Quantum Mechanical Approximation Research Articles

Optimal semiclassical regularity of projection operators and strong Weyl law

Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of quantum mechanics, projection operators can be seen as the analogue of characteristic functions of subsets of the phase space, which are discontinuous functions. We prove that projection operators indeed converge to characteristic functions of the phase space and that in terms of quantum Sobolev spaces, they exhibit the same maximal regularity as characteristic functions. This can be interpreted as a semiclassical asymptotic on the size of commutators in Schatten norms. Our study answers a question raised in Chong et al. [J. Eur. Math. Soc. (unpublished) (2024)] about the possibility of having projection operators as initial data. It also gives a strong convergence result in Sobolev spaces for the Weyl law in phase space.

Nanocomposite materials as observed by mass-selective neutron spectroscopy

Abstract This work provides a current, critical view of the application of MAss-selective Neutron SpEctroscopy (MANSE) to nanocomposite materials. MANSE is a unique technique made possible owing to the existence of the pulsed neutron sources. At present, the only operating MANSE spectrometer in the world, VESUVIO, is located at the ISIS Neutron and Muon Source in the UK. We start by providing a brief description of the neutron Compton scattering, the anatomy of a mass-selective neutron spectrometer, and the experimental data treatment. We continue by briefly outlining the main quantum mechanical concepts, models and approximations relevant both to the ab initio prediction and experimental measurement of main MANSE observables. Next, we present several recent exemplars chosen to highlight the use of MANSE in the field of nanocomposites. Our examples include, in chronological order, encapsulated nanoparticles in amorphous silica gel, bioactive glass-ionomer cement, Cu-Ti-C composites, and sodium carboxymethyl starch-based binders in the presence of a mineral matrix. We close by providing our view of the ongoing and future challenges and opportunities in the mass-selective neutron investigation of NQEs in nanocomposite materials.

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows.

Machine learning (ML) is increasingly becoming a common tool in computational chemistry. At the same time, the rapid development of ML methods requires a flexible software framework for designing custom workflows. MLatom 3 is a program package designed to leverage the power of ML to enhance typical computational chemistry simulations and to create complex workflows. This open-source package provides plenty of choice to the users who can run simulations with the command-line options, input files, or with scripts using MLatom as a Python package, both on their computers and on the online XACS cloud computing service at XACScloud.com. Computational chemists can calculate energies and thermochemical properties, optimize geometries, run molecular and quantum dynamics, and simulate (ro)vibrational, one-photon UV/vis absorption, and two-photon absorption spectra with ML, quantum mechanical, and combined models. The users can choose from an extensive library of methods containing pretrained ML models and quantum mechanical approximations such as AIQM1 approaching coupled-cluster accuracy. The developers can build their own models using various ML algorithms. The great flexibility of MLatom is largely due to the extensive use of the interfaces to many state-of-the-art software packages and libraries.

Bank Deposits as Money Quanta

According to the Accounting View of Money (AVM), the money issued by commercial banks in the form of demand deposits features a hybrid nature, since deposits can be shown to consist of a share of deposits bearing the characteristics of debt (debt-deposits) and a share of deposits bearing the characteristics of equity (equity-deposits), in a mix that depends on factors that relate to the issuing banks and the environment where they operate and interact, which may change over time. Following this important finding of the AVM, it is only consequential to associate the hybrid nature of bank deposits with the dual nature of the objects which is typical in quantum physics, and to investigate whether and how the application of quantum analytical methods and ideas to a form of money showing dualistic features could be used to extract valuable economic information. This article studies demand deposits (which represents the prevailing form of money in all contemporary economies) as a possible form of “money quanta”, that is, quantities reflecting some aspects tipical of quantum physics, and analyzes it using a quantum model to describe some relevant aspects of it, including for instance how banks’ power to create money (i.e., issue deposits typically via the credit channel) is affected by the interactions taking place between the banks and between the banks and their environments, and how system efficiency and stability change in relation to changes in bank behaviors. This article lays the foundations of money quanta and is the first step towards a better understanding of the relevance of quantum mechanical tools and ideas in connection with the study of economics and finance.

