Framework Of Quantum Mechanics Research Articles

Higher-order phase-space moments for off-diagonal rotating Morse oscillators

The present paper proposes an advancement beyond the recent mathematical formulation [Cherroud O and Yahiaoui S-A 2023 Eur. Phys. J. Plus. 138 534], by extending their approach to the evaluation of off-diagonal matrix elements 〈xˆmpˆl〉n,n′J,J′ for the rotation-vibration Morse oscillators. Calculations are conducted within the framework of phase-space quantum mechanics, considering (r → r eq). This methodology facilitates the derivation of analytical expressions for 〈xˆs〉n,n′J,J′ and 〈pˆs〉n,n′J,J′ matrix elements, where s = 1, 2, …. This approach enables the evaluation of both diagonal ( n=n′,J=J′≠0 ) and off-diagonal ( n≠n′,J=J′≠0 ) matrix elements through a more explicit and compact analytic formula, applicable for cases where J≠J′ as well as for scenarios involving non-rotating effects J=J′=0 .

Unveiling structural features, chemical reactivity, and bioactivity of a newly synthesized purine derivative through crystallography and computational approaches

We introduce the synthesis and characterization of a novel purine derivative, 2-amino-6‑chloro-N,N-diphenyl-7H-purine-7-carboxamide. X-ray crystallography was utilized to elucidate its molecular and crystal structure. A comprehensive crystal packing analysis uncovered a network of diverse intermolecular interactions, including classical and unconventional hydrogen bonding. Remarkably, a unique halogen···π (C—Cl···π(ring)) interaction was identified and theoretically analyzed within a multi-approach quantum mechanics (QM) framework, revealing its lone-pair⋯π (n→π*) nature. Furthermore, insights into the electronic and chemical reactivity properties are provided by means of Conceptual Density Functional Theory (CDFT) at wB97X-D/aug-cc-pVTZ level. The compound's drug-likeness, pharmacokinetics, and toxicology profiles are assessed using ADMETlab 2.0. Finally, molecular docking simulations were conducted to evaluate its bioactivity as a potential cyclooxygenase-2 (COX-2) inhibitor. This study significantly advances our understanding of purine structure and reactivity, offering valuable insights for the development of targeted purine-based COX-2 inhibitors and anticancer therapeutics.

Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator

Miller’s rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller’s rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller’s rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller’s rule, and we illustrate this point by means of a numerical example.

Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: a chiral Planar Hall Effect

Within a Supersymmetric Quantum Mechanics (SUSY-QM) framework, the (3+1) Dirac equation describing a Dirac material in the presence of external parallel electric and magnetic fields is solved. Considering static but non-uniform electric and magnetic profiles with translational symmetry along the y-direction, the Dirac equation is transformed into two decoupled pairs of Schrödinger equations, one for each chirality of the fermion fields. Taking trigonometric and hyperbolic profiles for the vector and scalar potentials, respectively, we arrive at SUSY partner Pöschl-Teller-like quantum potentials. Restricting to the conditions of the potentials that support an analytic zero-mode solution, we obtain a nontrivial current density perpendicular to the electric and magnetic fields, thus, defining a plane where these three vectors become coplanar, indicating the possibility of realizing the Planar Hall Effect. Furthermore, this non-vanishing current density is the sum of current densities for the left- and right-chiralities, suggesting that the net current is a consequence of chiral symmetry. Possible application in current steering of solitonic nature through a Type-I Weyl semimetal is discussed.

Homotopical foundations of parametrized quantum spin systems

In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum mechanics. We define the notion of quantum state types. These are certain lax-monoidal functors from the category of finite-dimensional Hilbert spaces to the category of topological spaces. The universal example takes a finite-dimensional Hilbert space [Formula: see text] to the pure state space of the quasi-local algebra of the quantum spin system with Hilbert space [Formula: see text] at each site of a specified lattice. The lax-monoidal structure encodes the tensor product of states, which corresponds to stacking for quantum systems. We then explain how to formally extract parametrized phases of matter from quantum state types, and how they naturally give rise to [Formula: see text]-spaces for an operad we call the “multiplicative” linear isometry operad. We define the notion of invertible quantum state types and explain how the passage to phases for these is related to group completion. We also explain how invertible quantum state types give rise to loop-spectra. Our motivation is to provide a framework for constructing Kitaev’s loop-spectrum of bosonic invertible gapped phases of matter. Finally, as a first step toward understanding the homotopy types of the loop-spectra associated to invertible quantum state types, we prove that the pure state space of any UHF algebra is simply connected.

Cost-Effective Approach for Modeling of Multiresonant Thermally Activated Delayed Fluorescence Emitters.

