Quantum Mechanical Perspective Research Articles

Revisiting Bloch oscillations in homogeneous and binary chains from an exact quantum mechanical perspective

AbstractWe present an exact analytic approach to study Bloch oscillations which allows to study cases where the semiclassical arguments are not valid. The method is focused on the velocity operator V. Two representative examples are addressed here: (i) the superposition of AC and DC electric fields in a one‐dimensional chain and (ii) the binary uni‐dimensional chain under the action of a static electric field. For the first case, it is demonstrated that, depending on the frequency of the AC field, an unidirectional movement emerges whose velocity depends on the magnitude of the AC and DC fields, on the phase of the AC field and on the convolution of the initial wavepacket with itself displaced by one lattice spacement. We also show the limit where the semiclassical approach can be used. For the second case, we show that the transition between two mini‐bands plays a significant role in the dynamics of the electronic wavepacket. In this case, the Bloch oscillations are characterized by two main frequencies and combinations of them.

Quantum-Inspired Multidirectional Associative Memory With a Self-Convergent Iterative Learning.

Quantum-inspired computing is an emerging research area, which has significantly improved the capabilities of conventional algorithms. In general, quantum-inspired hopfield associative memory (QHAM) has demonstrated quantum information processing in neural structures. This has resulted in an exponential increase in storage capacity while explaining the extensive memory, and it has the potential to illustrate the dynamics of neurons in the human brain when viewed from quantum mechanics perspective although the application of QHAM is limited as an autoassociation. We introduce a quantum-inspired multidirectional associative memory (QMAM) with a one-shot learning model, and QMAM with a self-convergent iterative learning model (IQMAM) based on QHAM in this paper. The self-convergent iterative learning enables the network to progressively develop a resonance state, from inputs to outputs. The simulation experiments demonstrate the advantages of QMAM and IQMAM, especially the stability to recall reliability.

The Nature of the Chemical Bond from a Quantum Mechanical Interference Perspective

AbstractThe analysis of the chemical bond in a variety of systems exhibiting distinct bonding patterns was performed using the Generalized Product Function Energy Partitioning (GPF‐EP) approach in order to verify the role played by quantum interference. Diatomic and polyatomic molecules, with single, double and triple bonds, with different degrees of polarity, linear or branched, cyclic or not, conjugated and aromatics, have been considered. In all cases the conclusion was exactly the same: for each bond of the molecule the energy partitioning results showed that the main contribution to the depth of the potential wells comes from the interference term. From the quantum interference perspective the minimum requirement for a chemical bond to be formed is one electron and two interfering one‐electron states belonging to different atoms. As a consequence, all chemical bonds are covalent in the sense that it takes a one‐electron state of each atom to form the bond, irrespective of its polarity.

Enhancing charge mobilities in organic semiconductors by selective fluorination: a design approach based on a quantum mechanical perspective.

Selective fluorination of organic semiconducting molecules is proposed as a means to achieving enhanced hole mobility. Naphthalene is examined here as a root molecular system with fluorination performed at various sites. Our quantum chemical calculations show that selective fluorination can enhance attractive intermolecular interactions while reducing charge trapping. Those observations suggest a design principle whereby fluorination is utilized for achieving high charge mobilities in the crystalline form. The utility of this design principle is demonstrated through an application to perylene, which is an important building block of organic semiconducting materials. We also show that a quantum mechanical perspective of nuclear degrees of freedom is crucial for a reliable description of charge transport.

A Reading of ‘Burnt Norton’ from the Perspective of Quantum Mechanics.

A Reading of ‘Burnt Norton’ from the Perspective of Quantum Mechanics.

Quantum model for mode locking in pulsed semiconductor quantum dots

Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is dramatically increased if the system is subjected to a magnetic field and to repeated optical pulsing. This enhancement is due to mode locking: oscillation frequencies resonant with the pulsing frequencies are enhanced, while off-resonant oscillations eventually die out. Because the resonant frequencies are determined by the pulsing frequency only, the system becomes immune to frequency shifts caused by the nuclear coupling and by slight variations between individual quantum dots. The effects remain even after the optical pulsing is terminated. In this work, we explore the phenomenon of mode locking from a quantum mechanical perspective. We treat the dynamics using the central-spin model, which includes coupling to 10--20 nuclei and incoherent decay of the excited electronic state, in a perturbative framework. Using scaling arguments, we extrapolate our results to realistic system parameters. We estimate that the synchronization to the pulsing frequency needs time scales in the order of $1\phantom{\rule{0.28em}{0ex}}\mathrm{s}$.

Optimal uncertainty relations in a modified Heisenberg algebra

Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations which are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min- and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min-entropy is exactly one bit.

ChemInform Abstract: Experimental and Quantum Chemical Approaches to Develop Highly Selective Nanocatalysts for CO2‐Free Power Circulation

AbstractReview: 31 refs.

Experimental and Quantum Chemical Approaches to Develop Highly Selective Nanocatalysts for CO2 -free Power Circulation.

Renewable electricity must be utilized to usefully suppress the atmospheric CO2 concentration and slow the progression of global warming. We have thus proposed a new concept involving CO2 -free electric power circulation systems via highly selective electrochemical reactions of alcohol/carboxylic acid redox couples. Design concepts for nanocatalysts able to catalyze highly selective electrochemical reactions are provided from both experimental and quantum mechanical perspectives.

Chaotic-periodic transition in a two-sided minority game

Phase transitions are being used increasingly to probe the collective behaviors of social human systems. In this study, we propose a different way of investigating such transitions in a human system by establishing a two-sided minority game model. A new type of agents who can actively transfer resources are added to our artificial bipartite resource-allocation market. The degree of deviation from equilibria is characterized by the entropy-like quantity of market complexity. Under different threshold values, Qth, two phases are found by calculating the exponents of the associated power spectra. For large values of Qth, the general motion of strategies for the agents is relatively periodic whereas for low values of Qth, the motion becomes chaotic. The transition occurs abruptly at a critical value of Qth. Our simulation results were also tested based on human experiments. The results of this study suggest that a chaotic-periodic transition related to the quantity of market information should exist in most bipartite markets, thereby allowing better control of such a transition and providing a better understanding of the endogenous emergence of business cycles from the perspective of quantum mechanics.

Quantum Mechanisms: Expanding the Boundaries of Power, Space, and Time in Global Security Studies

This inaugural issue of the Journal of Global Security Studies stakes out important new frontiers in security studies, pushing the boundaries of the possible in power politics (Goddard and Nexon), space (Adamson), and time (Ward). Goddard and Nexon attempt to wrest global security studies away from the traditional international relations (IR) perspective of states as primary actors acting within the structure of anarchy; Adamson calls for a “spatial turn” in IR, drawing attention to geographies that challenge the dominant conception of the world as a set of territorially defined entities; and Ward challenges the field to move beyond description and prescription. They offer a broad pluralistic view that focuses attention on collective mobilization processes rather than covering laws, erases boundaries between states, and promotes prediction as a goal for theories. However, expanding the boundaries of power, space, and time in global security studies cannot be fully realized within traditional IR philosophies of science. To reap these benefits requires a rejection of the traditional neo-Newtonian view of mechanisms in favor of a quantum mechanical perspective. Ward begins with a discussion of the Antikythera Mechanism, constructed to predict future events based on the Ancient Greek (pre-Keplerian) understanding of the motion of celestial bodies. The use of this (literal) mechanism as a starting place for discussing predictions in political science is quite apt, in that social science is still stuck with a neo-Newtonian conception of mechanisms for both prediction and explanation. Jon Elster aptly describes this orthodoxy in this paean to methodological individualism: “To explain is to provide a mechanism , to open up the black box and show the nuts and bolts, the cogs and wheels, the desires and beliefs that generate the aggregate outcomes” (emphasis in original; Elster 1985, 5). For Elster, as for many in social science, mechanisms are …

Instantons, Wilson lines, and D-branes

We revisit the well-studied D0-D4 system of D-branes and its relationship to the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction. It is well known that the D0-branes appear as instantons in the D4-brane worldvolume. We add a Wilson line to the D4-brane in the guise of an extended fundamental string and determine how this affects the D0-brane dynamics. As the D0-brane moves in the presence of the Wilson line, it experiences a Lorentz force, proportional to its Yang-Mills gauge connection. From the perspective of the D0-brane quantum mechanics, this force emerges through the ADHM construction of the self-dual gauge connection.

