Quantum Mechanical Behavior Research Articles

Effective information bounds in modified quantum mechanics

A common feature of collapse models and an expected signature of the quantization of gravity at energies well below the Planck scale is the deviation from ordinary quantum-mechanical behavior. Here, we analyze the general consequences of such modifications from the point of view of quantum information theory and we anticipate applications to different quantum systems. We show that quantum systems undergo corrections to the quantum speed limit which, in turn, imply the modification of the Heisenberg limit for parameter estimation. Our results hold for a wide class of scenarios beyond ordinary quantum mechanics. For some nonlocal models inspired by quantum gravity, the bounds are found to oscillate in time, an effect that could be tested in future high-precision quantum experiments.

Janus-faced nature of q-deformed states and estimation of the quadrature moments from optical tomogram

In this work, we derive the optical tomograms of various q-deformed quantum states. We found that irrespective of the deformation parameter q, the Janus-faced nature of the quantum states manifests in their corresponding optical tomograms. A general method to estimate the quadrature moments from the optical tomograms of any q-deformed states is also derived. We also note that this technique can be used in high-precision experiments to observe deviations from the standard quantum mechanical behavior.

The temperature effect on the q-deformed optomechanical oscillator motion

In this paper, we study the quantum mechanical behavior of a deformed bare optomechanical oscillator interacting with a heat bath. This statistical study takes into account the temperature effect and the time dependency. Many material realizations can be inspired from our work during the experimental process to adjust many physical parameter values to have the right mechanical sensitivity of these materials.

A whale optimization algorithm based on atom-like structure differential evolution for solving engineering design problems

The whale optimization algorithm has received much attention since its introduction due to its outstanding performance. However, like other algorithms, the whale optimization algorithm still suffers from some classical problems. To address the issues of slow convergence, low optimization precision, and susceptibility to local convergence in the whale optimization algorithm (WOA). Defining the optimization behavior of whale individuals as quantum mechanical behavior, a whale optimization algorithm based on atom-like structure differential evolution (WOAAD) is proposed. Enhancing the spiral update mechanism by introducing a sine strategy guided by the electron orbital center. Improving the random-walk foraging mechanism by applying mutation operations to both the electron orbital center and random individuals. Performing crossover operations between the newly generated individuals from the improved mechanisms and random dimensions, followed by a selection process to retain superior individuals. This accelerates algorithm convergence, enhances optimization precision, and prevents the algorithm from falling into local convergence. Finally, implementing a scouting bee strategy, where whale individuals progressively increase the number of optimization failures within a limited parameter L. When a threshold is reached, random initialization is carried out to enhance population diversity. Conducting simulation experiments to compare the improved algorithm with the whale optimization algorithm, other optimization algorithms, and other enhanced whale optimization algorithms. The experimental results indicate that the improved algorithm significantly accelerates convergence, enhances optimization precision, and prevents the algorithm from falling into local convergence. Applying the improved algorithm to five engineering design problems, the experimental results demonstrate that the improved algorithm exhibits good applicability.

Nuclear quantum effects in the acetylene:ammonia plastic co-crystal.

Organic molecular solids can exhibit rich phase diagrams. In addition to structurally unique phases, translational and rotational degrees of freedom can melt at different state points, giving rise to partially disordered solid phases. The structural and dynamic disorder in these materials can have a significant impact on the physical properties of the organic solid, necessitating a thorough understanding of disorder at the atomic scale. When these disordered phases form at low temperatures, especially in crystals with light nuclei, the prediction of material properties can be complicated by the importance of nuclear quantum effects. As an example, we investigate nuclear quantum effects on the structure and dynamics of the orientationally disordered, translationally ordered plastic phase of the acetylene:ammonia (1:1) co-crystal that is expected to exist on the surface of Saturn's moon Titan. Titan's low surface temperature (∼90K) suggests that the quantum mechanical behavior of nuclei may be important in this and other molecular solids in these environments. By using neural network potentials combined with ring polymer molecular dynamics simulations, we show that nuclear quantum effects increase orientational disorder and rotational dynamics within the acetylene:ammonia (1:1) co-crystal by weakening hydrogen bonds. Our results suggest that nuclear quantum effects are important to accurately model molecular solids and their physical properties in low-temperature environments.

Introducing the Framework of a "Dynamic" Higher Dimensional Spacetime. How Time Behaves in it. Similarities with Quantum Mechanical and Relativistic Behavior

Introducing the Framework of a "Dynamic" Higher Dimensional Spacetime. How Time Behaves in it. Similarities with Quantum Mechanical and Relativistic Behavior

Microscopic quantum mechanical Marcus theory for chemical reactions and its relationship to theButler‐Volmerequation used in redox flow battery analysis

AbstractThe vanadium redox flow battery has been intensively examined since the 1970s. What is missing is a connection between the current‐overpotential Butler‐Volmer equation, which provides an extremely helpful starting point for analytical and numerical studies, and microscopic quantum mechanical behavior at the atomic level. Such a connection will allow further advancements beyond the macroscopic, though very useful and insightful, modeling already done in the literature. Here we show rigorously the connection between the Butler‐Volmer transfer coefficients, and the Marcus Gibbs free energy quantum mechanical parameters, and develop the equation directly in terms of the quantum mechanical parameters.