Multiresonant thermally activated delayed fluorescence (MR-TADF) emitters have recently attracted great interest for application in organic light-emitting diodes due to their remarkable electroluminescent efficiency and narrow emission spectra. It is therefore essential to establish computational methodologies that can accurately model the excited states of these materials at manageable computational costs. With regard to MR-TADF design and their associated photophysics, previous works have highlighted the importance of wave function-based methods, at much higher computational costs, over the traditional time-dependent density functional theory approach. Herein, we employ two independent techniques built on different quantum mechanical frameworks, highly correlated wave function-based STEOM-DLPNO-CCSD and range-separated double hybrid density functional, TD-B2PLYP, to investigate their performance in predicting the excited state energies in MR-TADF emitters. We demonstrate a remarkable mean absolute deviation (MAD) of ∼0.06 eV in predicting ΔEST compared to experimental measurements across a large pool of chemically diverse MR-TADF molecules. Furthermore, both methods yield superior MAD in estimating S1 and T1 energies over earlier reported SCS-CC2 computed values [J. Chem. Theory Comput. 2022, 18, 4903]. The short-range charge-transfer nature of low-lying excited states and narrow fwhm values, hallmarks of this class of emitters, are precisely captured by both approaches. Finally, we show the transferability and robustness of these methods in estimating rates of radiative and nonradiative events with adequate agreement against experimental measurements. Implementing these cost-effective computational approaches is poised to streamline the identification and evaluation of potential MR-TADF emitters, significantly reducing the reliance on costly laboratory synthesis and characterization processes.

Investigation of the Adsorption Properties of Electrically Conductive Pyrolyzed Polyacrylonitrile Modified with Chromium (III) Oxide to Obtain Highly Efficient Gas Sensors

Introduction. Obtaining highly sensitive gas sensors is an urgent task, the solution to which will allow you to accurately and quickly assess changes in the air-gas composition of a given medium. Gas sensors based on metal-containing pyrolyzed polyacrylonitriles (Me-pPAN) are among the cheapest and most environmentally friendly gas-sensitive materials with a fast response. One of the types of sensor materials included in the Me-pPAN list is pyrolyzed polyacrylonitrile (pPAN) modified with a chromium (III) oxide molecule. The reasons for selective adsorption of pPAN and Me-pPAN to pollutant gases, which would allow controlling this process and obtaining sensory materials with increased sensitivity to gases, are not enough studied. Therefore, the aim of this work was to establish the main causes of selective adsorption of semiconductor electrically conductive films by modeling methods in the framework of molecular and quantum mechanics. Materials and Methods. The authors used modeling methods in the framework of molecular and quantum mechanics (MM2), the density functional theory (COSMO) method and the semi-empirical PM7 method in the MOPAC software package. Results. MM2 and PM7 methods were used to obtain models of adsorption complexes of "Cr-pPAN – gas-pollutant" systems. Thermodynamic parameters of the system were calculated for standard environmental conditions. The dependence of the adsorption of pollutant gases on the surface of Cr-pPAN on temperature has been established. Discussion and Conclusion. As a result of calculating the thermodynamic parameters of gas-pollutant–pPAN/Me-pPAN systems and obtaining positive values of Gibbs energies of these systems, it was confirmed that the adsorption of polluting gases on the surface of Cr-pPAN was not a spontaneous phenomenon and was effective at high temperatures. Considering that when chromium (III) oxide was introduced into the pPAN matrix, the charge on nitrogen atoms increased. It could be concluded that a chromium (III) oxide molecule had a positive effect on the semiconductor properties of pPAN. It was found that the adsorption of polluting gases (SO2 and NO2) was most likely on the surfaces of pPAN and Cr-pPAN. The results obtained in the work can be used to obtain gas-sensitive materials with specified metrological characteristics.

States, observables and symmetries in p-adic quantum mechanics

In the framework of quantum mechanics constructed over a quadratic extension of the field of p-adic numbers, we consider an algebraic definition of physical states. Next, the corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a p-adic counterpart of the POVMs associated with a quantum system over the complex numbers. Differently from the standard complex setting, the space of all states of a p-adic quantum system has an affine — rather than convex — structure. Thus, a symmetry transformation may be defined, in a natural way, as a map preserving this affine structure. We argue that the group of all symmetry transformations of a p-adic quantum system has a richer structure wrt the case of standard quantum mechanics over the complex numbers.

Dirac materials in parallel electromagnetic fields generated by supersymmetry

In a Supersymetric Quantum Mechanics framework, the Dirac equation describing a Dirac material in the presence of electromagnetic fields is solved. Considering parallel static non-uniform electromagnetic fields, the Dirac equation is transformed into a two-dimensional system of equations. By means of variable separation, we can define one-dimensional eigenfunctions, which are solutions for two pairs of supersymmetric partner Schrödinger-like Hamiltonians. For Pöschl-Teller-like quantum potentials, we look for conditions that guarantee the existence of bound states, and determine an analytic zero-mode solution for the Dirac equation.

