted at the Coconut Farm of the Horticultural College and Research Institute, Tamil Nadu Agricultural University, Coimbatore. Utilizing a Randomized Block Design (RBD) with eight treatments replicated three times, the study aimed to investigate the impact of spacing levels on cocoa yield traits. The treatments involved in the experiment included a double row of cocoa planted between two rows of coconut trees, with spacing configurations as follows: T1 (3m x 1.2m), T2 (3m x 2m), T3 (3m x 2.5m), and T4 (3m x 3m). Additionally, a single row of cocoa between two coconut rows was examined, with spacings represented by T5 (1.5m), T6 (2m), T7 (2.5m), and T8 (3m). Results revealed significant variations among spacing treatments, with cocoa at 3m spacing demonstrating the highest productivity, yielding 43.47 pods per tree and 1021.48 g of dry beans per tree. Noteworthy findings included T1 (3m x 1.2m) exhibiting the longest pods (16.64 cm), T6 (2m) the widest pod girth (21.67 cm), and T8 (3m) producing the heaviest pods (204.50 g). Additionally, T6 yielded the highest total beans per pod (37.34) and dry bean weight (25.44 g), T4 had the heaviest single fresh bean (1.63 g), and T2 demonstrated the highest single dry bean weight (0.70 g). These findings offer valuable insights for optimizing cocoa cultivation practices, emphasizing the importance of spacing configurations in maximizing yield and bean characteristics.

Photocatalytic degradation of metformin on a rectangular baffled reactor: CFD modeling and validation investigation

Solar-irradiated photocatalysis is an advanced oxidation process (AOP) commonly used for water purification due to its excellent potential to break down a diverse range of persistent organic compounds into non-toxic byproducts. Reactor design is crucial in the photocatalysis process's efficiency, effectiveness, and scalability. Computational fluid dynamics (CFD) is an effective tool to study and comprehend reactor designs, reduce system cost, design time, and optimise reactor performance. This investigation focuses on designing and developing a rectangular baffled photocatalytic reactor that can effectively degrade metformin (MTF). The experimental study optimized the value of pH and catalyst dosage for efficient removal. The photoreactor demonstrated an efficiency of 58.14 % and was validated. The CFD results, including velocity profile and mass fraction of metformin, strongly agreed with the experimental results with an R2 value of 0.9826. The combination of various baffle sizes and spacing configurations was modeled and analyzed to develop a rectangular baffled photocatalytic reactor with maximum removal efficiency. The inclusion of baffles increased the flow path, improved mixing and enhanced the degrading efficiency. The investigation findings indicated the highest degradation efficiency of 78.03 % with the seven number of baffles.

Constructing and Evaluating Machine-Learned Interatomic Potentials for Li-Based Disordered Rocksalts.

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking.

Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the signproblem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.

Wave Function and Information

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e., its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called “quantum potential” in this context is briefly discussed.

Development of Parallel On-the-Fly Crystal Algorithm for Global Exploration of Conical Intersection Seam Space.

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

On the canonicity of the singularities of quotients of the Fulton-MacPherson compactification

We prove that quotients of the Fulton-MacPherson compactification of configuration spaces of smooth projective varieties of dimension > 1 >1 by permutation groups have canonical singularities.

Variational Integrators on Manifolds for Constrained Mechanical Systems

Abstract Variational integrators play a pivotal role in the simulation and control of constrained mechanical systems. Current Lagrange multiplier-free variational integrators for such systems are concise but inevitably face issues with parameterization singularities, hindering global integration. To tackle this problem, this paper proposes a novel method for constructing variational integrators on manifolds without introducing Lagrange multipliers, offering the benefit of avoiding singularities. Our approach unfolds in three key steps: (1) the local parameterization of configuration space; (2) the formulation of forced discrete Euler–Lagrange equations on manifolds; and (3) the construction and implementation of high-order variational integrators. Numerical tests are conducted for both conservative and forced mechanical systems, demonstrating the excellent global energy behavior of the proposed variational integrators.

Quotient singularities in the Grothendieck ring of varieties

Let G G be a finite group, X X be a smooth complex projective variety with a faithful G G -action, and Y Y be a resolution of singularities of X / G X/G . Larsen and Lunts asked whether [ X / G ] − [ Y ] [X/G]-[Y] is divisible by [ A 1 ] [\mathbb {A}^1] in the Grothendieck ring of varieties. We show that the answer is negative if B G BG is not stably rational and affirmative if G G is abelian. The case when X = Z n X=Z^n for some smooth projective variety Z Z and G = S n G=S_n acts by permutation of the factors is of particular interest. We make progress on it by showing that [ Z n / S n ] − [ Z ⟨ n ⟩ / S n ] [Z^n/S_n]-[Z\langle n\rangle / S_n] is divisible by [ A 1 ] [\mathbb {A}^1] , where Z ⟨ n ⟩ Z\langle n\rangle is Ulyanov’s polydiagonal compactification of the n n th configuration space of Z Z .