Physics

We investigate the non-relativistic scattering of a plane wave by a vertical segment formulating the problem in terms of the Lippmann–Schwinger equation in two spatial dimensions. Adjusting the coupling strength function we show how to implement the scattering by a system of multiple slits and by a Cantor set. We present detailed calculations of the scattered wave function for the line segment, as well as for the single, double, and multiple slits. We define reflection and transmission functions that are position-dependent in a defined region. From these results, we obtain the probability densities and differential and total cross-sections for these problems. Full article

In this paper, we analyze the application of an analytical gluon distribution based on double-asymptotic scaling to the photoproduction of vector mesons in coherent $pp$, $pA$, and $AA$ collisions at LHC energies, using the color dipole formalism. Predictions for the rapidity distribution are presented for ${\rho }^0$, $J/\psi$, $\psi \left(2S\right)$, and $\mathrm{{\rm Y}}\left(1S\right)$ mesons photoproduction. An analysis of the uncertainties associated with different implementations of the dipole–proton amplitude is performed. The vector meson photoproduction accompanied by electromagnetic dissociation is also analyzed. Full article

The large-scale dynamics of the universe is generally described in terms of the time-dependent scale factor $a\left(t\right)$. To make contact with observational data, the $a\left(t\right)$ function needs to be related to the observable $z\left(r\right)$ function, redshift versus distance. Model fitting of data has shown that the equation that governs $z\left(r\right)$ needs to contain a constant term, which has been identified as Einstein’s cosmological constant. Here, it is shown that the required constant term is not a cosmological constant but is due to an overlooked geometric difference between proper time t and look-back time $t_{\mathrm{lb}}$ along lines of sight, which fan out isotropically in all directions of the 3D (3-dimensional) space that constitutes the observable universe. The constant term is needed to satisfy the requirement of spatial isotropy in the local limit. Its magnitude is independent of the epoch in which the observer lives and agrees with the value found by model fitting of observational data. Two of the observational consequences of this explanation are examined: an increase in the age of the universe from 13.8 Gyr to 15.4 Gyr, and a resolution of the $H_0$ tension, which restores consistency to cosmological theory. Full article

External fields modify the confinement potential and electronic structure in a multiple quantum well system, affecting the light–matter interaction. Here, we present a theoretical study of the modulation of the nonlinear optical response simultaneously employing an intense non-resonant laser field and an electric field. Considering four occupied subbands, we focus on a GaAs/AlGaAs symmetric multiple quantum well system with five wells and six barriers. By solving the Schrödinger equation through the finite element method under the effective mass approximation, we determine the electronic structure and the nonlinear optical response using the density matrix formalism. The laser field dresses the confinement potential while the electric field breaks the inversion symmetry. The combined effect of both fields modifies the intersubband transition energies and the overlap of the wave functions. The results obtained demonstrate an active tunability of the nonlinear optical response, opening up the possibility of designing optoelectronic devices with tunable optical properties. Full article

The macroscopic magnetic properties of magnetorheological elastomers (MREs) are influenced by their microstructure, yet limited investigations has been conducted on this subject to date. In this paper, a microstructure-based model is proposed to investigate the magnetization response of MREs. The dipole theory is employed to compute the local magnetic field, and a fitting equation derived from finite element analysis is used to correct the magnetic field. The Fröhlich–Kennelly equation is applied to describe the nonlinear magnetic properties of the particle material. Based on experimental observations, a body-centered tetragonal (BCT) model is established to describe the magnetization properties of anisotropic MREs. The proposed model is validated by comparison with experimental data and can be utilized to predict the effective susceptibility of MREs. The effects of particle volume fraction, the direction of the external magnetic field, and the shape of the MRE samples can also be analyzed using this model. Full article

We consider a multilevel atom, such as a hydrogen atom, interacting with the quantum electromagnetic field in the dressed ground state of the interacting system. Using perturbation theory within the dipole approximation, we evaluate the dressed ground state and investigate the effect of atomic self-dressing on several field and atomic observables. Specifically, we obtain general expressions of the renormalized electric and magnetic field fluctuations and energy densities around the atom, and analyze their scaling with the distance from the atom, obtaining approximated expressions in the so-called near and far zones. We also investigate nonlocal spatial field correlations around the atom. We stress how the quantities we evaluate can be probed through two- and three-body nonadditive Casimir–Polder dispersion interactions. We also investigate the effect of self-dressing—namely, the virtual transitions occurring in the dressed ground state—on atomic observables, such as the average potential energy of the electron in the nuclear field. This also allows us to obtain a more fundamental quantum basis for the Welton interpretation of the Lamb shift of a ground-state hydrogen atom, in terms of the atomic self-dressing processes. Full article

We construct the Green functions (or Feynman’s propagators) for the Schrödinger equations of the form $i{\psi }_t+{\displaystyle \frac{1}{4}}{\psi }_{xx}\pm t{x}^2\psi =0$ (for the wave function $\psi$ and its time (t) and x-space derivatives) in terms of Airy functions and solve the Cauchy initial value problem in the coordinate and momentum representations. Particular solutions of the corresponding nonlinear Schrödinger equations with variable coefficients are also found. A special case of the quantum parametric oscillator is studied in detail first. The Green function is explicitly given in terms of Airy functions and the corresponding transition amplitudes are found in terms of a hypergeometric function. The general case of the quantum parametric oscillator is considered then in a similar fashion. A group theoretical meaning of the transition amplitudes and their relation with Bargmann’s functions is established. The relevant bibliography, to the best of our knowledge, is addressed. Full article

In this paper, the chaotic behavior and subharmonic bifurcation in a dynamical model for charged dilation-AdS black holes are investigated in extended phase space using analytical and numerical methods. An analytical expression for the chaotic critical value at the disturbance amplitude is obtained using the Melnikov method, revealing the monotonicity of the threshold values for chaos with charge and frequency, and the coupling parameters between the expansion field and the Maxwell field are studied. It is shown that chaos can be controlled through the system parameters. Meanwhile, an analytical expression for the critical value of the bifurcation of subharmonic orbits at disturbance amplitudes is acquired using the subharmonic Melnikov method. The relationship between the threshold value and the vibration frequency and the order of the subharmonic orbit is studied. This demonstrates that the system undergoes chaotic motion via infinite odd-order subharmonic bifurcations. Finally, numerical simulations are used to verify the analytical results. Full article

Phase change materials (PCMs) are widely used in latent heat thermal energy storage systems (LHTESSs), but their low thermal conductivity limits performance. This study numerically investigates the enhancement of thermal efficiency in LHTESSs using nano-enhanced PCM (NePCM), composed of paraffin wax embedded with copper (Cu) nanoparticles. The NePCM is confined within a trapezoidal cavity, with the base serving as the heat source. Four different cavity heights were analyzed: cases 1, 2, 3, and 4 with the heights D of 24 mm, 18 mm, 15 mm, and 13.5 mm, respectively. The finite element method was employed to solve the governing equations. The influence of two hot base temperatures (333.15 K and 338.15 K) and Cu nanoparticle volume fractions ranging from 0% to 6% was examined. The results show that incorporating Cu nanoparticles at 6 vol% (volume fraction) enhanced thermal conductivity and reduced melting time by 10.71%. Increasing the base temperature to 338.15 K accelerated melting by 65.55%. Among all configurations, case 4 exhibited the best performance, reducing melting duration by 15.12% compared to case 1. Full article

In this paper, an equation describing nonlinear wave phenomena on the surface of magnetically active plasma in the approximation of the complete homogeneity of processes along the direction of the constant magnetic field is obtained. One of its solutions, in the form of a pulse having the shape of rapidly decaying oscillations with a changing period, is found to essentially depend on the magnitude of the magnetic field and shown to be approximately described by a specially selected analytical function. A detailed analytical analysis of the properties of another solitary wave formation existing under conditions of resonant coincidence of its carrier frequency with the corresponding value of its eigen surface oscillations in the considered cold semi-infinite plasma, in which a constant magnetic field is directed along its boundary, is also carried out. The conditions for the excitation of wave disturbances are determined, and analytical expressions that adequately describe the space–time structure of nonlinear waves are proposed. Full article