Big-bang is a boundary condition

There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The standard quantum mechanical framework requires a notion of time evolution and a proper definition of an invariant inner product having a probability interpretation, both of which are seemingly problematic in quantum gravity. We show that these two issues can actually be solved by introducing the embedding coordinates as dynamical variables à la Isham and Kuchar. The extended theory is identical to general relativity but has a larger group of gauge symmetries. The Wheeler-DeWitt equations describe the change of the wave-function from one arbitrary spacelike slice to another, however the constraint algebra makes this evolution purely kinematical and furthermore enforces the wave-function to be constrained in the subspace of zero-energy states. An inner product can also be introduced having all the necessary requirements. In this formalism big-bang appears as a finite field space boundary on which certain boundary conditions must be imposed for mathematical consistency. We explicitly illustrate this point both in the full theory and in the minisuperspace approximation.

Anti-[formula omitted] transformations and complex non-Hermitian [formula omitted]-symmetric superpartners

We propose a new algebraic formalism for constructing complex non-Hermitian PT-symmetric superpartners by extending a conventional shape-invariant superpotential into the complex domain. The resulting potential is an unbroken super- and parity-time (PT)-symmetric shape-invariant potential with real energy eigenvalues, maintaining this property for all parameter values. In order to restore the probabilistic interpretation within a true quantum theory, a new inner product called the CPT-inner product is defined in PT-symmetric quantum mechanics, replacing the Dirac Hermitian inner product. In this work, we propose a new version of the inner product called the anti-PT (APT)-inner product, 〈A|B〉≡|A〉APT.|B〉, which replaces the previous versions without any additional considerations. This PT-supersymmetric quantum mechanics framework also allows for the unification of various areas of physics, including classical optics and quantum mechanics. To validate the theory, we present exact solutions for optical waveguides and the quantum tunneling probability, demonstrating excellent agreement with experimental data for the probability of crossing the potential barrier in the 3H(d,n)4He reaction.

Computation of the complex energy shift of decaying states in intense laser fields

We present a specific calculation concerning laser-assisted decaying systems with non-Hermitian spectral calculations merged with the (t,t’)-formalism to estimate the possible intense laser-field-induced corrections to the lifetime of quasi-stationary states. The perturbed complex energy shift caused by the external vector potential which represents the linearly and circularly polarized laser field is calculated in details. This wavefunction-centered method implies the unsuitability of the radiation gauge and length gauge when quasi-stationary states are considered and described within the framework of non-hermitian quantum mechanics since in this case the A2 term cannot be transformed out.

Uncertainty relations for the relativistic Jackiw-Nair anyon: A first-principles derivation

In this paper we have explicitly computed the position-position and position-momentum (Heisenberg) uncertainty relations for the model of relativistic particles with arbitrary spin, proposed by Jackiw and Nair (Jackiw R. and Nair V. P. Phys. Rev. D, 43 (1991) 1933) as a model for anyon, in a purely quantum mechanical framework. This supports (via Schwarz inequality) the conjecture that anyons live in a 2-dimensional non-commutative space. We have computed the non-trivial uncertainty relation between anyon coordinates, , using the recently constructed anyon wave function (Majhi J. et al., Phys. Rev. Lett., 123 (2019) 164801), in the framework of Bialynicki-Birula I. and Bialynicka-Birula Z., New J. Phys., 21 (2019) 07306. We also compute the Heisenberg (position-momentum) uncertainty relation for anyons. Lastly we show that the identical formalism when applied to electrons, yield a trivial position uncertainty relation, consistent with their living in a 3-dimensional commutative space.

Arbitrary (k, l) States-Solutions of the Dirac and Schrödinger Equations Interacting with Improved Spatially-Dependent Mass Coulomb Potential with an improved Coulomb-like tensor interaction Model for H-atoms from 3D-RNCS and 3D-NRNCS symmetries

The deformed Dirac equation has been investigated, in the context of 3D-relativistic noncommutative space (3D-RNCS) symmetries, using the improved spatially dependent mass Coulomb potential with an improved Coulomb-like tensor interaction (ISDM(CP-CLTI)) model under the conditions of spin symmetry and pseudospin symmetry. The ISDM(CP-CLTI) model is the combining the spatially dependent mass Coulomb potential with the Coulomb-like tensor interaction (CP-CLTI) and the two central terms that are generated to the topological defects of spacespace. Within the confines of the parametric Bopp shift method and conventional perturbation theory, the new relativistic and non-relativistic energy eigenvalues for the hydrogen atoms ( H-atoms), such as He+,Li+2, and Be3+ under the ISDM(CP-CLTI) model have been derived. The novel values Encsp(n,C,m0,m1,H,Θ,τ,χ,j,l,s,m) and Encps(n,C,m0,m1,H,Θ,τ,χ,j,l,l̃,s̃,m̃) that we discovered examined to be dependent on the noncommutativity parameters (NP) (Θ,σ,χ), mixed potential depths C/q,m0,m1,H), and quantum atomic discrete quantum numbers (j,k,l,s,m,l̃,s̃,m̃). We have obtained several interesting special examples within the framework of relativistic extended quantum mechanics, which we believe will be of interest to the expert researcher. We were able to retrieve the typical results of relativistic and non-relativistic examples in the literature when we applied the three simultaneous constraints (Θ,σ,χ)→(0,0,0). Compared to previous models that are known from the literature, our new model had novel physical characteristics.

