Search Results (29)

Miller’s rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for the classical Lorentz model with a weak anharmonic perturbation. Recently, we developed a mathematical framework which enabled us to prove that Miller’s rule is equally valid for quantum anharmonic oscillators, despite different dynamics due to zero-point fluctuations and further quantum-mechanical effects. However, our previous derivation applied only to one-dimensional oscillators and to the special case of second- and third-harmonic generation in a monochromatic electric field. Here we extend the proof to three-dimensional quantum anharmonic oscillators and also treat all orders of the nonlinear response to an arbitrary multi-frequency field. This makes the results applicable to a much larger range of physical systems and nonlinear optical processes. The obtained generalized Miller formulae rigorously express all tensor elements of the frequency-dependent nonlinear susceptibilities in terms of the linear susceptibility and thus allow a computationally inexpensive quantitative prediction of arbitrary parametric frequency-mixing processes from a small initial dataset. Full article

The influence of zero-point fluctuations on photon propagation in a vacuum is investigated without using normal ordering and renormalization procedures, but in a frame of the conformally unimodular metric for a description of the fluctuating gravitational field. The complete formula for decoherence time is presented. Full article

The quantum electromagnetic (EM) field is formulated in the Weyl–Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle, it is possible to interpret within WW all experiments involving the EM field interacting with macroscopic bodies, the latter treated classically. In the WW formalism, the essential difference between classical electrodynamics and the quantum theory of the EM field is just the assumption that there is a random EM field-filling space, i.e., the existence of a zero-point field with a Gaussian distribution for the field amplitudes. I analyze a typical optical test of a Bell inequality. The model admits an interpretation compatible with local realism, modulo a number of assumptions assumed plausible. Full article

Tunnel magnetoresistance (TMR) sensors, known for their high sensitivity, efficiency, and compact size, are ideal for detecting weak currents, particularly leakage currents in smart grids. However, temperature variations can negatively impact their accuracy. This work investigates the effects of temperature variations on measurement accuracy. We analyzed the operating principles and temperature characteristics of TMR sensors and proposed a high-precision, software-based temperature compensation method using cubic spline interpolation combined with polynomial regression and zero-point self-calibration. Additionally, a field-programmable gate array (FPGA)-based temperature compensation circuit was designed and implemented. An experimental platform was established to comprehensively evaluate the sensor’s performance under various temperature conditions. Experimental results demonstrate that this method significantly enhances the sensor’s temperature stability, reduces the sensitivity temperature drift coefficient, and improves zero-point drift stability, outperforming other compensation methods. After compensation, the sensor’s measurement accuracy in complex temperature environments is substantially improved, enabling effective weak current detection in smart grids across diverse environments. Full article

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations that have been fully carried out to date are discussed in two main cases: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh–Jeans radiation; and second, where only these radiation fields exist within a cavity. The emphasis here is on the first, more complicated, case, where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in classical statistical mechanics, involving probabilistic notions of phase-space occupation, the calculations to date for both particles and fields, or for fields alone, follow the caloric entropy method, where the notions of heat flow, adiabatic surfaces, and isothermal conditions are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have successfully gone. Full article

I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space ≠ spacetime. II. The arena of observations—and, more generally, of all events (i.e., everything) in the real physical world—is the classical four-dimensional physical spacetime. III. The “Born rule” is the random process “magically” transforming I into II. Wavefunctions are superposed and entangled only in the abstract space I, never in spacetime II. Attempted formulations of quantum theory directly in real physical spacetime actually constitute examples of “locally real” theories, as defined by Clauser and Horne, and are therefore already empirically refuted by the numerous tests of Bell’s theorem in real, controlled experiments in laboratories here on Earth. Observed quantum entities (i.e., events) are never superposed or entangled as they: (1) exclusively “live” (manifest) in real physical spacetime and (2) are not described by entangled wavefunctions after “measurement” effectuated by III. When separated and treated correctly in this way, a number of fundamental problems and “paradoxes” of quantum theory vs. relativity (i.e., spacetime) simply vanish, such as the black hole information paradox, the infinite zero-point energy of quantum field theory and the quantization of general relativity. Full article