The shape parameters and energy spectra of the decoupled ${\mathrm{h}}_{11/2}$ bands in isotopes ${}^{99,101,103}\mathrm{Ru}$, ^{101,103,105,107}Pd and ^{101,103,105,107}Cd are analyzed using the particle-plus-rotor model and cranked shell model calculations. The quasiparticle-plus-rotor (PRM) model calculations are performed, considering both soft and rigid triaxial cores, using the constant-moment-of-inertia (CMI) and variable-moment-of-inertia (VMI) approaches. The asymmetry parameter $\gamma$ obtained from the PRM model calculations is found to be consistent with the results obtained from the cranked shell model calculations when the core exhibited CMI behavior. Full article

This study presents a theoretical investigation into the interference properties of three photons in a six-port optical beam splitter, commonly referred to as a tritter. We examine various configurations of the relative phase differences among the input photons. Our findings reveal that fully constructive interference periodically occurs at a single output port for specific constant phase differences, while fully destructive interference simultaneously manifests at the remaining two output ports. These distinctive interference patterns arise across a wide range of specific phase difference combinations among the input photons. We suggest that these unique interference characteristics provide new insights into the potential implementation of a three-party quantum key distribution protocol. Such three-photon interference phenomena are crucial for facilitating symmetric secure key distribution among three parties. Full article

The hadronic phase and its dynamics in relativistic heavy-ion collisions are topics of immense discussion. The hadronic phase contains various massive hadrons with an abundance of the lightest hadron, i.e., $\pi$-mesons (pions). In this paper, we consider that pions are in the thermal equilibrium in the hadronic phase and use second-order viscous hydrodynamics for a medium of massive pions to obtain its expansion to the boundary of the kinetic freeze-out. We achieve the kinetic freeze-out boundary with the Knudsen number $\mathrm{Kn}>1$ limit. When this condition is met, hydrodynamics expansion breaks down, and the mean free path becomes sufficiently large in comparison with the system size so that the particle yields are preserved. Further, we investigate the effect of the massive fluid on the resonance particle yields, including re-scattering and regeneration, along with the natural decay widths of the resonances. The resonances can play an essential role in determining the characteristics of the hadronic phase as they have sufficiently small lifetimes, which may be comparable to the hadronic phase lifetime. In the current study, we predict the hadronic phase lifetime, which is further used to determine the $K^{*}{\left(892\right)}^0/K$, $\varphi \left(1020\right)/K$, and $\rho {\left(770\right)}^0/\pi$ yield ratios at the kinetic freeze-out. We calculate these ratios as a function of charged particle multiplicity and transverse momentum and compare the findings with experimental data. Our calculations qualitatively agree with the experimental data, indicating a possible hydrodynamical evolution of the hadronic phase. Full article

In this paper, we analyze the distribution of bi-partite correlations in pure symmetric N-qubit states during local deterministic measurements, which ensure the same value of the reduced purities in the outcome states. It is analytically shown that all reduced purities grow in the process of deterministic measurements. This allows us to characterize the stability of bi-partite entanglement during the optimal correlation transfer under single-qubit measurements in the asymptotic limit $N\gg 1$. Full article

In his recent paper, Vlatko Vedral claims that the Schrödinger picture can describe quantum systems as locally as the Heisenberg picture, relying on a product notation for the density matrix. Here, I refute that claim. I show that the so-called ‘local factors’ in the product notation do not correspond to individual systems and therefore fail to satisfy Einsteinian locality. Furthermore, the product notation does not track where local gates are applied. Finally, I expose internal inconsistencies in the argument: if, as is also stated, the Schrödinger-picture locality ultimately depends on the explicit bookkeeping of all operations, then the explanatory power of the product notation is de facto undermined. Full article

