Nonzero Potential Research Articles

A Highly Accurate Technique to Obtain Exact Solutions to Time‐Fractional Quantum Mechanics Problems with Zero and Nonzero Trapping Potential

In this study, the highly accurate analytical Aboodh transform decomposition method (ATDM) in the sense of Caputo fractional derivative is used to determine the approximate and exact solutions of both linear and nonlinear time‐fractional Schrodinger differential equations (SDEs) with zero and nonzero trapping potential that describe the nonrelativistic quantum mechanical activity. The Adomian decomposition method (ADM) and the Aboodh transform of Caputo’s fractional derivative are combined in this method. The recurrence and absolute error of the four problems are analyzed to evaluate the efficiency and consistency of the presented method. In addition, numerical results are also compared with other methods such as the fractional reduced differential transform method (FRDTM), the homotopy analysis method (HAM), and the homotopy perturbation method (HPM). The results obtained by the proposed method show excellent agreement with these methods, which indicates its effectiveness and reliability. This technique has the benefit of not requiring any minor or major physical parameter assumptions in the problem. As a result, it may be used to solve both weakly and strongly nonlinear problems, overcoming some of the inherent constraints of classic perturbation approaches. To solve nonlinear fractional‐order differential equations, just a few computations are necessary. As a consequence, it outperforms homotopy analysis and homotopy perturbation approaches significantly. The procedure is quick, precise, and easy to implement. Convergence analysis of the series solution is also offered.

An investigation of -symmetry breaking in tight-binding chains

We consider non-Hermitian -symmetric tight-binding chains where gain/loss optical potentials of equal magnitudes ±iγ are arbitrarily distributed over all sites. The main focus is on the threshold γ c beyond which -symmetry is broken. This threshold generically falls off as a power of the chain length, whose exponent depends on the configuration of optical potentials, ranging between 1 (for balanced periodic chains) and 2 (for unbalanced periodic chains, where each half of the chain experiences a non-zero mean potential). For random sequences of optical potentials with zero average and finite variance, the threshold is itself a random variable, whose mean value decays with exponent 3/2 and whose fluctuations have a universal distribution. The chains yielding the most robust -symmetric phase, i.e. the highest threshold at fixed chain length, are obtained by exact enumeration up to 48 sites. This optimal threshold exhibits an irregular dependence on the chain length, presumably decaying asymptotically with exponent 1, up to logarithmic corrections.

Generalized m-quasi-Einstein metric on certain almost contact manifolds

In this paper, we study the generalized m-quasi-Einstein metric in the context of contact geometry. First, we prove if an H-contact manifold admits a generalized m-quasi-Einstein metric with non-zero potential vector field V collinear with ?, then M is K-contact and ?-Einstein. Moreover, it is also true when H-contactness is replaced by completeness under certain conditions. Next, we prove that if a complete K-contact manifold admits a closed generalized m-quasi-Einstein metric whose potential vector field is contact thenMis compact, Einstein and Sasakian. Finally, we obtain some results on a 3-dimensional normal almost contact manifold admitting generalized m-quasi-Einstein metric.

Spectral invariants of Dirichlet-to-Neumann operators on surfaces

We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schrödinger operators on Riemannian surfaces with boundary. For the zero potential, we recover the well-known spectral asymptotics for the Steklov problem. For non-zero potentials, we obtain new geometric invariants determined by the spectrum. In particular, for constant potentials, which give rise to the parameter-dependent Steklov problem, the total geodesic curvature on each connected component of the boundary is a spectral invariant. Under the constant curvature assumption, this allows us to obtain some interior information from the spectrum of these boundary operators.

Can Lower Carbon Aviation Fuels (LCAF) Really Complement Sustainable Aviation Fuel (SAF) towards EU Aviation Decarbonization?

