Quantum Potential Research Articles

A delta barrier in a well and the exact time evolution of its eigenstates

The analytic nature of the transmission coefficient for a δ-function barrier makes it a useful tool to examine a variety of technologically important applications, such as photoemission from semiconductors with an alkali coating, the examination of tunneling times for wave packets incident on a barrier, and for parameterizing tunneling through the narrow barrier of a normal-superconducting point contact. The analytic model of a δ-function barrier inside a confining well is extended to the finite height and width rectangular barrier (a delta-function sequence). Methods to exactly evaluate the eigenstates are given and their dependencies are examined. The time evolution of a superposition of the lowest eigenstates is considered for barriers having comparable Gamow tunneling factors so as to quantify the impact of barrier height and shape on time evolution in a simple and exact system and, therefore, serve as a proxy for tunneling time. Last, density profiles and associated quantum potentials are examined for coupled wells to show changes induced by weaker and wider barriers.

New insights into holonomic brain theory: implications for active consciousness

This pioneering research on how specific molecules deep inside our brains form a dynamic information holarchy in phase space, linking mind and consciousness, is not only provocative but also revolutionary. Holonomic is a dynamic encapsulation of the holonic view that originates from the word “holon” and designates a holarchical rather than a hierarchical, dynamic brain organization to encompass multiscale effects. The unitary nature of consciousness being interconnected stems from a multiscalar organization of the brain. We aim to give a holonomic modification of the thermodynamic approach to the problem of consciousness using spatiotemporal intermittency. Starting with quasiparticles as the minimalist material composition of the dynamical brain where interferences patterns between incoherent waves of quasiparticles and their quantum-thermal fluctuations constrain the kinetic internal energy of endogenous molecules through informational channels of the negentropically-derived quantum potential. This indicates that brains are not multifractal involving avalanches but are multiscalar, suggesting that unlike the hologram, where the functional interactions occur in the spectral domain, the spatiotemporal binding is multiscalar because of self-referential amplification occurring via long-range correlative information. The associated negentropic entanglement permeates the unification of the functional information architecture across multiple scales. As such, the holonomic brain theory is suitable for active consciousness, proving that consciousness is not fundamental. The holonomic model of the brain’s internal space is nonmetric and nonfractal. It contains a multiscalar informational structure decoded by intermittency spikes in the fluctuations of the negentropically-derived quantum potential. It is therefore, a more realistic approach than the platonic models in phase space.

New insights into holonomic brain theory: implications for active consciousness

This pioneering research on how specific molecules deep inside our brains form a dynamic information holarchy in phase space, linking mind and consciousness, is not only provocative but also revolutionary. Holonomic is a dynamic encapsulation of the holonic view that originates from the word “holon” and designates a holarchical rather than a hierarchical, dynamic brain organization to encompass multiscale effects. The unitary nature of consciousness being interconnected stems from a multiscalar organization of the brain. We aim to give a holonomic modification of the thermodynamic approach to the problem of consciousness using spatiotemporal intermittency. Starting with quasiparticles as the minimalist material composition of the dynamical brain where interferences patterns between incoherent waves of quasiparticles and their quantum-thermal fluctuations constrain the kinetic internal energy of endogenous molecules through informational channels of the negentropically-derived quantum potential. This indicates that brains are not multifractal involving avalanches but are multiscalar, suggesting that unlike the hologram, where the functional interactions occur in the spectral domain, the spatiotemporal binding is multiscalar because of self-referential amplification occurring via long-range correlative information. The associated negentropic entanglement permeates the unification of the functional information architecture across multiple scales. As such, the holonomic brain theory is suitable for active consciousness, proving that consciousness is not fundamental. The holonomic model of the brain’s internal space is nonmetric and nonfractal. It contains a multiscalar informational structure decoded by intermittency spikes in the fluctuations of the negentropically-derived quantum potential. It is therefore, a more realistic approach than the platonic models in phase space.

Reduced role of the wavefunctions' curvature of quantum potentials in non-standard quantum systems

In standard quantum systems where the mass of the particles is a constant, the quantum potential is exclusively dictated by the curvature of the wavefunction. Quantum systems with spatially dependent (effective) mass distributions appear in different systems, such as an electron in a semiconductor, quantum dots, and quantum liquids. In this letter, we show a class of quantum systems where the effective mass distribution governs the quantum potential rather than the wavefunctions' curvature for the entire region occupied by the wavefunction or at least for a sub-region in space. This gives a new insight into the role of the wavefunction's curvature in non-standard quantum systems, followed by the quantum potential in which quantum effects emerged in the Madelung reformulation of the Schrödinger equation.