Wave-field interpretation of quantum mechanics

In this paper, we address a gap in the conventional interpretations of quantum mechanics, specifically the requirement for a more comprehensive description of particle and light phenomena. We introduce an alternative interpretation underpinned by the traditional mathematical framework of quantum mechanics, thus ensuring compatibility with established principles. Central to our proposition is the concept that particles and light fundamentally manifest as a ubiquitous wave field, each point of which is imbued with unique energy characteristics. This perspective provides a consistent resolution to the long-standing quantum measurement problem and offers a fresh lens through which to understand the intricacies of phenomena such as the double-slit experiment. Our proposed interpretational approach represents a crucial first step towards more comprehensive research, aiming to provide analytical proof and design experiments that verify this wave field interpretation.

High-Energy Quantum Dynamics of the 15N + o-14N14N Rovibrational Activation and Isotope Exchange Processes.

We report full quantum reaction probabilities, computed within the framework of time-independent quantum mechanics using hyperspherical coordinates, for the 15N + 14N14N inelastic and reactive collision processes, restricted to total angular momentum J = 0, for kinetic energies up to 4.5 eV. We take advantage of the nonzero (i = 1) nuclear spin of 14N, leading to the existence of two nuclear spin isomers of 14N14N, namely, ortho- and para-14N14N, to restrict the study to the ortho molecular nitrogen species, with even rotational quantum number j = 0, 2, ... states. Specifically, we start with diatomic reagents ortho-14N14N in the initial rotational state j = 0. A comparison with similar works previously published by other groups using time-dependent wave packet and quasi-classical trajectory methods for the 14N + 14N14N fully symmetric collision is given. We find that reactive processes 15N + 14N14N involving atom exchange do not happen for collision energies less than 2.2 eV. Collisions at energies of around 2.0 eV are most effective for populating reactants' rovibrational states, that is, for inelastic scattering, whereas those at energies close to 5.0 eV yield a newly formed 14N15N isotopologue in a wide variety of excited vibrational levels.

Dynamical Coupling between Particle and Antiparticle in Relativistic Quantum Mechanics: A Multistate Perspective on the Energy–Momentum Relation

A molecular formalism based on a decomposed energy space constructed by a modular basis of matter and radiation is proposed for relativistic quantum mechanics. In the proposed formalism, matter radiation interactions are incorporated via the dynamical transformation of the coupled particle/antiparticle pair in a multistate quantum mechanical framework. This picture generalizes relativistic quantum mechanics at minimal cost, unlike quantum field theories, and the relativistic energy–momentum relation is interpreted as energy transformations among different modules through a multistate Schrödinger equation. The application of two-state and four-state systems using a time-dependent Schrödinger equation with pair states as a basis leads to well-defined solutions equivalent to those obtained from the Klein–Gordon equation and the Dirac equation. In addition, the particle–antiparticle relationship is well manifested through a particle conjugation group. This work provides new insights into the underlying molecular mechanism of relativistic dynamics and the rational design of new pathways for energy transformation.

Deriving the generalized momentum operators from covariant derivatives

The generalized momentum operators are derived in the framework of non-relativistic quantum mechanics, taking into account an especial assumption on the covariant derivative. According to this assumption, a scalar density doesn’t change under the action of covariant derivative. The Hermitian form of the covariant derivative is discussed. It is shown that, with the help of the adjoint of covariant derivatives, generalized momentum operators can be derived. The inverse of covariant derivative is calculated. It is shown that the inverse of generalized momentum operators can be deduced from the inverse of covariant derivatives.

DKP equation in Wigner–Dunkl quantum mechanics framework

This paper explores the topic of relativistic particles with zero spins from a unique perspective. Our approach is derived from the Dunkl derivative, which we used to investigate this issue. By examining the ([Formula: see text])-dimensional DKP equation, we obtain eigenfunctions. Additionally, we replace the standard partial derivative with the Dunkl derivative and solve the relativistic particle problem in a box using the new formalism. We then determine the energy spectrum for this scenario. Following this, we investigate the scattering of the potential step problem and the Ramsauer–Townsend effect separately. Finally, we calculate the coefficients of transmission and reflection.

Discriminating quantum gravity models by gravitational decoherence

Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.