The present work provides an analysis of the potential impact of fossil-based Low Carbon Aviation Fuels (LCAF) for the European aviation sector, with a time horizon to 2050. LCAF are a crude-derived alternative to kerosene, offering some Green House Gas (GHG) savings, and have been defined by ICAO as eligible fuels for mitigating the environmental impact of aviation. A methodological framework to evaluate the EU technical potential for LCAF production is developed, based on data on crude utilization for jet fuel production in EU refineries, relevant carbon intensity reduction technologies, market prices, and aviation fuel volumes. Two different baselines for fossil-derived kerosene carbon intensity (CI) are considered: a global figure of 89 gCO2e/MJ and an EU-27-specific one of 93.1 gCO2eq/MJ. Three scenarios considering increasing levels of CI reduction are then defined, taking into account the current and potential commercial availability of some of the most relevant carbon intensity reduction technologies. The analysis demonstrates that, even if LCAF could offer GHG saving opportunities, their possible impact, especially when compared to the ambition level set in the most recent European legislative proposals, is very limited in most of the analysed scenarios, with the exception of the most ambitious ones. At 2030, a non-zero technical potential is projected only in the higher CI reduction scenario, ranging between 1.8% and 14.2% of LCAF market share in the EU-27 (equal to 0.6 to 4.75 Mtoe), depending on the considered Baseline for CI. At 2050, almost all considered scenarios project a larger technical potential, ranging between 6.9% and 22.2% for the global Baseline (2.21 to 7.13 Mtoe), and between 1.8% and 16.2% for the EU-27 Baseline (0.58 to 5.2 Mtoe). LCAF additional costs to current production costs are also discussed, given their relevance in large-scale deployment of these technologies, and are projected to range between 39 and 46.8 USD/toe.

Gathering Energy of the Stray Currents in Electrified Railways Environment for Power Supply

The paper presents a new, unconventional energy harvesting (EH) method for supplying low-power devices on electrified railway lines that utilises stray currents and the non-zero potential of the rails to the ground. The EH device gathers the energy and stores it in batteries. It could even work in extremely unfavourable weather conditions and could be easily placed in almost any location. The presented real-life data show that the average available power is less than 250 mW and the average useful power is about 100 mW. This is enough to supply ultra-low power microcontrollers, which only occasionally use energy-consuming modules to perform measurements or communicate. The disadvantage of the EH method is the introduction of resistance between the rail and the earth, which increases stray currents and could increase the electrochemical corrosion of the rail. To reduce the impact of this resistance, a method for balancing the flowing charge is proposed. After balancing, the average of the flowing current is zero and electrochemical corrosion should be reduced. The proposed charge balancing algorithms could reduce the unbalanced charge to nearly zero at the expense of energy gathering efficiency, which decreases by 20–40%.

Self-powered ultraviolet photodiode based on lateral polarity structure GaN films

In this work, we report on a self-powered ultraviolet photodiode realized using lateral polarity structure (LPS) GaN films. The opposite nature of the polarization charge yields different barrier heights at the standard Ni/Au Schottky contact interface of N-polar and III-polar GaN films. As a result, a natural nonzero built-in potential is obtained in the LPS GaN photodiode, which showed photoresponsivity even at 0 V applied bias. The self-powered mechanism inside such an LPS GaN photodiode is discussed in detail by a combination of simulation prediction and experimental validation. Furthermore, a variation in the doping concentration of the adjacent III- and N-polar GaN domain is shown to improve the photoresponsivity compared to the conventional III-polar photodiode. Thus, this work validates that the LPS GaN photodiode is a promising candidate to realize self-powered operation and a general design rule for the photodiode with in-plane built-in potential.

Simulation of cyclic voltammetry in structural supercapacitors with pseudocapacitance behavior

Cyclic voltammetry is an important technique to characterize the electrochemical performance and reaction kinetics in electrical and electrochemical energy storage devices under various conditions. In this study, a physics-based model is developed to simulate cyclic voltammetry measurements of reduced graphene oxide with aramid nanofiber (rGO-ANF) composite structural supercapacitors through multiphysics computational modeling and compared against experimental results. The presence of asymmetric forward and reverse sweeps in the cyclic voltammetry curves suggests pseudo-capacitance behavior associated with the oxygen-functionalized group. A multistep kinetics modeling approach is used to evaluate various kinetic processes that can occur at different potential values employing both Butler-Volmer and Tafel equations. Parametric studies were also performed to investigate the effects of scan rate, equilibrium potential, exchange current density, and transfer coefficient on cyclic voltammetry curves. The results demonstrate that nonzero equilibrium potential is more accurate for rGO-ANF supercapacitors and a low exchange current density of 10−6 A m−2 shows better agreement with the experimental measurements. The multistep modeling of cyclic voltammetry accompanied with experimental cyclic voltammetry curves provides a more accurate and comprehensive analysis of the kinetics and thermodynamics of structural supercapacitors and enables better design and control of device performance and life cycle.

Intrinsic Vibrational Angular Momentum from Nonadiabatic Effects in Noncollinear Magnetic Molecules.

We show that in noncollinear magnetic molecules, nonadiabatic (dynamical) effects due to the electron-vibron coupling are time-reversal symmetry breaking interactions for the vibrational field. Because the electronic wave function cannot be chosen as real in these molecules, a nonzero geometric vector potential (Berry connection) arises. As a result, an intrinsic nonzero vibrational angular momentum occurs even for nondegenerate modes and in the absence of external probes. The vibronic modes can then be seen as elementary quantum particles carrying a sizeable angular momentum. As a proof of concept, we demonstrate the magnitude of this topological effect by performing nonadiabatic first principles calculations on platinum clusters and by showing that these molecules host sizeable intrinsic phonon angular momenta comparable to the orbital electronic ones in itinerant ferromagnets.

Casimir and electrostatic forces from Bi2Se3 thin films of varying thickness

We explore here the decisive role of film thickness on Casimir and electrostatic forces from topological insulating ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ films. The forces were measured for the Au-${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ system under ambient conditions to simulate realistic applications. It is shown that the electrostatic forces associated with a nonzero contact potential of ${V}_{\mathrm{o}}\ensuremath{\sim}200\phantom{\rule{0.28em}{0ex}}\mathrm{mV}$ played a dominant role, and could not be compensated for thinner films ($\ensuremath{\le}20\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ thick). However, for thicker films the measured force, after voltage compensation, started to approach the genuine Casimir force in very good agreement with Lifshitz theory. Our results point out that any gradual deviation from theory for thinner films underlies the presence of strong electrostatic effects.

Generalized Schwartz–Gunning theorem and Weyl type lemmas for the Schrödinger operator

In this work, we study Schrödinger type equations with domain in a complex space and their solutions in the classical as well as in the sense of the space of currents. For such an equation with a (possibly) complex parameter and a (possibly) nonzero potential, conditions are given under which an analogue of the Weyl's lemma holds, meaning that each solution within the space of currents is distributionally realizable (in a suitable sense) by a semismooth, or by a semi-real-analytic function. Motivated by the Schwartz–Gunning theorem on the holomorphy of a locally integrable function, conditions guaranteeing a regular current on a general domain to be realized by a function which is (locally) a solution of the Schrödinger equation are obtained. Also, generalized Helmholtz formulas are derived and utilized in studying some special classes of zero-degree currents in regard to the property of μ-harmonicity or weak-harmonicity.

Quantum Potentiality in Inhomogeneous Cosmology

For the Szekeres system which describes inhomogeneous and anisotropic spacetimes we make use of a point-like Lagrangian, which describes the evolution of the physical variables of the Szekeres model, in order to perform a canonical quantization and to study the quantum potentiality of the Szekeres system in the content of de Broglie–Bohm theory. We revise previous results on the subject and we find that for a specific family of trajectories with initial conditions which satisfy a constraint equation, there exists additional conservation laws for the classical Szekeres system which are used to define differential operators and to solve the Wheeler–DeWitt equation. From the new conservation laws we construct a wave function which provides a nonzero quantum potential term that modifies the Szekeres system. The quantum potential corresponds to new terms in the dynamical system such that new asymptotic solutions with a nonzero energy momentum tensor of an anisotropic fluid exist. Therefore, the silent property of the Szekeres spacetimes is violated by quantum correction terms, which results in the quantum potential adding pressure to the solution.

High-Resolution Structures of K+ Channels.

Potassium channels are present in every living cell and essential to setting up a stable, non-zero transmembrane electrostatic potential which manifests the off-equilibrium livelihood of the cell. They are involved in other cellular activities and regulation, such as the controlled release of hormones, the activation of T-cells for immune response, the firing of action potential in muscle cells and neurons, etc. Pharmacological reagents targeting potassium channels are important for treating various human diseases linked to dysfunction of the channels. High-resolution structures of these channels are very useful tools for delineating the detailed chemical basis underlying channel functions and for structure-based design and optimization of their pharmacological and pharmaceutical agents. Structural studies of potassium channels have revolutionized biophysical understandings of key concepts in the field - ion selectivity, conduction, channel gating, and modulation, making them multi-modality targets of pharmacological regulation. In this chapter, I will select a few high-resolution structures to illustrate key structural insights, proposed allostery behind channel functions, disagreements still open to debate, and channel-lipid interactions and co-evolution. The known structural consensus allows the inference of conserved molecular mechanisms shared among subfamilies of K+ channels and makes it possible to develop channel-specific pharmaceutical agents.

The effects on CMB power spectra and bispectra from the polarization rotation and its correlations with temperature and E-polarization

The Chern-Simons term, through which the cosmic Axion-like field couples to the electromagnetic field, has the effect to rotate CMB polarization directions and to break the CPT symmetry. This rotation will change the CMB power spectra, no matter isotropic or anisotropic the rotation angle is. In this paper we revisit this issue by further considering the correlations between the anisotropic rotation angle α and the CMB temperature and CMB E polarization fields. These correlations could be generated in the Axion-like models with nonzero potential under the adiabatic initial condition. We first investigate how these correlations contribute further modifications to the CMB power spectra, then calculate the CMB bispectra for the temperature and rotated polarization fields. These bispectra would vanish if the Tα and Eα correlations are absent. So, they are useful in searching for CPT violation and the Tα and Eα correlations arisen in the Axion-like models.

Stability analysis for cylindrical Couette flow of compressible fluids

A new analysis of basic Couette flow is based on an action principle for compressible fluids with a Hamiltonian as well as a kinetic potential. An effective criterion for stability recognizes the tensile strength of water. This interpretation relates the problem to capillary action and to metastable configurations (Berthelot’s negative pressure experiment of 1850). We calculate the pressure and density profiles and find that the first instability of basic Couette flow is localized near the bubble point. This theoretical prediction has been confirmed by recent experiments. The theory is the result of merging the two versions of classical hydrodynamics, as advocated by Landau for superfluid helium II. In an inspired paper, Landau, L. [“Theory of the superfluidity of helium II,” Phys. Rev. 60, 356–358 (1941)] introduced the idea of two independent flows, “phonons” and “rotons,” with strong emphasis on the idea that there is only one kind of fluid. The dynamical variables include two flows but only one density variable. In this paper, two-flow dynamics is created by merging two actions, neither by choosing between them nor by combining the two vector fields as in the Navier–Stokes equation. At rest, as contributions to the mass flow, they cancel, but a non-zero kinetic energy, kinetic potential, and non-zero angular momentum remain, and are manifest as liquid tension, as it is well known to exist through the observation of the meniscus and configurations with negative pressure. The immediate effect of merging the two versions of classical hydrodynamics in a unique theory based on an action principle is to provide a Hamiltonian and a kinetic potential for compressible fluids with rotational flow. This theory gives a very satisfactory characterization of the limit of stability of the most basic Couette flow. The inclusion of a vector field that is not a gradient has the additional effect of introducing spin, which explains a most perplexing experimental discovery: the ability of frozen helium to remember its angular momentum (spin).

Non-linearly realized discrete symmetries

While non-linear realizations of continuous symmetries feature derivative interactions and have no potential, non-linear realizations of discrete symmetries feature non-derivative interactions and have a highly suppressed potential. These Goldstone bosons of discrete symmetries have a non-zero potential, but the potential generated from quantum corrections is inherently very highly suppressed. We explore various discrete symmetries and to what extent the potential is suppressed for each of them.

Hybrid Metric-Palatini Gravity: Black Holes, Wormholes, Singularities, and Instabilities

The hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. We discuss static, spherically symmetric vacuum solutions of HMPG with the aid of its scalar-tensor representation. This scalar-tensor theory coincides with general relativity with a conformally coupled scalar field (which can be canonical or phantom), therefore the known solutions of this theory are re-interpreted in terms of HMPG. In particular, in the case of zero scalar field potential $V (\phi)$, such that both Riemannian and Palatini Ricci scalars are zero, generic asymptotically flat solutions either contain naked singularities or describe traversable wormholes, and there are only special cases of black hole solutions with extremal horizons. There is also a one-parameter family of solutions with an infinite number of extremal horizons between static regions. Examples of analytical solutions with nonzero potentials $V (\phi)$ are also described, among them black hole solutions with simple horizons which are generic but, for canonical scalars, they require (at least partly) negative potentials. With phantom scalars there are ``black universe'' solutions that lead beyond the horizon to an expanding universe instead of a singularity. Most of the solutions under consideration turn out to be unstable under scalar monopole perturbations, but some special black hole solutions are stable.

Optical Aharonov—Bohm Effect

A variant of the experiment to observe the optical Aharonov—Bohm effect has been discussed. In the experiment, a unipolar subcycle light pulse has been proposed as a source of the vector potential acting on electrons and having zero electric field strength in the region of a nonzero vector potential. Such a relation between the field and potential appears because the unipolar pulse has a nonzero electric area. An unusual situation where the fact of the passage of the pulse in one of the arms of two-beam interferometer is stored for a very long time after the passage and can be recorded in a two-beam electronic interferometer by a shift of fringes has been discussed. Detailed analysis of the phase shift under the influence of the vector potential created by the inhomogeneous unipolar pulse removes this contradiction and shows the equality of phase incursions in both arms that is unobvious at first glance.

A highly sensitive double-layer structured nanodevice for moisture induced power generation

With the increasing global energy demand, traditional energy sources are gradually failing to meet society’s needs while also having a potential of being harmful to the environment. As such, energy generating technologies capable of converting ubiquitous environmental energy into usable forms, such as electricity, have received increasing attention. In this research, a power generating device composed of a graphene (G) and titanium dioxide nanowire (TiO2 NWs) double-layer structure is prepared by an electrophoretic deposition method. Since both materials have special nanochannel structures and non-zero zeta potential, they can convert environmental energy into electricity through the diffusion, ionization, and natural evaporation of water. Furthermore, the efficiency of this novel sensor is much higher than their respective single-layer devices. By application of only 6 μl of water, the open circuit voltage (UOC) generated on the G-TiO2 sensor is as high as 1.067 ± (0.008) V. In comparison, TiO2 NWs single layer can only generate a UOC around 500 mV, and graphene itself can only produce a UOC no more than 250 mV under the same condition. Additionally, the effect of different deposition times of graphene on the surface morphology and thickness of graphene film is explored, and the effects of these changes in microstructure on performance is discussed in depth. Aside from power generation, the high sensitivity of the device to different volumes of water brings its use in the detection of trace amounts of water, and its high efficiency of energy conversion suggests a potential application as a power supply. This research not only provides a satisfactory candidate for inexpensive and efficient evaporative power generation, but also builds a foundation for developing new, intelligent, and self-powered electronic technologies.

Analytical solutions of the time-fractional non-linear Schrodinger equation with zero and non zero trapping potential through the Sumudu decomposition method

Sumudu decomposition method is used to construct the approximate analytical solutions of time-fractional nonlinear Schrodinger equations with zero and nonzero trapping potential. The Sumudu decomposition method is a combined form of the Sumudu transform and the Adomian decomposition method. The fractional derivatives are defined in the Caputo sense. The exact solutions of some nonlinear Schrodinger equations are given as a special case of our approximate analytical solutions. The computations show that the described method is easy to apply, and it needs smaller size of computation as compared to the other existing methods. Further, the solutions are derived in a convergent series form which shows the effectiveness of the method for solving a wide variety of nonlinear fractional differential equations.