Quantum Mechanics Research Articles

Intensity-Product-Based Optical Sensing to Beat the Diffraction Limit in an Interferometer.

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.

Tropical Mirror

We describe the tropical curves in toric varieties and define the tropical Gromov-Witten invariants. We introduce amplitudes for the higher topological quantum mechanics (HTQM) on special trees and show that the amplitudes are equal to the tropical Gromov-Witten invariants. We show that the sum over the amplitudes in $A$-model HTQM equals the total amplitude in B-model HTQM, defined as a deformation of the $A$-model HTQM by the mirror superpotential. We derived the mirror superpotentials for the toric varieties and showed that they coincide with the superpotentials in the mirror Landau-Ginzburg theory. We construct the mirror dual states to the evaluation observables in the tropical Gromov-Witten theory.

Solvent effect on the excited state photophysics of Imiquimod: A DFT/TD-DFT and spectroscopic study

Solvation plays an important role in chemistry and biology. The role of the solvent is crucial in any chemical processes such as tautomerization that controls the structure and function of biomolecules. The current study aims to explore how different solvent medium affects the tautomeric forms of an antitumor drug, Imiquimod (IMQ). We have used several spectroscopical methods, including UV–Vis absorption spectroscopy, steady-state and time-resolved fluorescence spectroscopy, and quantum mechanical (QM) calculations. Our results revealed that solvent, indeed, plays a significant role in the modulation of the photophysics of the drug. IMQ has three emission bands in protic and aprotic solvents and two bands in non-polar medium associated with different forms of the drug. Using time-resolved technique, and comparing with the predicted lifetimes from QM calculations, we succeed to assign these three forms as cation, tautomer and neutral of IMQ with 1.6 ns, 2.0 ns and 4.0 ns lifetime values, respectively. Since IMQ is a nucleobase analogue and one of the most effective medications for skin tumors; these findings about which specie of IMQ is present in a given medium, and beyond, how the medium alters the photophysics of the molecule may provide deeper insights into its structure and function.

Revisiting the Schwarzschild black hole solution: A distributional approach

We present a novel perspective on the Schwarzschild, Reissner–Nordstrom, and Massless Black Holes solutions, a cornerstone of general relativity, by employing a distributional approach. The conventional solutions are shown to be incomplete, failing to capture the true nature of the gravitational field near the black hole’s singularity. Drawing from advanced concepts in functional analysis and distribution theory, we derive generalized solutions that resolves the apparent singularities and provides new insights into the behavior of matter and energy in the vicinity of a black hole. Our findings suggest the possibility of quantum tunneling, allowing particles to traverse the event horizon under specific conditions. This work not only offers a more rigorous treatment of the Schwarzschild, Reissner–Nordstrom and Massless Black Hole solutions but also paves the way for a deeper understanding of black hole physics and the interplay between general relativity and quantum mechanics.

Computational studies on the catalytic potential of the double active site for enzyme engineering

Proteins possessing double active sites have the potential to revolutionise enzyme design strategies. This study extensively explored an enzyme that contains both a natural active site (NAS) and an engineered active site (EAS), focusing on understanding its structural and functional properties. Metadynamics simulations were employed to investigate how substrates interacted with their respective active sites. The results revealed that both the NAS and EAS exhibited similar minimum energy states, indicating comparable binding affinities. However, it became apparent that the EAS had a weaker binding site for the substrate due to its smaller pocket and constrained conformation. Interestingly, the EAS also displayed dynamic behaviour, with the substrate observed to move outside the pocket, suggesting the possibility of substrate translocation. To gain further insights, steered molecular dynamics (SMD) simulations were conducted to study the conformational changes of the substrate and its interactions with catalytic residues. Notably, the substrate adopted distinct conformations, including near-attack conformations, in both the EAS and NAS. Nevertheless, the NAS demonstrated superior binding minima for the substrate compared to the EAS, reinforcing the observation that the engineered active site was less favourable for substrate binding due to its limitations. The QM/MM (Quantum mechanics and molecular mechanics) analyses highlight the energy disparity between NAS and EAS. Specifically, EAS exhibited elevated energy levels due to its engineered active site being located on the surface. This positioning exposes the substrate to solvents and water molecules, adding to the energy challenge. Consequently, the engineered enzyme did not provide a significant advantage in substrate binding over the single active site protein. Further, the investigation of internal channels and tunnels within the protein shed light on the pathways facilitating transport between the two active sites. By unravelling the complex dynamics and functional characteristics of this double-active site protein, this study offers valuable insights into novel strategies of enzyme engineering. These findings establish a solid foundation for future research endeavours aimed at harnessing the potential of double-active site proteins in diverse biotechnological applications.

