Quantum Mechanical Description Research Articles

Image potential in lossy dielectrics

The interaction of a point charge with surrounding media (the image potential) is analyzed using the quantum-mechanical description of dielectrics that consistently takes losses in media into account. We have derived a real dielectric function (without an imaginary part) appropriate for lossy dielectrics which, compared to the lossless one, significantly changes the image potential in the standard (first-order) calculations. However, when one adds to the Hamiltonian all higher-order terms caused by the losses, one finds that the image potential remains the same, as if there were no losses in media. Our calculations are approximative when analyzing complicated systems with various lossy dielectrics, but in some simple and essential cases (e.g., a dielectric plate) we are able to give the exact proof.

Real-Time Quantum Dynamics of Long-Range Electronic Excitation Transfer in Plasmonic Nanoantennas.

Using large-scale, real-time, quantum dynamics calculations, we present a detailed analysis of electronic excitation transfer (EET) mechanisms in a multiparticle plasmonic nanoantenna system. Specifically, we utilize real-time, time-dependent, density functional tight binding (RT-TDDFTB) to provide a quantum-mechanical description (at an electronic/atomistic level of detail) for characterizing and analyzing these systems, without recourse to classical approximations. We also demonstrate highly long-range electronic couplings in these complex systems and find that the range of these couplings is more than twice the conventional cutoff limit considered by Förster resonance energy transfer (FRET)-based approaches. Furthermore, we attribute these unusually long-ranged electronic couplings to the coherent oscillations of conduction electrons in plasmonic nanoparticles. This long-range nature of plasmonic interactions has important ramifications for EET; in particular, we show that the commonly used "nearest-neighbor" FRET model is inadequate for accurately characterizing EET even in simple plasmonic antenna systems. These findings provide a real-time, quantum-mechanical perspective for understanding EET mechanisms and provide guidance in enhancing plasmonic properties in artificial light-harvesting systems.

A quantum-mechanical perspective on linear response theory within polarizable embedding.

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole structures as well as residues of the individual terms are discussed. In addition to providing a thorough justification for the descriptions used in polarizable embedding models, this theoretical analysis clarifies which form of the response function to use and highlights complications in separating out subsystem contributions to molecular properties. The basic features of the presented expressions and various approximate forms are illustrated by their application to a composite model system.

The correlation theory of the chemical bond

The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture.

An alternative approach to unifying chemistry with quantum mechanics

Harold Kincaid in Individualism and the Unity of Science postulates a model of unity-without-reduction in order to accurately describe the relation between individualism and macroeconomics. I present this model and apply it to the description of the relation between chemistry and quantum mechanics. I argue that, when it comes to the description of molecular structure, chemistry and quantum mechanics are unified in Kincaid’s sense. Specifically, the two disciplines contribute to the formation of a unified body of knowledge with respect to molecular structure.

Quantum models as classical cellular automata

A synopsis is offered of the properties of discrete and integer-valued, hence “natural”, cellular automata (CA). A particular class comprises the “Hamiltonian CA” with discrete updating rules that resemble Hamilton’s equations. The resulting dynamics is linear like the unitary evolution described by the Schrödinger equation. Employing Shannon’s Sampling Theorem, we construct an invertible map between such CA and continuous quantum mechanical models which incorporate a fundamental discreteness scale l. Consequently, there is a one-to-one correspondence of quantum mechanical and CA conservation laws. We discuss the important issue of linearity, recalling that nonlinearities imply nonlocal effects in the continuous quantum mechanical description of intrinsically local discrete CA - requiring locality entails linearity. The admissible CA observables and the existence of solutions of the l-dependent dispersion relation for stationary states are mentioned, besides the construction of multipartite CA obeying the Superposition Principle. We point out problems when trying to match the deterministic CA here to those envisioned in ‘t Hooft’s CA Interpretation of Quantum Mechanics.