The Higgs oscillator on the hyperbolic plane and light-front holography

The Light Front Holographic (LFH) wave equation, which is the conformal scalar equation on the plane, is revisited from the perspective of the supersymmetric quantum mechanics, and attention is drawn to the fact that it naturally emerges in the small hyperbolic angle approximation to the "curved" Higgs oscillator on the hyperbolic plane, i.e. on the upper part of the two-dimensional hyperboloid of two sheets, a space of constant negative curvature. Such occurs because the particle dynamics under consideration reduces to the one dimensional Schr\"odinger equation with the second hyperbolic P\"oschl-Teller potential, whose flat-space (small-angle) limit reduces to the conformally invariant inverse square distance plus harmonic oscillator interaction, on which LFH is based. In consequence, energies and wave functions of the LFH spectrum can be approached by the solutions of the Higgs oscillator on the hyperbolic plane in employing its curvature and the potential strength as fitting parameters. Also the proton electric charge form factor is well reproduced within this scheme by means of a Fourier-Helgason hyperbolic wave transform of the charge density. In conclusion, in the small angle approximation, the Higgs oscillator on the hyperbolic plane is demonstrated to satisfactory parallel essential outcomes of the Light Front Holographic QCD. The findings are suggestive of associating the hyperboloid curvature of the with a second scale in LFH, which then could be employed in the definition of a chemical potential.

Length dependence of electron transport through molecular wires--a first principles perspective.

One-dimensional wires constitute a fundamental building block in nanoscale electronics. However, truly one-dimensional metallic wires do not exist due to Peierls distortion. Molecular wires come close to being stable one-dimensional wires, but are typically semiconductors, with charge transport occurring via tunneling or thermally-activated hopping. In this review, we discuss electron transport through molecular wires, from a theoretical, quantum mechanical perspective based on first principles. We focus specifically on the off-resonant tunneling regime, applicable to shorter molecular wires (<∼4-5 nm) where quantum mechanics dictates electron transport. Here, conductance decays exponentially with the wire length, with an exponential decay constant, beta, that is independent of temperature. Different levels of first principles theory are discussed, starting with the computational workhorse - density functional theory (DFT), and moving on to many-electron GW methods as well as GW-inspired DFT + Sigma calculations. These different levels of theory are applied in two major computational frameworks - complex band structure (CBS) calculations to estimate the tunneling decay constant, beta, and Landauer-Buttiker transport calculations that consider explicitly the effects of contact geometry, and compute the transmission spectra directly. In general, for the same level of theory, the Landauer-Buttiker calculations give more quantitative values of beta than the CBS calculations. However, the CBS calculations have a long history and are particularly useful for quick estimates of beta. Comparing different levels of theory, it is clear that GW and DFT + Sigma calculations give significantly improved agreement with experiment compared to DFT, especially for the conductance values. Quantitative agreement can also be obtained for the Seebeck coefficient - another independent probe of electron transport. This excellent agreement provides confirmative evidence of off-resonant tunneling in the systems under investigation. Calculations show that the tunneling decay constant beta is a robust quantity that does not depend on details of the contact geometry, provided that the same contact geometry is used for all molecular lengths considered. However, because conductance is sensitive to contact geometry, values of beta obtained by considering conductance values where the contact geometry is changing with the molecular junction length can be quite different. Experimentally measured values of beta in general compare well with beta obtained using DFT + Sigma and GW transport calculations, while discrepancies can be attributed to changes in the experimental contact geometries with molecular length. This review also summarizes experimental and theoretical efforts towards finding perfect molecular wires with high conductance and small beta values.

Coating Polycyclic Aromatic Hydrocarbon Cations with Helium Clusters: Snowballs and Slush.

The classical and quantum structures of cationic polycyclic aromatic hydrocarbon molecules (benzene, pyrene, coronene, and circumcoronene) coated by helium atoms have been theoretically investigated using a variety of computational methods. Classical shell filling, as determined from global optimization, is generally found to proceed by epitaxial additions on the graphitic surfaces before peripheral closure. From the quantum mechanical perspective provided by path-integral molecular dynamics simulations, vibrational delocalization is found to generally decrease the size of this first solvation shell, but also to give rise to a variety of situations in which the helium atoms are more or less localized depending on their environment, with strong finite size effects depending both on the hydrocarbon cation and the number of coating helium atoms. While the graphitic planes tend to bind helium sufficiently to give rise to snowball precursors, the peripheral regions are less dense and more delocalized, not as liquid as the outer layers but within an intermediate slushy character.