QUANTUM PATHFINDERS: NAVIGATE THE SHORTEST ROUTE

The problem of finding the shortest path between two points in a graph is a fundamental problem in computer science and has many applications in fields such as transportation, logistics, and networking. Dijkstra's algorithm is a classical algorithm commonly used to solve this problem, but its time complexity can be prohibitively high for large graphs. Quantum computing, on the other hand, offers a promising approach to solving this problem with significantly improved time complexity. In this research paper, we explore the potential of quantum computing for solving the shortest path problem, including an overview of Dijkstra's algorithm and its limitations, the quantum computing approach using quantum phase estimation, and a comparison of the time complexities of classical and quantum algorithms. We also discuss the challenges that need to be addressed for quantum computing to realize its potential in solving practical shortest-path problems.

Spacetime Superoscillations and the Relativistic Quantum Potential

Spacetime Superoscillations and the Relativistic Quantum Potential

The Impact of Quantum Computing on Cryptography

Abstract: The purpose of this paper's abstract is to explain how quantum computing works in terms of current cryptography and to provide the reader a rudimentary understanding of post-quantum algorithms. Community key encoding methods affected, symmetric structures affected, the influence on hash purposes, upright quantum cryptography, distinctions amongst quantum and standard computing, obstacles in quantum computation, and quantum procedures (Shor's and Grover's). The PostQuantum Cryptography section specifically discusses various mathematically based quantum crucial circulation techniques, lattice-built cryptography, multivariate-built cryptography, hash-based signs, and code-based encoding. One of the modern technologies in today's society is quantum computation. The advance of quantum computing applications is the focus of numerous communities and research institutions worldwide. Another developing field at the moment that is becoming stable is artificial intelligence. The major goal of this work is to determine the effects of the development of quantum computing research on applications involving artificial intelligence. Hence, computational methods are utilised in the study's methodology. So that this study's findings about the expanding impact of quantum computing research for a particular application of artificial intelligence can be drawn. The impact and potential of quantum computing on the subject of artificial intelligence is also discussed in this study, along with how quantum computing affects that discipline.

Observation of Bohm trajectories and quantum potentials of classical waves

In 1952 David Bohm proposed an interpretation of quantum mechanics, in which the evolution of states results from trajectories governed by classical equations of motion but with an additional potential determined by the wave function. There exist only a few experiments that test this concept and they employed weak measurement of non-classical light. In contrast, we reconstruct the Bohm trajectories in a classical hydrodynamic system of surface gravity water waves, by a direct measurement of the wave packet. Our system is governed by a wave equation that is analogous to the Schrödinger equation which enables us to transfer the Bohm formalism to classical waves. In contrast to a quantum system, we can measure simultaneously their amplitude and phase. In our experiments, we employ three characteristic types of surface gravity water wave packets: two and three Gaussian temporal slits and temporal Airy wave packets. The Bohm trajectories and their energy flows follow the valleys and bounce off the hills in the corresponding quantum potential landscapes.

Experimental quantum end-to-end learning on a superconducting processor

Machine learning can be enhanced by a quantum computer via its inherent quantum parallelism. In the pursuit of quantum advantages for machine learning with noisy intermediate-scale quantum devices, it was proposed that the learning model can be designed in an end-to-end fashion, i.e., the quantum ansatz is parameterized by directly manipulable control pulses without circuit design and compilation. Such gate-free models are hardware friendly and can fully exploit limited quantum resources. Here, we report the experimental realization of quantum end-to-end machine learning on a superconducting processor. The trained model can achieve 98% recognition accuracy for two handwritten digits (via two qubits) and 89% for four digits (via three qubits) in the MNIST (Mixed National Institute of Standards and Technology) database. The experimental results exhibit the great potential of quantum end-to-end learning for resolving complex real-world tasks when more qubits are available.