General classical and quantum-mechanical description of magnetic resonance: an application to electric-dipole-moment experiments

A general theoretical description of a magnetic resonance is presented. This description is necessary for a detailed analysis of spin dynamics in electric-dipole-moment experiments in storage rings. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are obtained for an arbitrary initial polarization. These formulas are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance with allowance for both rotating fields. A general quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is shown. Quasimagnetic resonances for particles and nuclei moving in noncontinuous perturbing fields of accelerators and storage rings are considered. Distinguishing features of quasimagnetic resonances in storage ring electric-dipole-moment experiments are investigated in detail. The exact formulas for the effect caused by the electric dipole moment are derived. The difference between the resonance effects conditioned by the rf electric-field flipper and the rf Wien filter is found and is calculated for the first time. The existence of this difference is crucial for the establishment of a consent between analytical derivations and computer simulations and for checking spin tracking programs. The main systematical errors are considered.

Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian

We study the relation between quantum fluctuations and the significant enhancement of the performance of quantum annealing in a mean-field Hamiltonian. First-order quantum phase transitions were shown to be reduced to second order by antiferromagnetic transverse interactions in a mean-field-type many-body-interacting Ising spin system in a transverse field, which means an exponential speedup of quantum annealing by adiabatic quantum computation. We investigate if and how quantum effects manifest themselves around these first- and second-order phase transitions to understand if the antiferromagnetic transverse interactions appended to the conventional transverse-field Ising model induce notable quantum effects. By measuring the proximity of the semiclassical spin-coherent state to the true ground state as well as the magnitude of the concurrence representing entanglement, we conclude that significant quantum fluctuations exist around second-order transitions, whereas quantum effects are much less prominent at first-order transitions. Although the location of the transition point can be predicted by the classical picture, system properties near the transition need quantum-mechanical descriptions for a second-order transition but not necessarily for first order. It is also found that quantum fluctuations are large within the ferromagnetic phase after a second-order transition from the paramagnetic phase. These results suggest that the antiferromagnetic transverse interactions induce marked quantum effects, and this fact would be related to closely to the significant enhancement of the performance of quantum annealing.

Core-hole-induced dynamical effects in the x-ray emission spectrum of liquid methanol.

We compute the x-ray emission spectrum of liquid methanol, with the dynamical effects that result from the creation of the core hole included in a semiclassical way. Our method closely reproduces a fully quantum mechanical description of the dynamical effects for relevant one-dimensional models of the hydrogen-bonded methanol molecules. For the liquid, we find excellent agreement with the experimental spectrum, including the large isotope effect in the first split peak. The dynamical effects depend sensitively on the initial structure in terms of the local hydrogen-bonding (H-bonding) character: non-donor molecules contribute mainly to the high-energy peak while molecules with a strong donating H-bond contribute to the peak at lower energy. The spectrum thus reflects the initial structure mediated by the dynamical effects that are, however, seen to be crucial in order to reproduce the intensity distribution of the recently measured spectrum.

Quantum-Mechanical Description of Ionization-Induced Generation of Tunable Mid-Infrared Pulses

The work is devoted to the analytical study of the excitation of low-frequency current density (with frequencies much smaller than the frequency of the optical wave) which radiates in mid-infrared band in the gas ionization by two-color laser pulses. We calculate the low-frequency current density using the analytical solution of time-dependent Schrödinger equation on the basis of strong-field approximation. Closed-form analytical formulas for the low-frequency current density are obtained for laser-pulse parameters corresponding the tunneling and multiphoton ionization regimes. The features of excitation of low-frequency current density are analyzed in both regimes.

Electron transport in ultra-thin films and ballistic electron emission microscopy

We have developed a calculation scheme for the elastic electron current in ultra-thin epitaxial heterostructures. Our model uses a Keldysh’s non-equilibrium Green’s function formalism and a layer-by-layer construction of the epitaxial film. Such an approach is appropriate to describe the current in a ballistic electron emission microscope (BEEM) where the metal base layer is ultra-thin and generalizes a previous one based on a decimation technique appropriated for thick slabs. This formalism allows a full quantum mechanical description of the transmission across the epitaxial heterostructure interface, including multiple scattering via the Dyson equation, which is deemed a crucial ingredient to describe interfaces of ultra-thin layers properly in the future.We introduce a theoretical formulation needed for ultra-thin layers and we compare with results obtained for thick Au(1 1 1) metal layers. An interesting effect takes place for a width of about ten layers: a BEEM current can propagate via the center of the reciprocal space () along the Au(1 1 1) direction. We associate this current to a coherent interference finite-width effect that cannot be found using a decimation technique. Finally, we have tested the validity of the handy semiclassical formalism to describe the BEEM current.

Electrical characteristics of metal–insulator–semiconductor and metal–insulator–semiconductor–insulator–metal capacitors under different high-k gate dielectrics investigated in the semi-classical and quantum mechanical models

In this paper the electrical characteristics of metal–insulator–semiconductor (MIS) and metal–insulator–semiconductor–insulator–metal (MISIM) capacitors with (100)-oriented p-type silicon as a substrate under different high- k gate dielectrics (SiO2, HfO2, La2O3 and TiO2) are investigated in the semi-classical and quantum mechanical models. We review the quantum correction in the inversion layer charge density for p-doped structures. The purpose of this paper is to point out the differences between the semi-classical and quantum mechanical charge descriptions at the insulator–semiconductor interface and the effect of the type of oxide and their position (gate oxide or buried oxide) in our structures. In particular, capacitance–voltage (C– V), relative position of the sub-band energies and their wavefunctions are studied to examine qualitatively and quantitatively the electron states and charging mechanisms in our devices. We find that parameters such as threshold voltage and device trans-conductance are enormously sensitive to the proper treatment of quantization effects.

Uniform Additivity in Classical and Quantum Information.

Information theory quantifies the optimal rates of resource interconversions, usually in terms of entropies. However, nonadditivity often makes evaluating entropic formulas intractable. In a few auspicious cases, additivity allows a full characterization of optimal rates. We study uniform additivity of formulas, which is easily evaluated and captures all known additive quantum formulas. Our complete characterization of uniform additivity exposes an intriguing new additive quantity and identifies a remarkable coincidence-the classical and quantum uniformly additive functions with one auxiliary variable are identical.

Charge density at the Al-=SUB=-2-=/SUB=-O-=SUB=-3-=/SUB=-/Si interface in Metal-Insulator-Semiconductor devices: semiclassical and quantum mechanical descriptions

In this paper, a quantum correction computation of the inversion layer of charge density was investigated. This study is carried out for a one-dimensional Metal-Insulator-Semiconductor (MIS) structure with (100) oriented P-type silicon as substrate. The purpose of this paper is to point out the differences between the semiclassical and quantum-mechanical charge description at the interface Al2O3/Si, and to identify some electronic properties of our MIS device using different thickness of the high-k oxide and diverse temperature with different carrier statitics (Fermi--Dirak statitics and Boltzmann statitics). In particular, the calculations of capacitance voltage (C-V), sheet electron density, a relative position of subband energies and their wave functions are performed to examine qualitatively and quantitatively the electron states and charging mechanisms in our device. DOI: 10.21883/FTP.2017.12.45185.8190

Rotational and steric effects in water dissociative chemisorption on Ni(111).

Powerful laser techniques have recently enabled quantum-state resolved molecular beam experiments for investigating gas-surface reactions, which have unveiled intriguing vibrational, rotational, and also steric effects. For reactions involving polyatomic molecules, e.g., the dissociative chemisorption of methane and water, the rotational and related steric effects are far less understood despite a large body of theoretical work having been able to reproduce the observed vibrational mode specificity and related bond selectivity semi-quantitatively or even within chemical accuracy. Herein, we report a high dimensional quantum dynamics study of water dissociation on Ni(111) on a first-principles potential energy surface, focusing on the reactivities of D2O in various rotational quantum states with different spatial orientations. Through an accurate quantum mechanical description of this asymmetric top, remarkable dependence of the reactivity on the orientation is observed. This dependence is site specific and rotational state specific. These single site rotational and steric effects are partially justified by a sudden model on the basis of the overlap between the rotational wavefunctions and the angular potential near the transition state, but rotational steering also plays a significant role which complicates the dynamics. Although site averaging weakens the influence of initial rotational excitations and leads to minor effects to the reactivity, steric effects are predicted to be observable if the water molecule is selectively excited and aligned by a linearly polarized laser.

How Thermodynamics and Quantum Mechanics Limit Electronic Computation?

In this communication new concept like the degree of assignment, the mass specific degree of assignment and a dynamic computer were introduced using concepts like second law of thermodynamics, Heisenberg’s uncertainty principle and entropy. The result formulated asserts that electronic computations are not out of the grasp of the second law of thermodynamics. Using Heisenberg’s uncertainty principle it is concluded that the total mass equivalent of the energy that is invested in signals communicating different elements of the computer cannot exceed the total mass of the system. While discussing quantum mechanical description main properties of algorithms and floating point numbers were used to provide a reasonable argument in favor of the wave interpretation of quantum mechanics as compared with other interpretations of quantum mechanics.

