Quantum Mechanics Research Articles

Modulation instability and optical wave profiles for the conformable Schrödinger–Poisson dynamical system

This manuscript studies the exact solitary wave profiles for the conformable Schrödinger–Poisson dynamical system. This system has a significant role in gravity’s quantum state operation approximates the interaction between quantum mechanics and gravitation. The diverse exact solitary wave profiles are constructed by using the Khater method. The different closed-form solutions are obtained such as dark, singular, hyperbolic, periodic, and plane waves. Moreover, the modulation instability is also discussed for this dynamical system. To, show the physical significance of desired results we plot the 3D and 2D plots along with the related contour graphs, which are also drawn. The constraint criteria for the exact solutions are also exposed.

Examining quantum gravity's effects on gravitational rainbows

This paper delves into the fundamental implications of quantum gravity on gravitational rainbows, an intriguing phenomenon resulting from the interaction between quantum mechanics and gravity. We explore the theoretical underpinnings of quantum gravity and how they affect light bending around enormous objects, providing insight into the phenomenon known as gravitational rainbows. We investigate the complex interplay between quantum gravity and gravitational events by thoroughly analyzing theoretical models, experimental findings, and computer simulations, providing insights into the essence of the cosmos. The results show that according to the basic theories of light propagation, light moves along the x-axis at a constant speed based on observing a straight-line route between the affine parameters and the x-coordinate. The analysis of shifting gravitational potentials reveals significant influences on the routes taken by light beams traveling through gravitational fields. The impact of quantum gravitational effects is emphasized by the gravitational potential spreading outward, reaching magnitudes of 10 × 1011 and decreasing towards zero outward. Moreover, the gravitational disturbance distribution is closest to the coordinate system center, with minor perturbations in the z-direction, especially in ℎxx and ℎyy. This distribution highlights how gravitational influences vary throughout space. Finally, the analysis shows that, due to a decrease in the impact parameter, the deflection angle of light increases as the angle of incidence lowers. Additionally, the deflection angle is directly influenced by the mass of the deflecting objects, suggesting a proportionate link between mass and deflection. These findings advance our knowledge of gravitational events in astrophysical and cosmological contexts and offer insight into how light behaves in gravitational fields.

Analytical Study of Coupled Schrödinger Equations with Fractional Damping: Decay Solutions and Stability Analysis

Coupled Schrödinger equations with fractional damping represent a complex yet fascinating area of study in quantum mechanics. This research paper delves into the analytical investigation of such systems, focusing on deriving decay solutions and conducting stability analysis. By combining theoretical frameworks with numerical methods, we explore the behavior of these coupled equations under varying parameters and conditions. Through a thorough analysis, we aim to deepen our understanding of the dynamics and stability properties of quantum systems subject to fractional damping, with potential implications for diverse fields ranging from quantum mechanics to condensed matter physics.

Analytical Study of Coupled Schrödinger Equations with Fractional Damping: Decay Solutions and Stability Analysis

Coupled Schrödinger equations with fractional damping represent a complex yet fascinating area of study in quantum mechanics. This research paper delves into the analytical investigation of such systems, focusing on deriving decay solutions and conducting stability analysis. By combining theoretical frameworks with numerical methods, we explore the behavior of these coupled equations under varying parameters and conditions. Through a thorough analysis, we aim to deepen our understanding of the dynamics and stability properties of quantum systems subject to fractional damping, with potential implications for diverse fields ranging from quantum mechanics to condensed matter physics.

A purely algebraic derivation of associated Laguerre polynomials

We present a fully algebraic derivation of the Laguerre polynomials. The derivation is based on the knowledge of the energy eigenvectors of quantum mechanics solution of hydrogen-like atom Schrödinger equation, and a suitable translation operator. The method is purely algebraic since it does not require any analytical calculations.

Quantum Mechanics, Fields, Black Holes, and Ontological Plurality

Quantum Mechanics, Fields, Black Holes, and Ontological Plurality

Entanglement inside a black hole before the Page time

We investigate the evolution of entanglement within an open, strongly coupled system interacting with a heat bath as its environment, in the frameworks of both the doubly holographic model and the Sachdev-Ye-Kitaev (SYK) model. Generally, the entanglement within the system initially increases as due to internal interactions; however, it eventually dissipates into the environment. In the doubly holographic setup, we consider an end-of-the-world brane in the bulk to represent an eternal black hole coupled with its radiation and the evolution of the global thermofield double (TFD) state. For small black holes, the reflected entropy between the bipartition exhibits a ramp-plateau-slump behavior, where the plateau arises due to the phase transition of the entanglement wedge cross-section before the Page time. Similarly, the mutual information between the bipartition displays a ramp-slop-stabilizing behavior. In quantum mechanics, we consider a double copy of the SYK-plus-bath system in a global TFD state, resembling an eternal black hole interacting with an environment. The Rényi mutual information within the double-copied SYK clusters exhibits a ramp-plateau-slope-stabilizing behavior. The dynamic behaviors of the entanglement quantities observed in these two models are attributable to the competition between the internal interaction of the system and the external interaction with the baths. Our study provides a fine-grained picture of the entanglement dynamics inside black holes before their Page time.