An Asymmetric Model Position Dependent Mass: Quantum Mechanical Study

We propose an asymmetric model position dependent mass and study its quantum mechanical behaviour on different potentials such as harmonic oscillator potential, double well potential, Gaussian single well potential and triangular single well model potential. It is observed from our study that the model asymmetric mass works well for weak coupling preserving the symmetric phase portrait. However, the dominance of asymmetric feature of the mass in the system clearly visible for higher values of the constant associated with the mass. Though, both position dependent mass and potential have significant role in controlling the spectral feature of the system, one may dominate over other for certain cases.

Density-Potential Functional Theory of Electrochemical Double Layers: Calibration on the Ag(111)-KPF6 System and Parametric Analysis.

The density-potential functional theory (DPFT) of electrochemical double layer (EDL) is upgraded by adopting (generalized) gradient approximations for kinetic, exchange, and correlation functionals of metal electrons. A new numerical scheme that is more stable and converges faster is proposed to solve the DPFT model. The DPFT model is calibrated with existing differential double-layer capacitance (Cdl) data of the EDL at Ag(111)-KPF6 aqueous interface at five concentrations at room temperature. Metal electronic effects are essential to explain why the two peaks of the camel-shaped Cdl curves are almost symmetric in spite of the size difference of the hydrated cations and anions. A systematic parametric analysis is then conducted in terms of key EDL properties, including the potential of zero charge and the differential capacitance. The parametric analysis, on the one hand, elucidates how quantum mechanical behaviors of metal electrons as well as interactions between metal electrons and the electrolyte solution impact the EDL properties and, on the other hand, identifies key parameters of the DPFT model, which should be calibrated using first-principles calculations and/or advanced experiments in the future.

DNA as grabbers and steerers of quantum emitters

Abstract The chemically synthesizable quantum emitters such as quantum dots (QDs), fluorescent nanodiamonds (FNDs), and organic fluorescent dyes can be integrated with an easy-to-craft quantum nanophotonic device, which would be readily developed by non-lithographic solution process. As a representative example, the solution dipping or casting of such soft quantum emitters on a flat metal layer and subsequent drop-casting of plasmonic nanoparticles can afford the quantum emitter-coupled plasmonic nanocavity (referred to as a nanoparticle-on-mirror (NPoM) cavity), allowing us for exploiting various quantum mechanical behaviors of light–matter interactions such as quantum electrodynamics (QED), strong coupling (e.g., Rabi splitting), and quantum mirage. This versatile, yet effective soft quantum nanophotonics would be further benefitted from a deterministic control over the positions and orientations of each individual quantum emitter, particularly at the molecule level of resolution. In this review, we will argue that DNA nanotechnology can provide a gold vista toward this end. A collective set of exotic characteristics of DNA molecules, including Watson-Crick complementarity and helical morphology, enables reliable grabbing of quantum emitters at the on-demand position and steering of their directors at the single molecular level. More critically, the recent advances in large-scale integration of DNA origami have pushed the reliance on the distinctly well-formed single device to the regime of the ultra-scale device arrays, which is critical for promoting the practically immediate applications of such soft quantum nanophotonics.

Exact solutions of a coupled space-time fractional nonlinear Schrödinger type equation in quantum mechanics

In this paper, we consider a coupled space-time fractional nonlinear Schrödinger type equation which can be used for describing nonrelativistic quantum mechanical behavior. Under the help of the fractional complex transform and the conformable fractional derivative sense, we apply the extended auxiliary equation method, the modified He’s semi-inverse method and the improved Weierstrass elliptic function method to obtain many exact solutions. These exact solutions include the bright, dark, bright-dark, bright-like and kinky-bright optical soliton solutions as well as trigonometric function solutions, the Jacobi elliptic function solutions and the general solutions in form of Weierstrass elliptic function. The behaviors of some obtained solutions are displayed through the 3D graphs for different fractional orders by using Matlab. The obtained results show that these proposed methods are straightforward, efficient and can provide more forms of exact solutions, which are helpful to understand the complex physical meaning of space-time fractional coupled nonlinear Schrödinger equation.

Bifurcation Oscillator as an Advanced Sensor for Quantum State Control.