The removal of color from dye wastewater is crucial, since dyes are extremely toxic and can cause cancer in a variety of life forms. Studies must be done to use cost-effective adsorbents for the removal of color from dye effluents to protect the environment. To our knowledge, virtually no research has been done to describe the possibility of using Calotropis gigantea leaf extract zinc hydroxide nanoparticles (CG-Zn(OH)₂NPs) as an adsorbent for the decolorization of Coomassie violet (CV) from the aqueous emulsion, either in batch mode or continuously. In the present batch investigation, CV dye is removed from the synthetic aqueous phase using CG-Zn(OH)₂NPs as an adsorbent. The synthesized nanoparticles were characterized using various instrumental techniques such as Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), thermogravimetric analysis (TGA), field emission scanning electron microscopy (FE-SEM), energy dispersive X-ray spectroscopy (EDS) and Brunauer–Emmett–Teller (BET) surface area and pore volume, a particle size analyser, and zero-point charge. The decolorization efficacy of CV dye from an aqueous phase by the adsorbent was examined in batch mode by varying process parameters. The consequences of various experimental variables were optimized using response surface methodology (RSM) to achieve the maximum decolorization efficiency (90.74%) and equilibrium dye uptake, q_e (35.12 mg g⁻¹). The optimum pH, dye concentration, CG-Zn(OH)₂NPs adsorbent dosage, and particle size were found to be 1.8, 225 mg L⁻¹, 5 g L⁻¹, and 78 μm, respectively for CV dye adsorption capacity at equilibrium. The adsorbent zero-point charge was found to be at pH 8.5. The Langmuir isotherm model provided a good representation of the equilibrium data in aqueous solutions, with a maximum monolayer adsorption capability (q_max) of 40.25 mg g⁻¹ at 299 K. The dye adsorption rate follows a pseudo-second-order kinetic model at various dye concentrations, which indicated that the reaction is more chemisorption than physisorption. The negative values of ΔG and positive values of ΔH at different temperatures indicate that the adsorption process is spontaneous and endothermic, respectively. Reusability tests revealed that the prepared nanoparticles may be used for up to three runs, indicating that the novel CG-Zn(OH)₂NPs seems to be a very promising adsorbent for the removal of Coomassie violet dye from wastewater. Full article

The study of the human psyche has elucidated a bipartite structure of logic reflecting the quantum–classical nature of the world. Accordingly, we posited an approach toward studying the brain by means of the quantum–classical dynamics of a mixed Weyl symbol. The mixed Weyl symbol can be used to describe brain processes at the microscopic level and, when averaged over an appropriate ensemble, can provide a link to the results of measurements made at the meso and macro scale. Within this approach, quantum variables (such as, for example, nuclear and electron spins, dipole momenta of particles or molecules, tunneling degrees of freedom, and so on) can be represented by spinors, whereas the electromagnetic fields and phonon modes can be treated either classically or semi-classically in phase space by also considering quantum zero-point fluctuations. Quantum zero-point effects can be incorporated into numerical simulations by controlling the temperature of each field mode via coupling to a dedicated Nosé–Hoover chain thermostat. The temperature of each thermostat was chosen in order to reproduce quantum statistics in the canonical ensemble. In this first paper, we introduce a general quantum–classical Hamiltonian model that can be tailored to study physical processes at the interface between the quantum and the classical world in the brain. While the approach is discussed in detail, numerical calculations are not reported in the present paper, but they are planned for future work. Our theory of brain dynamics subsumes some compatible aspects of three well-known quantum approaches to brain dynamics, namely the electromagnetic field theory approach, the orchestrated objective reduction theory, and the dissipative quantum model of the brain. All three models are reviewed. Full article

In this paper, the nexus between the Bell-state measurement and extracting phase information from the zeropoint field is investigated. For this purpose, the Wigner representation in the Heisenberg picture is applied in a Bell-type experiment in which the polarisation-entangled photon pairs generated in a type-II parametric down-conversion do not overlap. The signal intensities at the detectors are calculated in a four-mode approximation, being expressed as functions of the modules and phases of the four zeropoint amplitudes entering the crystal. A general criterion for identifying the correlated detectors is proposed based on the equality of the signal intensities, and without involving the calculation of the joint detection probabilities. In addition, from the analyses in the rectilinear and diagonal basis, it is shown that the distinguishability of the polarisation Bell states, which is in direct correspondence with the joint detection events in each experiment, can be related to the knowledge of the phases of the vacuum field entering the entanglement source, and giving rise to correlated detections. To this purpose, it is conjectured that a detection event is associated with a maximum value of the signal intensity averaged in the modules of the zeropoint amplitudes, as a function of the vacuum phases. Full article

The position probability density function is calculated for a classical electric dipole harmonic oscillator bathed in zero-point plus Planckian electromagnetic fields, as considered in the physical theory of stochastic electrodynamics (SED). The calculations are carried out via two new methods. They start from a general probability density expression involving the formal integration over all probabilistic values of the Fourier coefficients describing the stochastic radiation fields. The first approach explicitly carries out all these integrations; the second approach shows that this general probability density expression satisfies a partial differential equation that is readily solved. After carrying out these two fairly long analyses and contrasting them, some examples are provided for extending this approach to quantities other than position, such as the joint probability density distribution for positions at different times, and for position and momentum. This article concludes by discussing the application of this general probability density expression to a system of great interest in SED, namely, the classical model of hydrogen. Full article

This paper provides elements in support of the random zero-point radiation field (zpf) as an essential ontological ingredient needed to explain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf, a drastic, qualitative change in the dynamics takes place, leading eventually to the quantum dynamics. In particular, we demonstrate that in parallel with the evolution of the canonical variables of the particle into quantum operators satisfying the basic commutator $\left[\widehat{x},\widehat{p}\right]=i\mathsf{\hslash }$, also the field canonical variables are transformed, giving rise to the corresponding creation and annihilation operators ${\widehat{a}}^{†},\widehat{a}$, satisfying $\left[\widehat{a},{\widehat{a}}^{†}\right]=1$. This allows for an explanation of quantum features such as quantum fluctuations, stationary states and transitions, and establishes a natural contact with (nonrelativistic) quantum electrodynamics. Full article

In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object must have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive close to the throat and that it is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein–Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint, which induces a decreasing oscillatory behavior. By imposing Dirichlet boundary conditions on a spherical shell in the neighborhood of the throat we can determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of the modes method. The zero-point energy is regularized using the Epstein–Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell. Full article

In an atom, the interaction of a bound electron with the vacuum fluctuations of the electromagnetic field leads to complex shifts in the energy levels of the electron, with the real part of the shift corresponding to a shift in the energy level and the imaginary part to the width of the energy level. The most celebrated radiative shift is the Lamb shift between the $2s_{1/2}$ and the $2p_{1/2}$ levels of the hydrogen atom. The measurement of this shift in 1947 by Willis Lamb Jr. proved that the prediction by Dirac theory that the energy levels were degenerate was incorrect. Hans Bethe’s non-relativistic calculation of the shift using second-order perturbation theory demonstrated the renormalization process required to deal with the divergences plaguing the existing theories and led to the understanding that it was essential for theory to include interactions with the zero-point quantum vacuum field. This was the birth of modern quantum electrodynamics (QED). Numerous calculations of the Lamb shift followed including relativistic and covariant calculations, all of which contain a nonrelativistic contribution equal to that computed by Bethe. The semi-quantitative models for the radiative shift of Welton and Power, which were developed in an effort to demonstrate physical mechanisms by which vacuum fluctuations lead to the shift, are also considered here. This paper describes a calculation of the shift using a group theoretical approach which gives the shift as an integral over frequency of a function, which is called the “spectral density of the shift.“ The energy shift computed by group theory is equivalent to that derived by Bethe yet, unlike in other calculations of the non-relativistic radiative shift, no sum over a complete set of states is required. The spectral density, which is obtained by a relatively simple computation, reveals how different frequencies of vacuum fluctuations contribute to the total energy shift. The analysis shows, for example, that half the radiative shift for the ground state 1S level in H comes from virtual photon energies below 9700 eV, and that the expressions of Power and Welton have the correct high-frequency behavior, but not the correct low-frequency behavior, although they do give approximately the correct value for the total shift. Full article

Recently, the treatment of effluent by agricultural waste biomass has significantly attracted wide interest among researchers due to its availability, efficacy, and low cost. The removal of toxic Remazol Brilliant Blue-R (RBBR) from aqueous solutions using HNO₃-treated Juglans nigra (walnut) shell biomass carbon as an adsorbent has been examined under various experimental conditions, such as initial pH, adsorbate concentration, adsorbent dosage, particle size, agitation speed, and type of electrolyte. The experiments are designed to achieve the maximum dye removal efficiency using the response surface methodology (RSM). The optimum pH, adsorbent dosage, and particle size were found to be 1.5, 7 g L⁻¹, and 64 μm, respectively for maximum decolorization efficiency (98.24%). The prepared adsorbent was characterized by particle size, Brunauer–Emmett–Teller (BET) surface area, pore volume, zero-point charge (pH_zpc), Fourier transform infrared spectroscopy (FT-IR), field emission scanning electron microscopy/energy dispersive X-ray spectroscopy (FE-SEM/EDX), X-ray diffraction (XRD), and thermogravimetric analysis (TGA). Based on fitting the experimental data with various models, the isotherm and kinetic mechanism are found to be more appropriate with Langmuir isotherm and pseudo-second-order kinetics. The adsorption mechanism can be described by the intra-particle diffusion model, Bangham, and Boyd plots. The overall rate of adsorption is controlled by the external film diffusion of dye molecules. The maximum monolayer adsorption capacity, (q_max) 54.38 mg g⁻¹ for RBBR dye, was obtained at a temperature of 301 K. From a thermodynamic standpoint, the process is endothermic, spontaneous, and the chemisorption process is favored at high temperatures. Desorption studies were conducted with various desorbing reagents in various runs and the maximum desorption efficiency (61.78% in the third run) was obtained using the solvent methanol. Reusability studies demonstrated that the prepared adsorbent was effective for up to three runs of operation. The investigation outcomes concluded that walnut shell biomass activated carbon (WSBAC) is a cost-effective, eco-friendly, and bio-sustainable material that can be used for synthetic dye decolorization in aqueous media. Full article

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves. Full article