Large deviations for trajectory observables of diffusion processes in dimension d > 1 in the double limit of large time and small diffusion coefficient

For diffusion processes in dimension d > 1, the statistics of trajectory observables over the time-window [0,T] can be studied via the Feynman–Kac deformations of the Fokker–Planck generator, which can be interpreted as Euclidean non-Hermitian electromagnetic quantum Hamiltonians. It is interesting to compare the four regimes corresponding to the time T, either finite or large, and to the diffusion coefficient D, either finite or small. (1) For finite T and finite D, one needs to consider the full time-dependent quantum problem that involves the full spectrum of the Hamiltonian. (2) For large time T→+∞ and finite D, one only needs to consider the ground-state properties of the quantum Hamiltonian to obtain the generating function of rescaled cumulants and to construct the corresponding canonical conditioned processes. (3) For finite T and D → 0, one only needs to consider the dominant classical trajectory and its action satisfying the Hamilton–Jacobi equation, as in the semi-classical Wentzel–Kramers–Brillouin (WKB) approximation of quantum mechanics. (4) In the double limit T→+∞ and D → 0, the simplifications in the large deviations in TD of trajectory observables can be analyzed via the two orders of limits, i.e. either from the limit D → 0 of the ground-state properties of the quantum Hamiltonians of (2), or from the limit of long classical trajectories T→+∞ in the semi-classical WKB approximation of (3). This general framework is illustrated in dimension d = 2 with rotational invariance.

Naturalized, Fundamental, and Feminist Metaphysics All at Once: The Case of Barad's Agential Realism

AbstractAn apparent antagonism exists between fundamentality-focused mainstream metaphysics such as naturalized metaphysics—a metaphysics inspired and constrained by the findings of our best science—and feminist metaphysics whose subject matter is typically non-fundamental social reality. Taking Karen Barad's agential realism as a case study, this paper argues that these may not be in conflict after all. Agential realism is a metaphysical framework founded on quantum mechanics which shares the characteristic features of naturalized metaphysics. But Barad finds warrant to extend the scope of agential realism all the way to theorizing about our lifeworld as exemplified by her profound influence on feminist new materialism. Thus, this case study indicates that there does not have to be a division between fundamental and feminist metaphysics. The broad intended scope of agential realism is challenged by the success of Newtonian mechanics as an approximation of quantum mechanics, but certain aspects of agential realism promise to be robust under such approximation. If this is so, then Barad provides us with a metaphysics that is naturalized, fundamental, and feminist all at once.

The role of the pion in the lineshape of the X(3872)

We determine the contribution of long-range pion interactions to the X(3872) dynamics, assuming it is a loosely bound D0D¯⁎0 molecule. Our result is based on the distorted wave Born approximation in non-relativistic quantum mechanics. Despite their long-range nature, we find that pion interactions cannot produce a large and negative effective range. Nonetheless, they introduce imaginary parts. In particular, they contribute to the total decay width of the X(3872) a term associated with, but not precisely corresponding to, the D⁎ width. Our approach can also be applied to the recently discovered Tcc+ state.

On the fractional perturbation theory and optical transitions in bulk semiconductors: Emergence of negative damping and variable charged mass

This study is devoted to the construction of a fractional perturbation theory which represents the basic technique of approximation in quantum mechanics. Our analysis is based on the fractional actionlike variational approach (FALVA) implementation of fractionality. After discussing the basic properties of fractional harmonic oscillator through the fractional Feynman's path integral approach, we have discussed the Rabi oscillations within the context of two-level quantum systems for simulated optical transition. In particular the case α>1 is correlated to the emergence of negative damping and negative probabilities which have been obtained in several quantum out-of-equilibrium systems. The fractional Fermi Golden rule and the fractional Heisenberg's uncertainty principle have been also obtained and their main properties and features have been discussed accordingly. We have discussed optical transitions in bulk semiconductors. It was observed that the fundamental properties of transitions rates are recovered if the charged particle moving inside the semiconductor is variable with time.

Eigenvalue asymptotics for the one-particle density matrix

The one-particle density matrix γ(x,y) for a bound state of an atom or molecule is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula λk∼(Ak)−8∕3, A≥0, as k→∞, for the eigenvalues λk of the self-adjoint operator Γ≥0 with kernel γ(x,y).

Description of covalent bond in terms of generalized charges: potential and dissociation energy of homonuclear compound

The theory of generalized charges is an asymptotic approximation of quantum mechanics for interatomic forces. It is based on the model of multicomponent electron gas, which extends the Thomas–Fermi model of inhomogeneous electron gas to pair electronic states. The present research takes in consideration the participation of the field of generalized charges in interatomic bonds. Herein, the definition of generalized charges (GC) by means of the overlap integral of the wave functions of valence electrons is given, and properties of GC are found out. Equations are derived for the potential and length of a homopolar bond, and dependence of these parameters on the generalized charges is shown. The dissociation energy of a diatomic molecule is expressed in terms of the nuclear charges, the function and multiplicity of the covalent bond, the angular momentum, and the vibrational energy of the binding electrons. The parametrization rules are substantiated and an a priori calculation of the dissociation energy of diatomic homonuclear molecules is carried out against the electronic configuration of the bond electrons and the nuclear charge. The calculation results for homonuclear compounds of the elements of the first four rows of the periodic table are shown to be of satisfactory accuracy.

Eigenvalue asymptotics for the one-particle kinetic energy density operator

The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix τ(x,y). Alongside the one-particle density matrix γ(x,y) it is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula λk∼(Bk)−2, B⩾0, as k→∞, for the eigenvalues λk of the self-adjoint operator T⩾0 with kernel τ(x,y).

Description of Quantum Mechanics as a Branch of Mathematical Physics That Deals with the Emission and Absorption of Energy by Matter

Quantum mechanics is the study of the emanation and retention of energy by issue, as well as the movement of material particles. Quantum mechanics is especially relevant to elementary particles and their relationship since it holds that energy and matter exist in tiny, discrete sums. The neutron is the main known molecule that permits exploratory admittance to each of the four basic powers as well as a wide scope of speculative collaborations. In this review, we analyzed the correlation for this study to analyze the relationship between the quantum mechanics, neutrons, and dark energy interactions and zeroed in on the idea of quantum mechanics and its arrangement with emission and absorption of energy.

Barriers to predictive high-throughput screening for spin-crossover

Current spin-crossover (SCO) energy calculations depend on nearly artisanal skill in picking quantum mechanical approximations and computational methods. That is incompatible with automated (work-flow-driven) screening. An acceptable methodology must be quantum mechanically sound, yield both basic structure and property values, and accurate ΔEHL without steering or tuning. Cost vs. accuracy causes focus on density functional theory (DFT). We show by a near-exhaustive study of schemes for calculating the basic molecular high-low spin energy difference, ΔEHL, that presently there is no combination of a constraint-based, non-empirical density functional approximation (DFA) and a set of well-defined semi-empirical corrections to it adequate for such a protocol. Somewhat successful hybrid DFA calculations of ΔEHL are too costly for high-throughput screening of condensed phases. Lower-cost alternatives combine a generalized gradient approximation (GGA) DFA with a Hubbard-U correction (DFT + U). But we show that neither U=0 nor any currently available unsteered U calculation gives a decent ΔEHL value for [Mn(taa)] without also degrading molecular structure or property predictions. Moving to the SCAN meta-GGA does not solve the problem. The revised-restored SCAN (r2SCAN) meta-GGA together with its deorbitalized version r2SCAN-L give improved but not wholly satisfactory results. We also document and diagnose several non-obvious technical and procedural sensitivities and inter-code differences. In addition to being a formidable challenge to DFA development, the lack we delineate is a major impediment to progress in the development of quantum materials and spintronics.

Swimmer dynamics in externally driven fluid flows: The role of noise

We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally-driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the effects of translational and rotational diffusion as well as tumbling, i.e. sudden jumps in the swimmer orientation. Regardless of whether diffusion or tumbling are the primary source of fluctuations, we find that noise significantly increases the probability that a swimmer crosses one-way barriers in the flow, which block the swimmer from returning to its initial position. We employ an asymptotic method for calculating the probability density of noisy swimmer trajectories in a given fluid flow, which produces solutions to the time-dependent Fokker-Planck equation in the weak-noise limit. This procedure mirrors the semiclassical approximation in quantum mechanics and similarly involves calculating the least-action paths of a Hamiltonian system derived from the swimmer's Fokker-Planck equation. Using the semiclassical technique, we compute (i) the steady-state orientation distribution of swimmers with rotational diffusion and tumbling and (ii) the probability that a diffusive swimmer crosses a one-way barrier. The semiclassical results compare favorably with Monte Carlo calculations.

Synthesis, theoretical structural explication, super cell configuration, Hardness, tribological data and void space illustration of Creatininium hydrogen maleate - CHM crystal by softwares and by experimental techniques

Designing of new solids with desired physical and chemical properties highly depends on the understanding of intermolecular interactions and packing arrangement of atoms in the molecule. Now a days Organic complexes play a vital role in research and social applications. In this Context the title compound is synthesized from the aqueous solutions of creatinine and maleic acid taken in the proper stoichiometric ratio. Miniature sized Creatininium Hydrogen Maleate (CHM) crystals are obtained after 16 days. As synthesized compound is subjected to XRD analysis, which showed that it is crystallized in monoclinic structure with space group P21/n. Hirshfeld analysis is also carried on CHM compound to visualize and quantify various types of non-covalent interactions that stabilizes the crystalline packing. Hirshfeld surface and the associated plots are generated using crystal Explorer software. Negative value of dnorm showed that intermolecular contacts are shorter than the Vanderwall’s radii of atoms. Super cell lattice cell fabrication is performed for 3x3x3 methodology to enunciate the omnipresent way of periodic frontier states of the crystal systems by means of a larger cluster with quantum mechanical approximations by direct and with the coloured potential way.