Computational chemistry unveiled: a critical analysis of theoretical coordination chemistry and nanostructured materials

Abstract The article discusses the profound impact of advancements in computing and software on theoretical simulations, marking a transformative era in computational chemistry. Focused on theoretical coordination chemistry, it delves into the historical context and underscores the contemporary importance of computational methods. Coordination materials, involving metal atoms surrounded by ligands, are highlighted for their pivotal roles across scientific disciplines. The manipulation of ligands and metal ions within these compounds offers diverse functionalities, from catalytic modifications to enhancing oxygen transport in biological systems. The comprehensive review explores the basics of coordination materials, detailing examples across various categories. Theoretical approaches, including quantum mechanics methods like density functional theory (DFT) and Monte Carlo simulations, are thoroughly examined. The article emphasizes crystallography techniques for Metal-Organic Frameworks (MOFs) and concludes by emphasizing the exponential growth in computing power, making modeling and simulation indispensable in molecular and material research. The development of an integrated computational strategy rooted in DFT is highlighted as a crucial advancement, bridging precision and computational practicality. This holistic approach advances understanding in coordination chemistry and nanostructured materials, paving the way for innovative applications and discoveries.

Max Delbruck: Founder of Molecular Genetics.

Max Delbrück (1906-1981) attended the University of Gottingen, where he studied astrophysics initially, switching later to theoretical physics. He earned his PhD in physics from Gottingen in 1930. Delbruck then moved to England and Denmark. It was during this time that he met Niels Bohr and his argument that quantum mechanics might have a wider application to biology-inspired Delbruck to pursue biology.

Ahlfors regularity of continua that minimize maxitive set functions

The primary objective of this paper is to establish the Ahlfors regularity of minimizers of set functions that satisfy a suitable maxitive condition on disjoint unions of sets. Our analysis focuses on minimizers within continua of the plane with finite 1-dimensional Hausdorff measure. Through quantitative estimates, we prove that the length of a minimizer inside the ball centered at one of its points is comparable to the radius of the ball. By operating within an abstract framework, we are able to encompass a diverse range of entities, including the inradius of a set, the maximum of the torsion function, and spectral functionals defined in terms of the eigenvalues of elliptic operators. These entities are of interest for several applications, such as structural engineering, urban planning, and quantum mechanics.

Understanding the market potential of crypto mining with quantum mechanics and golden cut-based picture fuzzy rough sets

Significant improvements should be made to increase the market potential of crypto mining. However, it is not financially feasible to make too many improvements because all actions lead to cost increases. In this context, it is necessary to determine the factors that most affect this process. Accordingly, the purpose of this study is to understand the main indicators to improve the market potential of crypto mining activities. Therefore, the main research question of this study is to identify which factors should be prioritized while generating appropriate strategies to increase these activities. In this context, a new model has been constructed to answer this question. First, significant indicators are identified based on the literature evaluation. After that, these factors are weighted via quantum picture fuzzy rough set-based M-SWARA. The main contribution of this study is the generation of a new decision-making model to understand the key issues related to the market potential of the crypto mining activities. The M-SWARA model is taken into consideration for criteria weighting. Owing to this issue, the causal relationships between the items can be identified. The findings demonstrate that reducing energy costs emerges as the most important factor for improving the market potential of the crypto mining industry. Furthermore, technological developments also play an important role in this regard.

