Quantum Mechanical Description Research Articles

Correction to baryon spectrum in holographic QCD

We study solitons in the context of Sakai-Sugimoto-Witten holographic model of QCD. In the large 't Hooft coupling limit, flat space instantons give an approximate description of baryons. We provide an ansatz through deforming the BPST instanton by zero modes and obtain a subleading correction to the effective action. We also consider the quantum mechanical description of the collective coordinates. The correction term appears as a perturbation to the potential of the Hamiltonian and hence we can derive a first order correction to the mass spectrum of baryons.

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.

Quantum work statistics in regular and classical-chaotic dynamical billiard systems.

In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we have chosen two two-dimensional billiard systems. Both systems are studied in the classical and the quantum mechanical settings. The classical conditional probability density p(E,L|E_{0},L_{0}) as well as the quantum mechanical transition probability P(n,l|n_{0},l_{0}) are calculated, which build the basis for the statistical analysis. We calculate the work distribution for one particle. The results in the quantum case in particular are of special interest since a suitable definition of mechanical work in small quantum systems is already controversial. Furthermore, we analyze the probability of both zero work and zero angular momentum difference. Using connections to an exactly solvable system analytical formulas are given for both systems. In the quantum case we get numerical results with some interesting relations to the classical case.

Electronic Dynamics of a Molecular System Coupled to a Plasmonic Nanoparticle Combining the Polarizable Continuum Model and Many-Body Perturbation Theory.

The efficiency of plasmonic metallic nanoparticles in harvesting and concentrating light energy in their proximity triggers a wealth of important and intriguing phenomena. For example, spectroscopies are able to reach single-molecule and intramolecule sensitivities, and important chemical reactions can be effectively photocatalyzed. For the real-time description of the coupled dynamics of a molecule’s electronic system and of a plasmonic nanoparticle, a methodology has been recently proposed (J. Phys. Chem. C. 120, 2016, 28774−28781) which combines the classical description of the nanoparticle as a polarizable continuum medium with a quantum-mechanical description of the molecule treated at the time-dependent configuration interaction (TDCI) level. In this work, we extend this methodology by describing the molecule using many-body perturbation theory: the molecule’s excitation energies, transition dipoles, and potentials computed at the GW/Bethe–Salpeter equation (BSE) level. This allows us to overcome current limitations of TDCI in terms of achievable accuracy without compromising on the accessible molecular sizes. We illustrate the developed scheme by characterizing the coupled nanoparticle/molecule dynamics of two prototype molecules, LiCN and p-nitroaniline.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface.

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Experimental violation of the Leggett-Garg inequality with a single-spin system

Investigation the boundary between quantum mechanical description and classical realistic view is of fundamental importance. The Leggett-Garg inequality provides a criterion to distinguish between quantum systems and classical systems, and can be used to prove the macroscopic superposition state. A larger upper bound of the LG function can be obtained in a multi-level system. Here, we present an experimental violation of the Leggett-Garg inequality in a three-level system using nitrogen-vacancy center in diamond by ideal negative result measurement. The experimental maximum value of Leggett-Garg function is $K_{3}^{exp}=1.625\pm0.022$ which exceeds the L\"uders bound with a $5\sigma$ level of confidence.

Higher Order Deformed Elliptic Ruijsenaars Operators

We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was previously introduced by Feigin and Silantyev. They provide a quantum mechanical description of two kinds of relativistic quantum mechanical particles which can be identified with particles and anti-particles in an underlying quantum field theory. We give direct proofs of the commutativity of our operators and of some other fundamental properties such as kernel function identities. In particular, we give a rigorous proof of the quantum integrability of the deformed Ruijsenaars model.

High Photon Number Entangled States and Coherent State Superposition from the Extreme Ultraviolet to the Far Infrared.

We present a theoretical demonstration on the generation of entangled coherent states and of coherent state superpositions, with photon numbers and frequencies orders of magnitude higher than those provided by the current technology. This is achieved by utilizing a quantum mechanical multimode description of the single- and two-color intense laser field driven process of high harmonic generation in atoms. It is found that all field modes involved in the high harmonic generation process are entangled, and upon performing a quantum operation, lead to the generation of high photon number optical cat states spanning from the far infrared to the extreme ultraviolet spectral region. This provides direct insights into the quantum mechanical properties of the optical field in the intense laser matter interaction. Finally, these states can be considered as a new resource for fundamental tests of quantum theory, quantum information processing, or sensing with nonclassical states of light.

Exploring far-from-equilibrium ultrafast polarization control in ferroelectric oxides with excited-state neural network quantum molecular dynamics.