Adiabatic driving, geometric phases, and the geometric tensor for classical states

We use the Hilbert space formulation of classical mechanics, known as the Koopman–von Neumann formalism, to study adiabatic driving, geometric phases, and the geometric tensor for classical states. In close relation to what happens to a quantum state, a classical Koopman–von Neumann eigenstate will acquire a geometric phase factor expiΦ after a closed variation of the parameters λ in its associated Hamiltonian. The explicit form of Φ is then derived for integrable systems, and its relation with the Hannay angle is shown. Additionally, we use quantum formulas to write an adiabatic gauge potential that generates adiabatic unitary flow between classical eigenstates, and we explicitly show the relationship between the potential and the classical geometric phase. We also define a classical analog of the geometric tensor, thus defining a Fubini–Study metric for classical states, and we use the singularities of the tensor to link the transition from Arnold–Liouville integrability to chaos with some of the mathematical formalism of quantum phase transitions. While the formulas and definitions we use originate in quantum mechanics, all the results found are purely classical, no classical or semiclassical limit is ever taken.

Abstract ladder operators for non self-adjoint Hamiltonians, with applications

Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract ladder operators considering in many details what happens if the Hamiltonian of the system is not self-adjoint. Among other results, we give an existence criterion for coherent states constructed as eigenstates of our lowering operators. In the second part of the paper we discuss two different examples of our framework: pseudo-quons and a deformed generalized Heisenberg algebra. Incidentally, and interestingly enough, we show that pseudo-quons can be used to diagonalize an oscillator-like Hamiltonian written in terms of (non self-adjoint) position and momentum operators which obey a deformed commutation rule of the kind often considered in minimal length quantum mechanics.

Two-photon charging of a quantum battery with a Gaussian pulse envelope

Quantum energy science is rapidly emerging as a domain interested in the generation, transfer and storage of energy at the quantum level. In particular, quantum batteries have the scope to exploit the wonders of quantum mechanics in order to boost their performance as compared to their electrochemical equivalents. Here we show how an exponential enhancement in stored energy can be achieved with a quantum battery thanks to a two-photon charging protocol. We consider theoretically a quantum battery modelled as a quantum harmonic oscillator, which when driven by a quadratic field (manifested by a Gaussian pulse envelope) gives rise to squeezing of the battery. This quantum squeezing ensures that the population of the battery is driven exponentially up its bosonic energy ladder. Our results demonstrate a plausible mechanism for quickly storing a vast amount of energy in a quantum object defined by continuous variables, which may be explored experimentally in a variety of quantum optical platforms.

Theory-driven design of graphene schiff base iron nanocomplex as catalyst for composite propellant

New graphene Schiff base iron nanocomplexes (S-792-Fe, S-550-Fe, and S-590-Fe) were designed and fabricated based on investigations of reactions mechanisms of AP pyrolysis, structural analysis of new materials and simulation results of quantum mechanics to deal with the long-standing contradiction between safety and performance for composite propellent combustion catalyst. By taking traditional catalyst Catocene as the benchmark, the S-550-Fe nanocomplexes exhibited competitive catalytic performances, much better anti-migration properties and significantly reduced impact and electrostatic sensitivities. After adding S-550-Fe, the burning rate of propellant enhanced from 13.87 to 19.77 mm s−1 at 15 MPa, and the impact and electrostatic sensitivities are improved to 50.2 cm and 172.12 mJ, respectively. The excellent catalytic performance of S-550-Fe is closely related to its molecular structure, which is manifested by an increase in charge density and a decrease in NH3 oxidation energy barriers. The promotion effects of S-550-Fe on desorption and oxidation of NH3 from the surface of AP is conducive to the rapid and complete pyrolysis of AP, which is reflected in the improvement of combustion rate and temperature gradient. The theory-driven design mode of this work may provide new pathways to tune combustion behaviors of composite propellants from the view of molecular-level insights.

Pomotrelvir and Nirmatrelvir Binding and Reactivity with SARS-CoV-2 Main Protease: Implications for Resistance Mechanisms from Computations.