An appearance of classical matter from the self-organizing process of quantum systems

We present a quantum effect where matter follows the classical Hamilton-Jacobi equation, which emerges from quantum systems with Riemannian structures, as in standard quantum systems such as semiconductor heterostructures, quantum plasmas, and quantum dots. The proposed effect is derived from solving a standard elliptic partial differential equation of the radial part of the wave function, which is equivalent to a vanished quantum potential of the system. We then analyze such an effect and examine how the classical matter tends to be denser at the boundary region of the system when the quantum system is given in a finite region in space. While the proposed effect is derived from the hydrodynamical formulation of quantum mechanics, the results are free from any interpretation of quantum mechanics.

Countering a fundamental law of attraction with quantum wave-packet engineering

Bohmian mechanics was designed to give rise to predictions identical to those derived by standard quantum mechanics, while invoking a specific interpretation of it - one which allows the classical notion of a particle to be maintained alongside a guiding wave. For this, the Bohmian model makes use of a unique quantum potential which governs the trajectory of the particle. In this work we show that this interpretation of quantum theory naturally leads to the derivation of interesting new phenomena. Specifically, we demonstrate how the fundamental Casimir-Polder force, by which atoms are attracted to a surface, may be temporarily suppressed by utilizing a specially designed quantum potential. We show that when harnessing the quantum potential via a suitable atomic wavepacket engineering, the absorption by the surface can be dramatically reduced. This is proven both analytically and numerically. Finally, an experimental scheme is proposed for achieving the required shape for the atomic wavepacket. All these may enable new insights into Bohmian mechanics as well as new applications to metrology and sensing.

Characteristics of Resonant Tunneling in Nanostructures with Spacer Layers

The effect of spacer layers on electron transport through two-barrier nanostructures was studied using the numerical solution of the time-dependent Schrodinger–Poisson equations with exact discrete open boundary conditions. The formulation of the problem took into account both the active region consisting of a quantum well and barriers, as well as the presence of highly doped contact layers and spacer layers. The use of the time formulation of the problem avoids the divergence of the numerical solution, which is usually observed when solving a stationary system of the Schrodinger–Poisson equations at small sizes of spacer layers. It is shown that an increase in the thickness of the emitter spacer leads to a decrease in the peak current through the resonant tunneling nanostructures. This is due to the charge accumulation effects, which, in particular, lead to a change in the potential in an additional quantum well formed in the emitter spacer region when a constant electric field is applied. The valley current also decreases as the thickness of the emitter spacer increases. The peak current and valley current are weakly dependent on the thickness of the collector spacer. The collector spacer thickness has a strong effect on the applied peak and valley voltages. The above features are valid for all three different resonant tunneling nanostructures considered in this study. For the RTD structures based on Al0.3Ga0.7As/GaAs, the optimized peak current value Ipmax = 5.6 × 109 A/m2 and the corresponding applied voltage Vp = 0.44 V. For the RTD structures based on AlAs/In0.8Ga0.2As, Ipmax = 14.5 × 109 A/m2 (Vp = 0.54 V); for RTD structures based on AlAs/In0.53Ga0.47As, Ipmax = 45.5 × 109 A/m2 (Vp = 1.75 V).

Exact and geometrical optics energy trajectories in Bessel beams via the quantum potential

The aim of the present work is to show that any monochromatic solution to the scalar wave equation in free space defines a conservative Hamiltonian system, describing a particle of mass m = 1 / 2 and energy E = 1 , under the influence of the so-called quantum potential. We remark that the integral curves of its Poynting vector, exact optics energy trajectories, define a particular subset of solutions to the corresponding Hamilton equations. Furthermore, we introduce the zero quantum potential straight lines concept, as the family of tangent lines to the integral curves of the Poynting vector at the zeros of the quantum potential. These general results are applied to a family of plane waves and to Bessel beams. In the case of Bessel beams, we present a detailed study of the trajectories determined by the corresponding Hamiltonian system, and we show that the zero quantum potential straight lines coincide with the geometrical light rays, geometrical optics energy trajectories. Furthermore, we show that the areal velocity, determined by the exact optics energy trajectories, for non-zero order Bessel beams is not a constant of motion. However, its projection along the z ^ direction is a constant of motion because L z is a constant.