Computational discovery of dual potential inhibitors of SARS-CoV-2 spike/ACE2 and Mpro: 3D-pharmacophore, docking-based virtual screening, quantum mechanics and molecular dynamics.

To find drugs against COVID-19, caused by the SARS-CoV-2, promising targets include the fusion of the viral spike with the human angiotensin-converting enzyme 2 (ACE2) as well as the main protease (Mpro). These proteins are responsible for viral entry and replication, respectively. We combined several state-of-the-art computational methods, including, protein-ligand interaction fingerprint, 3D-pharmacophores, molecular-docking, MM-GBSA, DFT, and MD simulations to explore two databases: ChEMBL and NANPDB to identify molecules that could both block spike/ACE2 fusion and inhibit Mpro. A total of 1,690,649 compounds from the two databases were screened using the pharmacophore model obtained from PLIF analysis. Five recent complexes of Mpro co-crystallized with different ligands were used to generate the pharmacophore model, allowing 4,829 compounds that passed this prefilter. These were then submitted to molecular docking against Mpro. The 5% top-ranked docking hits from docking result having scores -8.32kcalmol-1 were selected and then docked against spike/ACE2. Only four compounds: ChEMBL244958, ChEMBL266531, ChEMBL3680003, and 1-methoxy-3-indolymethyl glucosinolate (4) displayed binding energies 8.21kcalmol-1 (for the native ligand) were considered as putative dual-target inhibitors. Furthermore, predictive ADMET, MM-GBSA and DFT/6-311G(d,p) were performed on these compounds and compared with those of well-known antivirals. DFT calculations showed that ChEMBL244958 and compound 4 had significant predicted reactivity values. Molecular dynamics simulations of the docked complexes were run for 100ns and used to validate the stability docked poses and to confirm that these hits are putative dual binders of the spike/ACE2 and the Mpro.

Discrete-time optimal control problems with time delay argument: New discrete-time Euler–Lagrange equations with delay

Discrete-time optimal control problems are a crucial type of control problems that deal with a dynamic system evolving in discrete time-steps. This paper introduces a new technique for solving linear discrete-time optimal control problems with state delays, applicable to both finite and infinite time horizons. Our method employs a Riccati matrix equation, optimizing control strategies and ensuring system stability through bounded control inputs. We adopt a Bolza problem for the performance index, which guides the classification of control issues. The technique simplifies problems into manageable Riccati matrix equations using the Euler–Lagrange equations and Pontryagin maximum principle, ensuring stability and necessary condition compliance. The paper validates the approach with numerical examples from quantum mechanics and classical physics, demonstrating its practicality and potential for broader application.

A note on the stability of the Cauchy horizon in regular black holes without mass inflation

Unlike generic models of regular black holes (BHs) with nonzero surface gravity on both Cauchy and event horizons, an inner-degenerate counterpart with zero Cauchy horizon surface gravity was recently proposed. For this regular BH solution with spherical symmetry, we examine the stability of the Cauchy horizon from both classic and quantum mechanics viewpoints. We find that the classical perturbations do not lead to mass inflation at the Cauchy horizon, indicating classically stability, while quantum fluctuations cause it to be unstable quantum mechanically.

