Quantum Potential Research Articles

Trajectory construction of Dirac evolution

We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which the real and imaginary parts of the wave function, angular versions of Majorana spinors, define conserved densities. We hence deduce an exact formula for the propagation of the Dirac spinor derived from the self-contained first-order dynamics of two sets of trajectories in 3-space together with a mass-dependent evolution operator. The Lorentz covariance of the trajectory equations is established by invoking the ‘relativity of the trajectory label'. We show how these results extend to the inclusion of external potentials. We further show that the angular version of Dirac's equation implies continuity equations for currents with non-negative densities, for which the Dirac current defines the mean flow. This provides an alternative trajectory construction of free evolution. Finally, we examine the polar representation of the Dirac equation, which also implies a non-negative conserved density but does not map into a stand-alone trajectory theory. It reveals how the quantum potential is tacit in the Dirac equation.

Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative

We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler–DeWitt equation of second order, showing that a Bohm–de Broglie interpretation can be constructed. That combination of fractional quantization and Bohmian interpretation provides us a new quantization method, in which the quantum potential is the criterion to say if a quantum solution is acceptable or not to be further studied. We show that a wide range of solutions for the scale factor is possible. Among all of those, a bouncing solution analogous to the perfect fluid cosmology seems to deserve special attention.

Dense plasmas with partially degenerate semiclassical ions: screening and structural properties

The screened interaction potential between ions taking into account the wave nature of ions is presented. The parameters considered in this paper correspond to those of dense plasmas with ideal or weakly coupled quantum electrons and semiclassical non-ideal ions. The wave nature of ions is described using the concept of quantum potentials. The obtained effective interaction potential between ions takes into account screening by electrons and ionic quantum nonlocality. It is shown that the polarization of electrons around an ion leads to a decrease in the ion’s effective thermal wavelength and, conversely, screening of the ion field by electrons becomes weaker due to the wave nature of the ion. Furthermore, on the basis of the derived ion–ion interaction potential, we investigate the structural properties of semiclassical non-ideal ions. For hydrogen plasmas, the ionic quantum nonlocality effect is significant at rS < 0.3. The obtained results are relevant to high energy density physics.

Conformal cyclic evolution of phantom energy dominated universe

From the Wheeler Dewitt solutions, the scale factor of the initial universe is discussed. In this study scale factors from Wheeler Dewitt solutions, loop quantum gravity, and phantom energy dominated stages are compared. Certain modifications have been attempted in scale factor and quantum potentials driven by canonical quantum gravity approaches. Their results are discussed in this work. Despite increment of phantom energy density avoidance of big rip is reported. Scale factors predicted from various models is discussed in this work. Relationship between scale factors and smooth continuation of aeon is discussed by the application of conformal cyclic cosmology. Quantum potentials for various models are correlated and a correction parameter is included on the cosmological constant. Phantom energy dominated, final stage non-singular evolution of the universe is reported. Eternal increment of phantom energy density without interacting with dark matter is reported for the consequence of evolution of the future universe. Also, the non-interacting solutions of phantom energy and dark matter are explained. As the evolution continues even after the final singularity is approached, the validity of conformal cyclic cosmology is predicted. Non zero values for the scale factor for the set of eigenvalues are reported with a graph

Aristotle and Quantum Mechanics: Potentiality and Actuality, Spontaneous Events and Final Causes

Aristotelian ideas have in the past been applied with mixed fortunes to quantum mechanics. One of the most persistent criticisms is that Aristotle’s notions of potentiality and actuality are burdened with a teleological character long ago abandoned in the natural sciences. Recently this criticism has been met with a model of the actualization of quantum potentialities in light of Aristotle’s doctrine of ‘spontaneous events’. This presumably restores the nowadays acceptable idea of efficient causation in place of Aristotle’s original doctrine of the ‘four causes’. In this article I challenge the model by arguing that when properly scrutinized Aristotle’s final cause poses no problems for an Aristotelian reading of quantum mechanics. Final causes in fact provide a better ontology for quantum mechanics than spontaneous causation. The idea of ‘spontaneity’ is unanalyzable and therefore of little use in quantum mechanics. In addition, it is ontologically sterile in the context of quantum measurement, as shown by a historical and conceptual review of the role of efficient causation in experimental physics.