Ferroelectric materials exhibit a rich range of complex polar topologies, but their study under far-from-equilibrium optical excitation has been largely unexplored because of the difficulty in modeling the multiple spatiotemporal scales involved quantum-mechanically. To study optical excitation at spatiotemporal scales where these topologies emerge, we have performed multiscale excited-state neural network quantum molecular dynamics simulations that integrate quantum-mechanical description of electronic excitation and billion-atom machine learning molecular dynamics to describe ultrafast polarization control in an archetypal ferroelectric oxide, lead titanate. Far-from-equilibrium quantum simulations reveal a marked photo-induced change in the electronic energy landscape and resulting cross-over from ferroelectric to octahedral tilting topological dynamics within picoseconds. The coupling and frustration of these dynamics, in turn, create topological defects in the form of polar strings. The demonstrated nexus of multiscale quantum simulation and machine learning will boost not only the emerging field of ferroelectric topotronics but also broader optoelectronic applications.

Classical nuclear motion: Does it fail to explain reactions and spectra in certain cases?

AbstractIs a classical description of nuclear motion sufficient when describing chemical reactions and spectra? This question is interesting because many researchers use a classical description of nuclear motion in molecular dynamics simulations. The present paper investigates some phenomena that were previously attributed to nuclear quantum effects. The question is if these phenomena can be modeled with traditional Car–Parrinello molecular dynamics, that is, with a method which treats nuclear motion classically and which is widely applied to the simulation of chemical reactions and spectra. We find that for the investigated system no additional paradigm is needed for describing chemical reactions. The special reactivity observed for carbenes can be attributed to the special environment represented by a noble gas matrix and to an additional transition state that was not considered before. Also the infrared spectrum of porphycene is perfectly modeled by traditional Car–Parrinello molecular dynamics. More studies are necessary to decide to what extent classical nuclear motion can replace the quantum mechanical description.

Spin current density functional theory of Weyl semimetals

Weyl fermions are massless solutions of the Dirac equation, described by two-component complex spinors. Such elusive objects emerge as quasiparticles in the so-called Weyl semimetals (WSM). The authors discuss the generalization of the standard one-component density functional theory to a two-component approach (the spin-current density functional theory) as well as its application to the practical quantum-mechanical description of WSMs through a self-consistent treatment of the spin-orbit coupling and nonlocal Fock exchange. In particular, the authors demonstrate the key role played by spin-current densities in the characterization of Weyl nodes in TaAs.

Quantum mechanical effects in protein oscillations

Protein Oscillation has been widely studied as one of the most interesting and promising topics to explain protein dynamics. There is a good understanding that protein oscillations follow non-equilibrium dynamics. Since classical physics is not enough to explain protein oscillations and a quantum mechanical description of oscillations is a more accurate phenomenon, we study protein oscillations based on a quantum mechanical oscillator.

Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors

There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states {mathbf {P}}—i.e., the set of one-dimensional projections on a complex Hilbert space H– and the orthomodular lattice {mathbf {L}} of closed subspaces of H. These six groups are isomorphic when the dimension of H is ge 3. The latter hypothesis is absolutely necessary in this identification. For example, the automorphisms group of all bijections preserving orthogonality and the order on {mathbf {L}} identifies with the bijections on {mathbf {P}} preserving transition probabilities only if dim(H)ge 3. Despite of the difficulties caused by M_2({mathbb {C}}), rank two algebras are used for quantum mechanics description of the spin state of spin-frac{1}{2} particles. However, there is a counterexample for Uhlhorn’s version of Wigner’s theorem for such state space. In this note we prove that in order that the description of the spin will be relativistic, it is not enough to preserve the projection lattice equipped with its natural partial order and orthogonality, but we also need to preserve the partial order set of all tripotents and orthogonality among them (a set which strictly enlarges the lattice of projections). Concretely, let M and N be two atomic JBW^*-triples not containing rank–one Cartan factors, and let {mathcal {U}} (M) and {mathcal {U}} (N) denote the set of all tripotents in M and N, respectively. We show that each bijection Phi : {mathcal {U}} (M)rightarrow {mathcal {U}} (N), preserving the partial ordering in both directions, orthogonality in one direction and satisfying some mild continuity hypothesis can be extended to a real linear triple automorphism. This, in particular, extends a result of Molnár to the wider setting of atomic JBW^*-triples not containing rank–one Cartan factors, and provides new models to present quantum behavior.

Solvation Free Energies in Subsystem Density Functional Theory.

For many chemical processes the accurate description of solvent effects are vitally important. Here, we describe a hybrid ansatz for the explicit quantum mechanical description of solute-solvent and solvent-solvent interactions based on subsystem density functional theory and continuum solvation schemes. Since explicit solvent molecules may compromise the scalability of the model and transferability of the predicted solvent effect, we aim to retain both, for different solutes as well as for different solvents. The key for the transferability is the consistent subsystem decomposition of solute and solvent. The key for the scalability is the performance of subsystem DFT for increasing numbers of subsystems. We investigate molecular dynamics and stationary point sampling of solvent configurations and compare the resulting (Gibbs) free energies to experiment and theoretical methods. We can show that with our hybrid model reaction barriers and reaction energies are accurately reproduced compared to experimental data.