We investigate the inhibition mechanism between pomotrelvir and the SARS-CoV-2 main protease using molecular mechanics and quantum mechanics / molecular mechanics simulations. Alchemical transformations where each Pi group of pomotrelvir was transformed into its counterpart in nirmatrelvir were performed to unravel the individual contribution of each group to the binding and reaction processes. We have shown that while a γ-lactam ring is preferred at position P1, a δ-lactam ring is a reasonable alternative. For the P2 position, tertiary amines are preferred with respect to secondary amines. Flexible side chains at P2 position can disrupt the preorganization of the active site, favouring the exploration of non-reactive conformations. The substitution of the P2 group of pomotrelvir by that of nirmatrelvir resulted in a compound, named as C2, that presents better binding free energy and a higher population of reactive conformations in the Michaelis complex. Analysis of the chemical reaction to form the covalent complex has shown a similar reaction mechanism and activation free energies for pomotrelvir, nirmatrelvir and C2. We hope that these findings could be useful to design better inhibitors to fight present and future variants of SARS-CoV-2 virus.

Pomotrelvir and Nirmatrelvir Binding andReactivity with SARS‐CoV‐2 Main Protease: Implications for Resistance Mechanisms from Computations

We investigate the inhibition mechanism between pomotrelvir and the SARS‐CoV‐2 main protease using molecular mechanics and quantum mechanics / molecular mechanics simulations. Alchemical transformations where each Pi group of pomotrelvir was transformed into its counterpart in nirmatrelvir were performed to unravel the individual contribution of each group to the binding and reaction processes. We have shown that while a γ‐lactam ring is preferred at position P1, a δ‐lactam ring is a reasonable alternative. For the P2 position, tertiary amines are preferred with respect to secondary amines. Flexible side chains at P2 position can disrupt the preorganization of the active site, favouring the exploration of non‐reactive conformations. The substitution of the P2 group of pomotrelvir by that of nirmatrelvir resulted in a compound, named as C2, that presents better binding free energy and a higher population of reactive conformations in the Michaelis complex. Analysis of the chemical reaction to form the covalent complex has shown a similar reaction mechanism and activation free energies for pomotrelvir, nirmatrelvir and C2. We hope that these findings could be useful to design better inhibitors to fight present and future variants of SARS‐CoV‐2 virus.

Coupling molecular density functional theory with converged selected configuration interaction methods to study excited states in aqueous solution.

This paper presents the first implementation of a coupling between advanced wavefunction theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations by incorporating an electrostatic potential generated by solvent charges into the electronic Hamiltonian. Solvent charges are deduced from the spatially and angularly dependent solvent particle density. Such a density is obtained through the minimization of the functional associated with the molecular mechanics (MM) Hamiltonian describing the interaction between the fluid particles. The introduced QM/MDFT framework belongs to QM/MM family of methods, but its originality lies in the use of MDFT as the MM solver, offering two main advantages. First, its functional formulation makes it competitive with respect to sampling-based molecular mechanics. Second, it preserves a molecular-level description lost in macroscopic continuum approaches. The excited state properties of water and formaldehyde molecules solvated into water have been computed at the selected configuration interaction (SCI) level. The excitation energies and dipole moments have been compared with experimental data and previous theoretical work. A key finding is that using the Hartree-Fock method to describe the solute allows for predicting the solvent charge around the ground state with sufficient precision for the subsequent SCI calculations of excited states. This significantly reduces the computational cost of the described procedure, paving the way for the study of more complex molecules.

Sir Roger James Elliott. 8 December 1928 — 16 April 2018

Roger James Elliott was a theoretical physicist and pioneer in the use of quantum theory in solid state physics, which happened a few years after the invention of quantum mechanics in the late 1920s and which spread into all areas of solid state physics during the years when Roger Elliott was active (roughly the second half of the twentieth century, 1950–2000). He specialized in the magnetic, semiconductor and optical properties of condensed matter, with a particular emphasis on the effects caused by disorder—that is, the absence of periodicity in alloys and amorphous materials. He studied at New College, Oxford, before working as a postdoc at Berkeley. He then returned to England, first to Harwell and then to a faculty position at the University of Reading. During this time he completed his seminal work on the general theory of the optical properties of excitons. He returned to Oxford in 1957, where he was to stay for the remaining 60 years, until his death in 2018. He was the Wykeham professor of physics from 1974 until 1988, and he was awarded the Maxwell Medal in 1968 and the Guthrie Medal in 1990, both from the Institute of Physics. He was knighted in 1987. In his later years he was very active in the Royal Society as Foreign Secretary and also in scientific publishing worldwide after he served as chief executive of Oxford University Press from 1988 until 1993.

Comment on Aurélien Drezet’s Defense of Relational Quantum Mechanics

Aurélien Drezet has attempted in Found. Phys. 54(1), 5 (2023) to defend Relational Quantum Mechanics (RQM) against our recent critique, entitled Relational Quantum Mechanics is incompatible with quantum mechanics, published in Quantum 7, 1015 (2023). Drezet not only misrepresents our work, but he also misconstructs the very theory (RQM) that he claims to defend.