Impact of quantum confinement on transport and the electrostatic driven performance of silicon nanowire transistors at the scaling limit

In this work we investigate the impact of quantum mechanical effects on the device performance of n-type silicon nanowire transistors (NWT) for possible future CMOS applications at the scaling limit. For the purpose of this paper, we created Si NWTs with two channel crystallographic orientations 〈110〉 and 〈100〉 and six different cross-section profiles. In the first part, we study the impact of quantum corrections on the gate capacitance and mobile charge in the channel. The mobile charge to gate capacitance ratio, which is an indicator of the intrinsic performance of the NWTs, is also investigated. The influence of the rotating of the NWTs cross-sectional geometry by 90° on charge distribution in the channel is also studied. We compare the correlation between the charge profile in the channel and cross-sectional dimension for circular transistor with four different cross-sections diameters: 5nm, 6nm, 7nm and 8nm. In the second part of this paper, we expand the computational study by including different gate lengths for some of the Si NWTs. As a result, we establish a correlation between the mobile charge distribution in the channel and the gate capacitance, drain-induced barrier lowering (DIBL) and the subthreshold slope (SS). All calculations are based on a quantum mechanical description of the mobile charge distribution in the channel. This description is based on the solution of the Schrödinger equation in NWT cross sections along the current path, which is mandatory for nanowires with such ultra-scale dimensions.

Role of coherence in transport through engineered atomic spin devices

We give a further step in the quantum mechanical description of engineered atomic spin structures by deriving a master equation of the Redfield type that governs the dynamics of the atomic spin density matrix. By generalizing this approach to charge-specific density matrices, we are able to describe magnetic transport quantities, such as the average inelastic current and the shot noise, accessible by tunneling spectroscopy. Our method suitably describes moderate lead-atom coupling regimes where quantum coherence effects cannot be disregarded. We contrast our approach with the existing descriptions in terms of rate equations and show examples where coherence effects are crucial to understand the physics of spin-polarized tunnel current through spin structures.

Modal decomposition of a propagating matter wave via electron ptychography

We employ ptychography, a phase-retrieval imaging technique, to show experimentally that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually independent modes of minimal rank. Partial coherence significantly determines the optical transfer properties of an electron microscope and so there has been much work on this subject. However, previous studies have employed forms of interferometry to determine spatial coherence between discrete points in the wave field. Here we use the density matrix to derive a formal quantum mechanical description of electron ptychography and use it to measure a full description of the spatial coherence of a propagating matter wave field, at least within the fundamental uncertainties of the measurements we can obtain.

A spectroelectrochemical investigation of nanoparticle and molecular resonances in surface enhanced Raman scattering from crystal violet and malachite green

The interaction between nanoparticle plasmonic states and molecular electronic states is central to the large enhancements observed in surface‐enhanced Raman scattering (SERS). In this work, we use a model previously used in a fully quantum mechanical description of SERS to explain the enhancement of nontotally symmetric modes for crystal violet (CV) and malachite green (MG) adsorbed on silver nanoparticles. Our explanation is consistent with recent observations of the absorption spectra of dyes on silver nanoparticles that show the absence of charge‐transfer in these systems. Resonance with plasmon and molecular states explains the enhancement of nontotally symmetric modes, with enhancement dominated by the plasmon states. Spectroelectrochemical SERS studies using the same silver nanoparticles that are used to generate SERS in solution show increased SERS intensity for CV with positive potential up to +0.4 V (vs Ag/AgCl), consistent with a red‐shifted plasmon resonance, and decreasing intensity with more positive potentials, consistent with oxidation of the silver nanoparticles. Both crystal violet and malachite green show similar spectroelectrochemical behaviour with 514.5 nm excitation. Our spectroelectrochemical data show that SERS intensities from silver nanoparticles can be optimised with appropriately applied potentials. This work has highlighted the need for more detailed studies of the spectroelectrochemistry of dyes adsorbed on silver nanoparticles to more fully understand how SERS intensities respond to applied potentials. Copyright © 2016 John Wiley & Sons, Ltd.