Integral puta u kvantnoj teorijama polja

Introduction/purpose: Starting from the Hamiltonian an alternative description of quantum mechanics has been given, based on the sum of all possible paths between an initial and a final point. Methods: Theoretical methods of mathematical physics. Integral method based on the path integral. Results: The method and concepts of the path integral could be applied to other branches of physics, not limited to quantum mechanics. Conclusions: The Path Integral approach gives a global description of fields, unlike the usual Lagrangian approach which is a local description of fields.

New form of Laguerre fractional differential equation and applications

Laguerre differential equation is a well known equation that appears in the quantum mechanical description of the hydrogen atom. In this paper, we aim to develop a new form of Laguerre Fractional Differential Equation (LFDE) of order $2\alpha$ and we investigate the solutions and their properties. For a positive real number $\alpha$, we prove that the equation has solutions of the form $L_{n,\alpha}(x)=\sum_{k=0}^na_kx^k$, where the coefficients of the polynomials are computed explicitly. For integer case $\alpha=1$ we show that these polynomials are identical to classical Laguerre polynomials. Finally, we solve some fractional differential equations by defining a suitable integral transform.

Quantification of mixtures of analogues of illicit substances by benchtop NMR spectroscopy

This paper investigates the possibility of using benchtop NMR spectroscopy for quantification of illicit drugs (methamphetamine) in binary and ternary mixtures with impurities and cutting agents (N-isopropylbenzylamine, phenethylamine and dimethylsulfone). To avoid handling regulated substances, methamphetamine in our experiments is substituted with amino-2-propanol, which has similar functional groups and chemical structure to methamphetamine and hence a related NMR spectrum. Binary and ternary mixtures at concentrations from 30 mmol/L up to 500 mmol/L for each of these species were measured using a 60 MHz benchtop spectrometer. The spectra were analysed using both integration and a model-based algorithm that relies on a full quantum mechanical description of the studied spin systems. Both techniques were able to quantify the composition of the mixtures. The root mean squared error in the measured concentration using the model-based algorithm was < 10 mmol/L, whereas the error using integration was typically > 20 mmol/L. Thus, we conclude benchtop NMR is viable for quantitative measurements of mixtures of illicit substances, particularly when coupled with a quantum mechanical model for the analysis.

Role of metal-nanostructure features on tip-enhanced photoluminescence of single molecules.

Tip-enhanced photoluminescence (TEPL) experiments have recently reached the ability to investigate single molecules exploiting resolution at the submolecular level. Localized surface plasmon resonances of metallic nanostructures have the capability of enhancing an impinging electromagnetic radiation in the proximity of their surface, with evident consequences both on absorption and emission of molecules placed in the same region. We propose a theoretical analysis of these phenomena in order to interpret TEPL experiments on single molecules, including a quantum mechanical description of the target molecule equilibrated with the presence of two nanostructures representative of the nanocavity usually employed in STMs. The approach has been applied to the zinc phthalocyanine molecule, previously considered in recent TEPL experiments [Yang et al., Nat. Photonics 14, 693-699 (2020)]. This work has the aim of providing a comprehensive theoretical understanding of the experimental results, particularly focusing on the investigation of the tip features that majorly influence the excitation and fluorescence processes of the molecule, such as the geometry, the dielectric function, and the tip-molecule distance.

Efficient Modeling of Charge Trapping at Cryogenic Temperatures—Part I: Theory

Charge trapping is arguably the most important detrimental mechanism distorting the ideal characteristics of MOS transistors, and nonradiative multiphonon (NMP) models have been demonstrated to provide a very accurate description. For the calculation of the NMP rates at room temperature or above, simple semiclassical approximations have been successfully used to describe this intricate mechanism. However, for the computation of charge transition rates at cryogenic temperatures, it is necessary to use the full quantum mechanical description based on Fermi’s golden rule. Since this is computationally expensive and often not feasible, we discuss an efficient method based on the Wentzel–Kramers–Brillouin (WKB) approximation in combination with the saddle point method and benchmark this approximation against the full model. We show that the approximation delivers excellent results and can, hence, be used to model charge trapping behavior at cryogenic temperatures.

Generalized Bloch model: A theory for pulsed magnetization transfer.

The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in water. Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radiofrequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, for example, observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation. Our model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations smaller than 300μs. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2μs. The proposed theory unifies the original Bloch model, Henkelman's steady-state theory for MT, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF-fields) and describes experimental data better than previous models.