Application of localization landscape theory and the k · p model for direct modeling of carrier transport in a type II superlattice InAs/InAsSb photoconductor system

Localization landscape (LL) theory is applied to directly model carrier transport in a type II superlattice (T2SL) InAs/InAsSb photoconductor system. It is difficult to apply the classical Poisson and drift–diffusion (DD) model to direct modeling of carrier transport in superlattice systems because quantum effects need to be considered. With the LL theory, it is possible to obtain the effective quantum potential seen by carriers. By coupling the LL theory with the Poisson–DD model and replacing the traditional conduction and valence potentials with effective quantum potentials, it is possible to directly model carrier transport in a T2SL system. We compare the results of this approach with experimental results and find very good agreement, which indicates that this method will provide an efficient tool for the T2SL design.

Dual wavefunctions in two–dimensional quantum mechanics

It is shown that the Schrödinger equation for a large family of pairs of two–dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Böhm potential. These solutions can be extended to three–dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two–dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two–dimensional dual wavefunction solutions with an optical (analogue) system.

Quantum mechanical analogue of optical microdisk resonators

Abstract The complex wave number plane furnishes us with a natural way to seek resonant modes of quantum potentials and optical cavities. In this work we present the solution of the quantum mechanical analogue of an optical microdisk resonator. The rich dynamical behavior of the states is shown for a circular potential barrier in response to continuous variations of the parameters of the potential. In particular, the flows of the resonances go to limit points which are zeros of Hankel functions in complex wave number coordinates and zeros of Bessel functions in an alternative complex potentiodynamic coordinate system.

Superoscillations and the quantum potential *

For quantum or other waves that are band-limited, the quantum potential in the Madelung–Bohm representation vanishes on the boundaries of regions where the waves are superoscillatory (i.e. where they vary faster than any of their Fourier components). This connection is illustrated by calculations of the quantum potential zeros for a superoscillatory superposition of plane waves, and by Aharonov–Bohm waves.

Temperature anisotropy relaxation processes in dense plasma

In this work the relaxation processes of dense plasmas were studied. The relaxation rate of a Maxwellian velocity distribution function that has an initially anisotropic temperature (T∥ ≠ T^) is an important physical process inertial confinement fusion plasmas. Relaxation characteristics in dense plasmas were studied on the basis of the effective potentials using the Coulomb logarithm. The effective potential is derived using the long wavelength expansion of the polarization function and quantum potential which takes into account the finite value of the interaction potential at close distance. In presented work temperature anisotropy relaxation processes in dense, non-isothermal plasma are considered. These interaction potential between particles take into account such collective effects as the ionization energy depression (reduction) and exchange-correlation effects. Therefore, this allowed us to examine the sensitivity of the computed relaxation time and the corresponding equilibrium plasma temperature on the quality of the description of the screening effect in dense plasmas.

Stochastic Quantum Hydrodynamic Model from the Dark Matter of Vacuum Fluctuations: The Langevin-Schr？dinger Equation and the Large-Scale Classical Limit

The work derives the quantum evolution in a fluctuating vacuum by introducing the related (dark) mass density noise into the Madelung quantum hydrodynamic model. The paper shows that the classical dynamics can spontaneously emerge on the cosmological scale allowing the realization of the classical system-environment super system. The work shows that the dark matter-induced noise is not spatially white and owns a well defined correlation function with the intrinsic vacuum physical length given by the De Broglie one. By departing from the quantum mechanics (the deterministic limit of the theory) in the case of microscopic systems whose dimension is much smaller than the De Broglie length, the model leads to the Langevin-Schrodinger equation whose friction coefficient is not constant. The derivation puts in evidence the range of application of the Langevin-Schrodinger equation and the approximations inherent to its foundation. Increasing the physical length of the system description, the classical physics can be achieved when the scale of the problem is much bigger both than the De Broglie length and the quantum potential range of interaction. The long-distance characteristics as well as the range of interaction of the non-local quantum potential are derived and analyzed in order to have a coarse-grained large-scale description. The process of measurement, in the large-scale classical limit, satisfies the minimum uncertainty conditions if interactions and information do not travel faster than the light speed, reconciling the quantum entanglement with the relativistic macroscopic locality.

Quantum Computing for Finance: State-of-the-Art and Future Prospects

This article outlines our point of view regarding the applicability, state-of-the-art, and potential of quantum computing for problems in finance. We provide an introduction to quantum computing as well as a survey on problem classes in finance that are computationally challenging classically and for which quantum computing algorithms are promising. In the main part, we describe in detail quantum algorithms for specific applications arising in financial services, such as those involving simulation, optimization, and machine learning problems. In addition, we include demonstrations of quantum algorithms on IBM Quantum back-ends and discuss the potential benefits of quantum algorithms for problems in financial services. We conclude with a summary of technical challenges and future prospects.

Hybrid approach for treating the depolarization of the solar lines of the Ba ii, Ca ii, and Mg ii ions by collisions

ABSTRACT Isotropic collisions between atoms of hydrogen and solar ions emitting polarized light contribute to reducing the observed polarization (depolarization). The aim of this work is to apply a hybrid method in order to provide new collisional depolarization rates of the 2P1/2 and 2P3/2 states of the Mg ii, Ca ii, and Ba ii ions. The hybrid method proposed in this work takes into account the spin effects in the calculation of the interaction potential and in the treatment of the collision dynamics. We detect the region of the interaction potential that is of importance in the determination of the depolarization rates. We conclude that the best strategy is to combine semiclassical and quantum potentials in order to build the so-called hybrid potentials. The dynamics of collisions proposed in this work is based on coupled differential equations that take into account the effects of the spins of the Mg ii, Ca ii, and Ba ii ions and the spin of the hydrogen. Hybrid depolarization rates are then inferred by solving the dynamics of collisions and using hybrid potentials. Comparison with previous quantum and semiclassical rates is presented. Our results should be of use for interpreting solar spectropolarimetric observations and our method can be applied to other ions.

Finslerian geometrization of quantum mechanics in the hydrodynamical representation

We consider a Finslerian type geometrization of the non-relativistic quantum mechanics in its hydrodynamical (Madelung) formulation, by also taking into account the effects of the presence of the electromagnetic fields on the particle motion. In the Madelung representation the Schr\"{o}dinger equation can be reformulated as the classical continuity and Euler equations of classical fluid mechanics in the presence of a quantum potential, representing the quantum hydrodynamical evolution equations. The equation of particle motion can then be obtained from a Lagrangian similar to its classical counterpart. After the reparametrization of the Lagrangian it turns out that the Finsler metric describing the geometric properties of quantum hydrodynamics is a Kropina metric. We present and discuss in detail the metric and the geodesic equations describing the geometric properties of the quantum motion in the presence of electromagnetic fields. As an application of the obtained formalism we consider the Zermelo navigation problem in a quantum hydrodynamical system, whose solution is given by a Kropina metric. The case of the Finsler geometrization of the quantum hydrodynamical motion of spinless particles in the absence of electromagnetic interactions is considered in detail, and the Zermelo navigation problem for this case is also discussed.

Oblique plane waves with bifurcation behaviors and chaotic motion for resonant nonlinear Schrodinger equations having fractional temporal evolution

This study deal with the oblique plane wave solutions with dynamical behaviours for (2 + 1)-dimensional resonant nonlinear Schrodinger equations having Bhom’s quantum potential with distinct law of nonlinearities (Kerr and parabolic law) and fractional temporal evolution. The considered equations are converted to solvable form by assuming conformable Khalil’s fractional derivatives. The bifurcation behaviors and chaotic motion for the existence of traveling waves are investigated by forming the planar dynamical system from the considered equations. The novel auxiliary ordinary differential equation method is therefore used to divulge several forms of plane wave solutions of these equations. It is investigated that the widths of resonant wave dynamics are significantly modified with the influence of obliqueness. The evaluated results may be very useful for better examining the resonant optical solitons in nonlinear dynamics because of obliqueness are existed in various nonlinear systems, specifically in optical bullets, Madelung fluids, etc.

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

We develop a model of Bose-Einstein condensate dark matter halos with a solitonic core and an isothermal atmosphere based on a generalized Gross-Pitaevskii-Poisson equation [P.H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)]. This equation provides a heuristic coarse-grained parametrization of the ordinary Gross-Pitaevskii-Poisson equation accounting for violent relaxation and gravitational cooling. It involves a cubic nonlinearity taking into account the self-interaction of the bosons, a logarithmic nonlinearity associated with an effective temperature, and a source of dissipation. It leads to superfluid dark matter halos with a core-halo structure. The quantum potential or the self-interaction of the bosons generates a solitonic core that solves the cusp problem of the cold dark matter model. The logarithmic nonlinearity generates an isothermal atmosphere accounting for the flat rotation curves of the galaxies. The dissipation ensures that the system relaxes towards an equilibrium configuration. In the Thomas-Fermi approximation, the dark matter halo is equivalent to a barotropic gas with an equation of state $P=2\pi a_s\hbar^2\rho^2/m^3+\rho k_B T/m$, where $a_s$ is the scattering length of the bosons and $m$ is their individual mass. We numerically solve the equation of hydrostatic equilibrium and determine the corresponding density profiles and rotation curves. Our model has no free parameter so it is completely predictive. Extension of this model to noninteracting bosons and fermions will be presented in forthcoming papers.

Uniting the wave and the particle in quantum mechanics

We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie–Bohm theory: its reliance on the quantum probability formula to justify the particle-guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author’s previous work, these problems are examined within an analytical framework by requiring that the wave–particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy, and momentum) with their Schrödinger counterparts. In conjunction with the condition of time-reversal covariance, this implies the de Broglie–Bohm law for the particle where the quantum potential mediates the wave–particle interaction (we also show how the time-reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite’s mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie–Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie’s objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled ‘double solution’ programme. A revised set of postulates for the de Broglie–Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system.

Entropic dynamics: reconstructing quantum field theory in curved space-time

The Entropic Dynamics reconstruction of quantum mechanics is extended to the quantum theory of scalar fields in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kuchař, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.

Jeans instability and turbulent gravitational collapse of Bose\u2013Einstein condensate dark matter halos

We consider the Jeans instability and the gravitational collapse of the rotating Bose–Einstein condensate dark matter halos, described by the zero temperature non-relativistic Gross–Pitaevskii equation, with repulsive interparticle interactions. In the Madelung representation of the wave function, the dynamical evolution of the galactic halos is described by the continuity and the hydrodynamic Euler equations, with the condensed dark matter satisfying a polytropic equation of state with index n=1. By considering small perturbations of the quantum hydrodynamical equations we obtain the dispersion relation and the Jeans wave number, which includes the effects of the vortices (turbulence), of the quantum pressure and of the quantum potential, respectively. The critical scales above which condensate dark matter collapses (the Jeans radius and mass) are discussed in detail. We also investigate the collapse/expansion of rotating condensed dark matter halos, and we find a family of exact semi-analytical solutions of the hydrodynamic evolution equations, derived by using the method of separation of variables. An approximate first order solution of the fluid flow equations is also obtained. The radial coordinate dependent mass, density and velocity profiles of the collapsing/expanding condensate dark matter halos are obtained by using numerical methods.

Bianchi type I, Schutz perfect fluid and evolutionary quantum cosmology

We study the classical and quantum cosmology of a universe in which the matter content is a perfect fluid and the background geometry is described by a Bianchi type I metric. To write the Hamiltonian of the perfect fluid we use the Schutz representation, in terms of which, after a particular gauge fixing, we are led to an identification of a clock parameter which may play the role of time for the corresponding dynamical system. In view of the classical cosmology, it is shown that the evolution of the universe represents a late time expansion coming from a big-bang singularity. We also consider the issue of quantum cosmology in the framework of the canonical Wheeler-DeWitt (WDW) equation. It is shown that the Schutz formalism leads to the introduction of a momentum that enters linearly into Hamiltonian. This means that the WDW equation takes the form of a Schr\"{o}dinger equation for the quantum-mechanical description of the model under consideration. We find the eigenfunctions and with the use of them construct the closed form expressions for the wave functions of the universe. By means of the resulting wave function we evaluate the expectation values and investigate the possibility of the avoidance of classical singularities due to quantum effects. We also look at the problem through Bohmian approach of quantum mechanics and while recovering the quantum solutions, we deal with the reason of the singularity avoidance by introducing quantum potential.