A formulation of quantum fluid mechanics and trajectories

A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics, describing both fluid flow and point mass trajectories. The familiar equations of energy, motion, and those of Lagrangian mechanics are obtained. An energy and continuity equation is demonstrated to be equivalent to the real and imaginary parts of the time dependent Schrödinger equation, respectively, where the Schrödinger equation is in density matrix form. For certain stationary states, using Lagrangian mechanics and a Hamiltonian function for quantum mechanics, equations for point-mass trajectories are obtained. For 1-body states and fluid flows, the energy equation and equations of motion are the Bernoulli and Euler equations of fluid mechanics, respectively. Generalizations of the energy and Euler equations are derived to obtain equations that are in the same form as they are in classical mechanics. The fluid flow type is compressible, inviscid, irrotational, with the nonclassical element of local variable mass. Over all space mass is conserved. The variable mass is a necessary condition for the fluid flow to agree with the zero orbital angular momentum for s states of hydrogen. Cross flows are examined, where velocity directions are changed without changing the kinetic energy. For one-electron atoms, the velocity modification gives closed orbits for trajectories, and mass conservation, vortexes, and density stratification for fluid flows. For many body states, under certain conditions, and by hypotheses, Euler equations of orbital-flows are obtained. One-body Schrödinger equations that are a generalization of the Hartree–Fock equations are also obtained. These equations contain a quantum Coulomb’s law, involving the 2-body pair function of reduced density matrix theory that replace the charge densities.

Molecular Docking, Quantum Mechanics and Molecular Dynamics Simulation of Anti-CAD Drugs Against High-Risk Xanthine Dehydrogenase Variants Associated with Oxidative Stress Pathways

Xanthine dehydrogenase (XDH) contributes significantly to generating reactive oxygen species in coronary artery disease (CAD). XDH has been proposed as a therapeutic target, but its genetic variants could affect protein structure and drug response. We aimed to assess protein structure modification occur due to genetic variants and to screen 215 CAD drugs for their utility in personalized CAD treatment against the XDH variants. A series of computational methods were implemented to identify pathogenic variants that cause XDH structure instability localized at the conserved regions contributing to functional significance. Then, the XDH structures with the pathogenic variants were modeled using two different approaches to select the best models for docking with the CAD drugs. Finally, the stability of the docked complexes and their ability to transfer electrons were evaluated using molecular dynamics (MD) simulations and quantum mechanics/molecular mechanics (QM/MM) calculation. Among 751 variants examined; R149C and Q919R showed high pathogenicity, localized in conserved regions could alter protein structure and function. Further, docking of CAD drugs against XDH (native, R149C and Q919R) showed vericiguat with higher affinity, ranging from -7.95 kcal/mol to -10.41 kcal/mol, than the well-known XDH inhibitor (febuxostat, -5.73 kcal/mol to -8.35 kcal/mol). This indicates that vericiguat will be effective in CAD treatment, regardless of the XDH variants. Additionally, MD simulation and QM/MM confirmed vericiguat stability and electron transfer ability to form hydrogen bonds with the XDH protein. In conclusion, vericiguat will be beneficial for the personalized treatment of CAD by inhibiting XDH variants. Additional clinical studies are necessary to confirm our findings.

A general law of the iterated logarithm for non-additive probabilities

Motivated by some interesting problems in mathematical economics, quantum mechanics and finance, non-additive probabilities have been used to describe the phenomena which are generally non-additive. In this paper, we further study the law of the iterated logarithm (LIL) for non-additive probabilities, based on existing results. Under the framework of sublinear expectation initiated by Peng, we give two convergence results of Vn≔∑i=1nXinϕ(n) under some reasonable assumptions, where {Xi}i=1∞ is a sequence of random variables and ϕ is a positive nondecreasing function. From these, a general LIL for non-additive probabilities is proved for negatively dependent and non-identically distributed random variables. It turns out that our result is a natural extension of the Kolmogorov LIL and the Hartman–Wintner LIL. Theorem 1 and Theorem 2 in this paper can be seen an extension of Theorem 1 in Chen and Hu (2014).

Spin Gapless Quantum Materials and Devices.

Quantum materials, with nontrivial quantum phenomena and mechanisms, promise efficient quantum technologies with enhanced functionalities. Quantum technology is held back because a gap between fundamental science and its implementation is not fully understood yet. In order to capitalize the quantum advantage, a new perspective is required to figureout and close this gap. In this review, spin gapless quantum materials, featured by fully spin-polarized bands and the electron/hole transport, are discussed from the perspective of fundamental understanding and device applications. Spin gapless quantum materials can be simulated by minimal two-band models and could help to understand band structure engineering in various topological quantum materials discovered so far. It is explicitly highlighted that various types of spin gapless band dispersion are fundamental ingredients to understand quantum anomalous Hall effect. Based on conventional transport in the bulk and topological transport on the boundaries, various spintronic device aspects of spin gapless quantum materials as well as their advantages in different models for topological field effect transistors arereviewed.

Correlated qubit coherences stimulated by thermal energy

Abstract Quantum coherence, the ability of a system to be in a quantum superposition of pure states, is a distinct feature of quantum mechanics that has no direct analog in classical mechanics. Quantum states that possess coherence efficiently outperform their classical counterparts in fundamental science and practical applications, including quantum metrology, computation, and simulation. Generation of coherence without the need to employ strong classical drives remains a challenging and not yet experimentally explored task. Beyond individual thermally-induced coherences already proposed for different experiments, correlated quantum coherences of multiple qubits represent a new target. We prove that correlated qubit coherence emerges thermally stimulated from incoherent states in hybrid superconducting and solid-state systems comprising non-interacting qubits coupled only via Dicke-type interaction to a shared thermal mechanical oscillator, exhibits coherences beyond the Tavis–Cummings coupling and, moreover, can be advantageous in quantum sensing.

Coherent distributions of the symmetry algebra of spinor regularization generator and hydrogen atom

A new approach is developed for solving spectral problems for operators with continuous spectrum, which consists in the integral transform of the problem by using coherent Schwartz distributions. The constructed family of coherent distributions is a complete analogue of the family of ordinary coherent states. More precisely, it satisfies all Gazeau–Klauder axioms satisfied by the usual coherent states. But in contrast to the coherent states belonging to the point spectrum of the annihilation operator (or operators), the coherent distributions belong to the continuous spectrum of some Hermitian operators. Therefore, the coherent distributions work better than the coherent states as the kernel of the integral representation of generalized eigenfunctions of operators with continuous spectrum. In this work, this approach is demonstrated with an example of solving a basic problem of quantum mechanics, i.e., the problem of the continuous part of the spectrum of the Hamiltonian of the hydrogen atom.

Extracting work from two gravitational cat states

Gravitational cat states in the context of gravity are superpositions of quantum states that exhibit macroscopically distinct gravitational fields. These states represent a unique blend of quantum mechanics and general relativity, providing insights into the behavior of quantum systems under gravitational influences. This study investigates the impact of thermal environments on the extractable work from gravitational cat states, which are quantum superpositions of distinct gravitational configurations. It aims to offer a comprehensive analysis of how temperature and gravitational interactions between states with masses m influence work extraction. The findings indicate that both an increase in temperature and the interactions between states reduce the amount of work that can be extracted from gravitational cat states, highlighting the delicate balance between thermal and gravitational effects in quantum systems.

Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace

We investigate the emergence of a quantum Big-Bounce in the context of an isotropic Universe, filled by a self-interacting scalar field, which plays the role of a physical clock. The bouncing cosmology is the result of a scattering process, driven by the scalar field potential, which presence breaks down the frequency separation of the Wheeler-DeWitt equation, treated in strict analogy to a relativistic quantum system. Differently from previous analyses, we consider a really perturbative self-interaction potential, affecting the dynamics in a finite range of the time labeled by the scalar clock (and in particular we remove the divergent character previously allowed). The main result of the present analysis is that, when the Relativistic Quantum Mechanics formalism is properly implemented in the Mini-superspace analogy, the probability amplitude for the bounce is, both in the standard and polymerized case, characterized by a maximum in correspondence of the quasi-classical condition of a Universe minimum volume.