A shortcut to the thermodynamic limit for quantum many-body calculations of metals

Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schrödinger equation are crucial for computational materials science. Methods such as coupled cluster theory show potential for widespread adoption if computational cost bottlenecks can be removed. For example, extremely dense k-point grids are required to model long-range electronic correlation effects, particularly for metals. Although these grids can be made more effective by averaging calculations over an offset (or twist angle), the resultant cost in time for coupled cluster theory is prohibitive. We show here that a single special twist angle can be found using the transition structure factor, which provides the same benefit as twist averaging with one or two orders of magnitude reduction in computational time. We demonstrate that this not only works for metal systems but also is applicable to a broader range of materials, including insulators and semiconductors.

The singularity structure of quantum-mechanical potentials

We investigate non-relativistic quantum mechanical potentials between fermions generated by various classes of QFT operators and evaluate their singularity structure. These potentials can be generated either by four-fermion operators or by the exchange of a scalar or vector mediator coupled via renormalizable or non-renormalizable operators. In the non-relativistic regime, solving the Schr\"odinger equation with these potentials provides an accurate description of the scattering process. This procedure requires providing a set of boundary conditions. We first recapitulate the procedure for setting the boundary conditions by matching the first Born approximation in quantum mechanics to the tree-level QFT approximation. Using this procedure, we show that the potentials are nonsingular, despite the presence of terms proportional to $r^{-3}$ and $\nabla_{i}\nabla_{j}\delta^{3}(\vec{r})$. This surprising feature leads us to propose the \emph{Quantum Mechanics Swampland}, in which the Landscape consists of non-relativistic quantum mechanical potentials that can be UV completed to a QFT, and the Swampland consists of pathological potentials which cannot. We identify preliminary criteria for distinguishing potentials which reside in the Landscape from those that reside in the Swampland. We also consider extensions to potentials in higher dimensions and find that Coulomb potentials are nonsingular in an arbitrary number of spacetime dimensions.

Machine Learning Force Fields: Recent Advances and Remaining Challenges.

In chemistry and physics, machine learning (ML) methods promise transformative impacts by advancing modeling and improving our understanding of complex molecules and materials. Each ML method comprises a mathematically well-defined procedure, and an increasingly larger number of easy-to-use ML packages for modeling atomistic systems are becoming available. In this Perspective, we discuss the general aspects of ML techniques in the context of creating ML force fields. We describe common features of ML modeling and quantum-mechanical approximations, so-called global and local ML models, and the physical differences behind these two classes of approaches. Finally, we describe the recent developments and emerging directions in the field of ML-driven molecular modeling. This Perspective aims to inspire interdisciplinary collaborations crossing the borders between physical chemistry, chemical physics, computer science, and data science.

On the Spectrum of the One-Particle Density Matrix

The one-particle density matrix $$\gamma(x, y)$$ is one of the key objects in quantum-mechanical approximation schemes. The self-adjoint operator $$\Gamma$$ with kernel $$\gamma(x, y)$$ is trace class, but no sharp results on the decay of its eigenvalues were previously known. The note presents the asymptotic formula $$\lambda_k \sim (Ak)^{-8/3}$$ , $$A \ge 0$$ , as $$k\to\infty$$ for the eigenvalues $$\lambda_k$$ of the operator $$\Gamma$$ and describes the main ideas of the proof.

Ab Initio Calculations of Free Energy of Activation at Multiple Electronic Structure Levels Made Affordable: An Effective Combination of Perturbation Theory and Machine Learning

While free energies are fundamental thermodynamic quantities to characterize chemical reactions, their calculation based on ab initio theory is usually limited by the high computational cost. This is particularly true if multiple levels of theory have to be tested to establish their relative accuracy, if highly expensive quantum mechanical approximations are of interest, and also if several different temperatures have to be considered. We present an ab initio approach that effectively couples perturbation theory and machine learning to make ab initio free energy calculations more affordable. Starting from results based on a certain production ab initio theory, perturbation theory is applied to obtain free energies. The large number of single point calculations required by a brute force application of this approach are here significantly decreased by applying machine learning techniques. Importantly, the training of the machine learning model requires only a small amount of data and does not need to be performed again when the temperature is decreased. The accuracy and efficiency of this method is demonstrated by computing the free energy of activation of the proton exchange reaction in the zeolite chabazite. Starting from an ab initio calculation based on a semilocal approximation of density functional theory, free energies based on significantly more expensive nonlocal van der Waals and hybrid functionals are obtained with only a few tens of additional single point calculations. In this way this work paves the route to quick free energy calculations using different levels of theory or approximations that would be too computationally expensive to be directly employed in molecular dynamics or Monte Carlo simulations.