Ionization processes of negative corona discharge. Part 2. Theory. Comparison with experiment

The purpose of the research is a theoretical analysis of ionization processes in the air, which are initiated by a high-voltage field generated by the negative needle-flat electrode electrode system. Methods. Fe, Cu, Al electrodes are used. Calculations are carried out using the methods of quantum mechanics and mathematical physics. Results. The processes of cold and thermoelectron emission of electrons, enhanced by an external high-voltage field (Schottky emission), are analyzed. The conditions under which the generation of charges from the cathode surface due to plasma-chemical reactions and the capture of surface electrons by electronegative oxygen molecules are decisive are investigated. Based on the PE theory, a theory of injection of negative ions from the cathode into an electronegative gas is constructed and the theory is compared with experiment. It has been shown that at small radii of curvature of needle tips, when E ≥ 106 V/cm, the generation of charges is due to cold emission of electrons. In average fields E ≈ 105 V/cm, electron emission is due to the Schottky effect. In fields E ≈ 104 V/cm and below, injection is caused by electrochemical processes and PE capture. A theory has been developed for PEs that appear at electric field intensities on the electrode of the order of several tens of kV/cm, that is, on flat and slightly curved negative electrodes. The capture of PE by electron-withdrawing molecules causes an injection current and, as a consequence, the ignition of a corona discharge. Analytical expressions for the surface density as a function of the local electric field strength, as well as an expression for the injection current, are obtained. The agreement between theory and experiment is satisfactory. Conclusion. An analysis of the development of CR on negative needles is given. A theory of PE at the cathode in strong electric fields was developed. Based on the results of measuring dark negative current-voltage characteristics, it is possible to determine the patterns of surface processes involving electronic transitions, in particular, determine the concentration of PE and injection currents.

Efficient detection of multidimensional single-photon time-bin superpositions

The ability to detect quantum superpositions lies at the heart of fundamental and applied aspects of quantum mechanics. The time-frequency degree of freedom of light enables encoding and transmitting quantum information in a multidimensional fashion compatible with fiber and integrated platforms. However, the ability to efficiently detect high-dimensional time-bin superpositions, a subset of encodings in the wider time-frequency paradigm, is not yet available. Here we show that multidimensional time-bin superpositions can be detected using a single time-resolved photon detector. Our approach uses off-the-shelf components and is based on the temporal Talbot effect—a time-frequency counterpart of the well-known near field diffraction effect. We provide experimental results and highlight the possible applications in quantum communication, quantum information processing, and time-frequency quantum state tomography.

Exploring Bacillus species xylanases for industrial applications: screening via thermostability and reaction modelling.

Xylanases derived from Bacillus species hold significant importance in various large-scale production sectors, with increasing demand driven by biofuel production. However, despite their potential, the extreme environmental conditions often encountered in production settings have led to their underutilisation. To address this issue and enhance their efficacy under adverse conditions, we conducted a theoretical investigation on a group of five Bacillus species xylanases belonging to the glycoside hydrolase GH11 family. Bacillus sp. NCL 87-6-10 (sp_NCL 87-6-10) emerged as a potent candidate among the selected biocatalysts; this Bacillus strain exhibited high thermal stability and achieved a transition state with minimal energy requirements, thereby accelerating the biocatalytic reaction process. Our approach aims to provide support for experimentalists in the industrial sector, encouraging them to employ structural-based reaction modelling scrutinisation to predict the ability of targeted xylanases. Utilising crystal structure data available in the Carbohydrate-Active enzymes database, we aimed to analyse their structural capabilities in terms of thermal-stability and activity. Our investigation into identifying the most prominent Bacillus species xylanases unfolds with the help of the semi-empirical quantum mechanics MOPAC method integrated with the DRIVER program is used in calculations of reaction pathways to understand the activation energy. Additionally, we scrutinised the selected xylanases using various analyses, including constrained network analyses, intermolecular interactions of the enzyme-substrate complex and molecular orbital assessments calculated using the AM1 method with the MO-G model (MO-G AM1) to validate their reactivity.

STRUCTURE AND DYNAMICS OF THE ENZYME-SUBSTRATE COMPLEX OF N-ACETYLASPARTYLGLUTAMATE SYNTHASE ACCORDING TO COMPUTER SIMULATION DATA

N-acetylaspartilglutamate is the most common dipeptide in brain cells, which is synthesized using the enzyme N-acetylaspartilglutamate synthase. Herein we utilize bioinformatics methods to predict the protein structure from the primary sequence of the coding gene, classical molecular dynamics to obtain a stable protein complex with N-acetylaspartate and glutamate ligands within the trajectory, as well as machine learning methods to analyze, describe and select potential reactive and non-reactive conformations of the model system describing the enzyme-substrate complex. Molecular dynamics simulations with combined quantum mechanics / molecular mechanics potentials were performed for a set of selected conformations and the potential reaction mechanism were characterized.