We study bifurcation behavior of a high-quality (high-Q) Josephson oscillator coupled to a superconducting qubit. It is shown that the probability of capture into the state of dynamic equilibrium is sensitive to qubit states. On this basis we present a new measurement method for the superposition state of a qubit due to its influence on transition probabilities between oscillator levels located in the energy region near the classical separatrix. The quantum-mechanical behavior of a bifurcation oscillator is also studied, which makes it possible to understand the mechanism of "entanglement" of oscillator and qubit states during the measurement process. The optimal parameters of the driving current and the state of the oscillator are found for performing one-qubit gates with the required precision, when the influence on the qubit from measurement back-action is minimal. A measurement protocol for state populations of the qubit entangled with the oscillator is presented.

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks.

The Schrödinger equation describes the quantum-mechanical behaviour of particles, making it the most fundamental equation in chemistry. A solution for a given molecule allows computation of any of its properties. Finding accurate solutions for many different molecules and geometries is thus crucial to the discovery of new materials such as drugs or catalysts. Despite its importance, the Schrödinger equation is notoriously difficult to solve even for single molecules, as established methods scale exponentially with the number of particles. Combining Monte Carlo techniques with unsupervised optimization of neural networks was recently discovered as a promising approach to overcome this curse of dimensionality, but the corresponding methods do not exploit synergies that arise when considering multiple geometries. Here we show that sharing the vast majority of weights across neural network models for different geometries substantially accelerates optimization. Furthermore, weight-sharing yields pretrained models that require only a small number of additional optimization steps to obtain high-accuracy solutions for new geometries.

Chemistry without the Born-Oppenheimer approximation.

Chemistry without the Born-Oppenheimer approximation.

A na\xefve HMO study of the casimir effect

The Casimir effect is discussed via an HMO treatment. At this schematic theoretical level, the Casimir effect might be considered as the result of the general quantum mechanical interaction behavior of two sets of particles.

Tunneling in the Hydrogen-Transfer Reaction from a Vitamin E Analog to an Inclusion Complex of 2,2-Diphenyl-1-picrylhydrazyl Radical with β-Cyclodextrin in an Aqueous Buffer Solution at Ambient Temperature.

Recently, increasing attention has been paid to quantum mechanical behavior in biology. In this study, we investigated the involvement of quantum mechanical tunneling in the hydrogen-transfer reaction from Trolox, a water-soluble analog of vitamin E (α-tocopherol), to 2,2-diphenyl-1-picrylhydrazyl radical (DPPH•) in a phosphate buffer solution (0.05 M, pH 7.0). DPPH• was used as a reactivity model of reactive oxygen species and solubilized in water using β-cyclodextrin (β-CD). The second-order rate constants, kH and kD, in 0.05 M phosphate buffer solutions prepared with H2O (pH 7.0) and D2O (pD 7.0), respectively, were determined for the reaction between Trolox and DPPH•, using a stopped-flow technique at various temperatures (283–303 K). Large kinetic isotope effects (KIE, kH/kD) were observed for the hydrogen-transfer reaction from Trolox to the β-CD-solubilized DPPH• in the whole temperature range. The isotopic ratio of the Arrhenius prefactor (AH/AD = 0.003), as well as the isotopic difference in the activation energies (19 kJ mol−1), indicated that quantum mechanical tunneling plays a role in the reaction.

Rotational Modulation of Ã2A″-State Photodissociation of HCO via Renner-Teller Nonadiabatic Transitions.

By examining the product-state distribution of a prototypical nonadiabatic predissociation system, HCO(Ã2A″-X̃2A'), we demonstrate that the dissociation dynamics is strongly modulated by parent rotational quantum numbers. The predissociation of the nominal (νC-H = 0, νbend, νC-O = 1) vibronic levels of the Ã2A″ state surprisingly gives rise to both vibrational ground and excited states of the CO product, despite the assumed spectator nature of the CO moiety. This anomaly is attributed to the dependence of the lifetime of the vibronic resonance facilitated by the Renner-Teller interaction on the parent rotational angular momentum quantum numbers coupled with transient intensity borrowing from nearby vibronic resonances with νC-O = 0. This unique phenomenon is a purely quantum mechanical behavior that has no classical analogue.

Statistical Properties of the Transverse-Motion Energy Levels for Channeling Electrons in a Silicon Crystal under Dynamical Chaos Conditions

The classical motion of particles in external fields is frequently chaotic although deterministic within the classical limit. Studying the quantum mechanical behavior of such systems amounts to the problematics of quantum chaos. Quantum chaos manifests itself primarily in the statistical properties of the energy-level arrays of such systems. However, the typical objects under consideration are systems of the type billiards with rigid walls. This paper studies the calculated energy levels of the transverse motion of relativistic electrons in the axial-channeling regime along the [100] direction of the silicon crystal which is described as motion in the smooth potential well. The nearest-level spacing distributions as well as the spectral rigidity are studied for the range of parameters where electron motion is chaotic within the classical limit. Both these characteristics demonstrate agreement with quantum-chaos-theory predictions.

Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment.

Position-dependent finite symmetric mass harmonic like oscillator: Classical and quantum mechanical study

Abstract We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.