Resolution of curvature singularities from quantum mechanical and loop perspective

We analyze the persistence of curvature singularities when analyzed using quantum theory. First, quantum test particles obeying the Klein-Gordon and Chandrasekhar-Dirac equation are used to probe the classical timelike naked singularity. We show that the classical singularity is felt even by our quantum probes. Next, we use loop quantization to resolve singularity hidden beneath the horizon. The singularity is resolved in this case.

Scale-estimation of quantum coherent energy transport in multiple-minima systems.

A generic and intuitive model for coherent energy transport in multiple minima systems coupled to a quantum mechanical bath is shown. Using a simple spin-boson system, we illustrate how a generic donor-acceptor system can be brought into resonance using a narrow band of vibrational modes, such that the transfer efficiency of an electron-hole pair (exciton) is made arbitrarily high. Coherent transport phenomena in nature are of renewed interest since the discovery that a photon captured by the light-harvesting complex (LHC) in photosynthetic organisms can be conveyed to a chemical reaction centre with near-perfect efficiency. Classical explanations of the transfer use stochastic diffusion to model the hopping motion of a photo-excited exciton. This accounts inadequately for the speed and efficiency of the energy transfer measured in a series of recent landmark experiments. Taking a quantum mechanical perspective can help capture the salient features of the efficient part of that transfer. To show the versatility of the model, we extend it to a multiple minima system comprising seven-sites, reminiscent of the widely studied Fenna-Matthews-Olson (FMO) light-harvesting complex. We show that an idealised transport model for multiple minima coupled to a narrow-band phonon can transport energy with arbitrarily high efficiency.

Description of Polar Chemical Bonds from the Quantum Mechanical Interference Perspective.

The Generalized Product Function Energy Partitioning (GPF-EP) method has been applied to a set of molecules, AH (A = Li, Be, B, C, N, O, F), CO and LiF with quite different dipole moments, in order to investigate the role played by the quantum interference effect in the formation of polar chemical bonds. The calculations were carried out with GPF wave functions treating all the core electrons as a single Hartree-Fock group and the bonding electrons at the Generalized Valence Bond Perfect-Pairing (GVB-PP) level, with the cc-pVTZ basis set. The results of the energy partitioning into interference and quasi-classical contributions along the respective Potential Energy Surfaces (PES) show that the main contribution to the depth of the potential wells comes from the interference term, which is an indication that all the molecules mentioned above form typical covalent bonds. In all cases, the stabilization promoted by the interference term comes from the kinetic contribution, in agreement with previous results. The analysis of the effect of quantum interference on the electron density reveals that while polarization effects (quasi-classical) tend to displace electronic density from the most polarizable atom toward the less polarizable one, interference (quantum effects) counteracts by displacing electronic density to the bond region, giving rise to the right electronic density and dipole moment.

Space charge emission in cylindrical diode

In this paper, a mathematical model to describe cylindrical electron current emissions through a physics approximation method is presented. The proposed mathematical approximation consists of analyzing and solving the nonlinear Poisson's equation, with some determined mathematical restrictions. Our findings tackle the problem when charge-space creates potential barrier that disable the steady-state of the beam propagation. In this problem, the potential barrier effects of electron's speed with zero velocity emitted through the virtual cathode happens. The interaction between particles and the virtual cathode have been to find the inter-atomic potentials as boundary conditions from a quantum mechanics perspective. Furthermore, a non-stationary spatial solution of the electrical potential between anode and cathode is presented. The proposed solution is a 2D differential equation that was linearized from the generalized Poisson equation. A single condition was used solely, throughout the radial boundary conditions of the current density formation.

Structural, dynamic, and vibrational properties during heat transfer in Si/Ge superlattices: A Car-Parrinello molecular dynamics study

The structural, dynamic, and vibrational properties during heat transfer process in Si/Ge superlattices are studied by analyzing the trajectories generated by the ab initio Car-Parrinello molecular dynamics simulation. The radial distribution functions and mean square displacements are calculated and further discussions are made to explain and probe the structural changes relating to the heat transfer phenomenon. Furthermore, the vibrational density of states of the two layers (Si/Ge) are computed and plotted to analyze the contributions of phonons with different frequencies to the heat conduction. Coherent heat conduction of the low frequency phonons is found and their contributions to facilitate heat transfer are confirmed. The Car-Parrinello molecular dynamics simulation outputs in the work show reasonable thermophysical results of the thermal energy transport process and shed light on the potential applications of treating the heat transfer in the superlattices of semiconductor materials from a quantum mechanical molecular dynamics simulation perspective.