In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, which is characterized by smooth behavior of key quantities; and the critical region, where these quantities exhibit singularities or strong fluctuations. Due to their starkly different properties, those regions are often perceived as being weakly related, if ever. However, here, we demonstrate that these regions are intimately connected, specifically showing how they have a relationship that can be explicitly revealed using self-similar approximation theory. The framework considered enables the prediction of observable quantities near the critical point based on information from the regular region, and vice versa. Remarkably, the method relies solely on asymptotic expansions with respect to a parameter, regardless of whether the expansion originates in the regular or critical region. The mathematical principles of self-similar theory remain consistent across both cases. We illustrate this consistency by extrapolating from the regular region to predict the existence, location, and critical indices of a critical point of an equation of state for a statistical system, even when no direct information about the critical region is available. Conversely, we explore extrapolation from the critical to the regular region in systems with discrete scale invariance, where log-periodic oscillations in observables introduce additional complexity. The findings provide insights and solutions applicable to diverse phenomena, including material fracture, stock market crashes, and earthquake forecasting. Full article

Within the framework of the XHe hypothesis, the positive results of the DAMA/NaI and DAMA/LIBRA experiments on the direct search for dark matter particles can be explained by the annual modulation of the radiative capture of dark atoms into low-energy bound states with sodium nuclei. Since this effect is not observed in other underground WIMP (weakly interacting massive particle) search experiments, it is necessary to explain these results by investigating the possibility of the existence of low-energy bound states between dark atoms and the nuclei of matter. Numerical modeling is used to solve this problem, since the study of the XHe–nucleus system is a three-body problem and leaves no possibility of an analytical solution. To understand the key properties and patterns underlying the interaction of dark atoms with the nuclei of baryonic matter, we develop the quantum mechanical description of such an interaction. In the numerical quantum mechanical model presented, takes into account the effects of quantum physics, self-consistent electromagnetic interaction, and nuclear attraction. This approach allows us to obtain a numerical model of the interaction between the dark atom and the nucleus of matter and interpret the results of direct experiments on the underground search for dark matter, within the framework of the dark atom hypothesis. Thus, in this paper, for the first time, steps are taken towards a consistent quantum mechanical description of the interaction of dark atoms, with unshielded nuclear attraction, with the nuclei of atoms of matter. The total effective interaction potential of the OHe–Na system has therefore been restored, the shape of which allows for the preservation of the integrity and stability of the dark atom, which is an essential requirement for confirming the validity of the OHe hypothesis. Full article

Quantum illumination (QI) is an entanglement-based protocol for improving LiDAR/radar detection of unresolved targets beyond what a classical LiDAR/radar of the same average transmitted energy can do. Originally proposed by Seth Lloyd as a discrete-variable quantum LiDAR, it was soon shown that his proposal offered no quantum advantage over its best classical competitor. Continuous-variable, specifically Gaussian-state, QI has been shown to offer a true quantum advantage, both in theory and in table-top experiments. Moreover, despite its considerable drawbacks, the microwave version of Gaussian-state QI continues to attract research attention. A recent QI study by Armanpreet Pannu, Amr Helmy, and Hesham El Gamal (PHE), however, has: (i) combined the entangled state from Lloyd’s QI with the channel models from Gaussian-state QI; (ii) proposed a new positive operator-valued measurement for that composite setup; and (iii) claimed that, unlike Gaussian-state QI, PHE QI achieves the Nair–Gu lower bound on QI target-detection error probability at all noise brightnesses. PHE’s analysis was asymptotic, i.e., it presumed infinite-dimensional entanglement. The current paper works out the finite-dimensional performance of PHE QI. It shows that there is a threshold value for the entangled-state dimensionality below which there is no quantum advantage, and above which the Nair–Gu bound is approached asymptotically. Moreover, with both systems operating with error-probability exponents 1 dB lower than the Nair–Gu bound, PHE QI requires enormously higher entangled-state dimensionality than does Gaussian-state QI to achieve useful error probabilities in both high-brightness (100 photons/mode) and moderate-brightness (1 photon/mode) noise. Furthermore, neither system has an appreciable quantum advantage in low-brightness (much less than 1 photon/mode) noise. Full article