A Compact Derivation of Quantum Potential in de Broglie–Bohm Theory

In the stochastic electrodynamics, various quantum effects on particles are supposed to emerge from the interactions of the particles with the fluctuating background field. We have adopted the same supposition and further supposed that the quantum potential arises from the velocity fluctuations of particles around their local averages. Based on these suppositions we have derived the expression of the quantum potential in the framework of de Broglie–Bohm theory, which is a reformulation of Schrödinger’s. Thus we are allowed to use the wave functions and Schrödinger operators explicitly so that we have been able to derive the quantum potential in simpler and more compact manner as compared with the stochastic electrodynamics’s. A new hydrodynamical version of Schrödinger equation is also presented, which has been found in the course of our study.

Organic Kainate Single Crystals for Second-Harmonic and Broadband THz Generation.

Organic crystals with unique nonlinear optical properties have been attracting attention owing to their capability to outperform their conventional nonorganic counterparts. Since nonlinear material responses are linked to a crystal's internal microscopic structure, molecular engineering of maximally unharmonic quantum potentials can boost macromolecular susceptibilities. Here, large-scale kainic acid (kainate) single crystals were synthesized, and their linear and nonlinear optical properties were studied in a broad spectral range, spanning the visible to THz spectral regions. The non-centrosymmetric zwitterionic crystallization, molecular structure, and intermolecular arrangement were found to act as additive donor-acceptor domains, enhancing the efficiency of the intrinsic second-order optical nonlinearity of this pure enantiomeric crystal. Molecular simulations and experimental analysis were performed to retrieve the crystals' properties. The crystals were predicted and found to have good transparency in a broad spectral range from the UV to the infrared (0.2-20 μm). Second-harmonic generation was measured for ultrashort pumping wavelengths between 800 and 2400 nm, showing an enhanced response around 600 nm. Broadband THz generation was demonstrated with a detection limited bandwidth of >8 THz along with emission efficiencies comparable to and prevailing those of commercial ZnTe crystals. The broadband nonlinear response and high transparency make kainate crystals extremely attractive for realizing a range of nonlinear optical devices.

Semiclassical trajectories in the double-slit experiment

We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.

Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states

In this work, we generate a family of quantum potentials that are non-rational extensions of the harmonic oscillator. Such a family can be obtained via two different but equivalent supersymmetric transformations. We construct ladder operators for these extensions as the product of the intertwining operators of both transformations. Then, we generate families of Barut–Girardello coherent states and analyze some of their properties as temporal stability, continuity on the label, and completeness relation. Moreover, we calculate mean-energy values, time-dependent probability densities, Wigner functions, and the Mandel Q-parameter to uncover a general non-classical behavior of these states.

Dynamics of Wave function Decay: The Quantum Entanglement and the Measure Process

By employing the stochastic extension of the Madelung quantum-hydrodynamic description within a discrete methodology, we establish a solution using the path integral approach to explore the progression of quantum states' superposition. This investigation aims to understand the eventual establishment of a stable end-state configuration amid the backdrop of gravitational background fluctuations. The model identifies the circumstances that lead to a limited range of interaction for the quantum potential, allowing for the emergence of sizeable, classically described macroscopic phenomena. The theory unveils the lowest achievable level of uncertainty in an open quantum system and investigate its congruence with the localized behaviors of macroscopic classical systems. The study examines agreements and differences with decoherence theory and the Copenhagen interpretation of quantum mechanics, and evaluates the impact of wave function decay on the measurement process. The work also shows that the model is able to explain the deviation of the deuterium state in nuclear physics from the quantum mechanics

Mechanical properties of the particle associated with the Laguerre–Gauss beams via the quantum potential point of view

The aim of the present work is to show that the Laguerre–Gauss beams determine a Hamiltonian system with two degrees of freedom for a particle of mass m = 1 under the action of the quantum potential determined by these beams. We show that the integral curves of the Poynting vector constitute a particular subset of solutions to the corresponding Hamilton equations and that the geometrical light rays associated with these twisted beams turn out to be the tangent straight lines to the exact optics energy trajectories at the zeroes of the quantum potential. By using the Hamiltonian formulation, we determine the velocity, the linear momentum, the angular momentum, the torque, and the areal velocity characterizing the particle associated with the Laguerre–Gauss beams.

Holographic realization of the prime number quantum potential.

We report the experimental realization of the prime number quantum potential VN (x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. As a further application, we also implement a potential whose spectrum is given by the lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes's sieve used for the primes. Our results pave the way toward the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers.