Physics, Volume 7, Issue 4 (December 2025) – 10 articles

The effect of the curvature of the boundary of semi-infinite cold plasma on the parameters and properties of surface oscillations localized near this boundary is considered. An analytical description of various cases of the impact of static deformation of the plasma boundary on the characteristics of the oscillating surface charge is obtained, and the results of the exact numerical solution of the initial equations are found to confirm the reliability of the derived analytical formulas. A significant role of the boundary perturbation shape in the formation of the spatial distribution of surface oscillation parameters is revealed. With the help of analytical formulas and precise numerical calculations, a description of this nonlinear interaction is presented. The availability of such a description is crucial both for determining the possibility of using the examined effect for specific applications and, on the other hand, for exciting it in plasma, which requires knowledge of the field structure features. Full article

By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derived. With this quantization, the smooth continuous Finsler structure is transformed into a quantized Hamilton structure through the kinematics of a free-falling quantum particle with a positive mass, along with the introduction of the relativistic generalized uncertainty principle (RGUP) that generalizes quantum mechanics by integrating gravity. This transformation ensures the preservation of the positive one-homogeneity of both Finsler and Hamilton structures, while the RGUP dictates modifications in the noncommutative relations due to integrating consequences of relativistic gravitational fields in quantum mechanics. The anisotropic conformal transformation of the resulting metric tensor and its inverse in higher-dimensional spaces has been determined, particularly highlighting their translations to the four-dimensional fundamental metric tensor and its inverse. It is essential to recognize the complexity involved in computing the fundamental inverse metric tensor during a conformal transformation, as it is influenced by variables like spatial coordinates and directional orientation, making it a challenging task, especially in tensorial terms. We conclude that the derivations in this study are not limited to the structure in tangent and cotangent bundles, which might include both spacetime and momentum space, but are also applicable to higher-dimensional contexts. The theoretical framework of quantization of general relativity based on quantizing its metric tensor is primarily grounded in the four-dimensional metric tensor and its inverse in pseudo-Riemannian geometry. Full article

The applicability of the first-order Fermi mechanism—a cornerstone of the diffusive shock acceleration (DSA) model—in explaining the cosmic ray spectrum is reexamined in light of recent observations from the Magnetospheric Multiscale (MMS) mission at Earth’s bow shock. It is demonstrated that the Fermi and DSA mechanisms lack physical justification and should be replaced by the physically correct ballistic surfing acceleration (BSA) mechanism. The results show that cosmic rays are energized by the convection electric field during ballistic surfing upstream of quasi-perpendicular shocks, independently of internal shock processes. The spectral index of cosmic rays is determined by the magnetic field compression and shock geometry: the acceleration is strongest in perpendicular shocks and vanishes in parallel shocks. The BSA mechanism reproduces the observed spectral indices, with $s=-2.7$ below the knee at ${10}^{16}$ eV and $s=-3$ above it. It is suggested that the spectral knee may correspond to particles whose gyroradii are comparable to the characteristic size of shocks in supernova remnants. The acceleration time to reach the knee energy, as predicted by the BSA, is in the order of 500 years. Full article

One of the main goals of the Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) is to investigate the properties of strongly interacting matter under high baryon densities and explore the QCD phase diagram. Fluctuations of conserved quantities like baryon number, electric charge, and strangeness are key probes for phase transitions and critical behavior, as are connected to thermodynamic susceptibilities predicted by lattice QCD calculations. In this paper, we report on up-to-the-fourth-order cumulants of (net-)proton number distributions in gold–gold ion collisions at the nucleon–nucleon center of mass energies $\sqrt{s_{NN}}$ = 3.5–19.6 GeV using the Parton–Hadron-Quantum-Molecular Dynamics (PHQMD) model. Protons and anti-protons are selected at midrapidity ($\left|y\right|$ < 0.5) within a transverse momentum range 0.4 $<p_T<$ 2.0 GeV/c of STAR experiment and 1.08 $<y<$ 2.08 and 0.4 $<p_T<$ 2.0 GeV/c of CBM acceptances. The results obtained from the PHQMD model are compared with the existing experimental data to undersatand potential signatures of critical behavior and to probe the vicinity of the critical end point in the CBM energy range. The results obtained here with the PHQMD calculations for $\kappa {\sigma }^2$ (the distribution kurtosis times variance squared) are consistent with the overall trend of the measurement results for the most central (0–5% centrality) collisions, although the calculations somewhat overestimate the experimental values. Full article

Molecular quantum electrodynamics is a powerful and effective tool for the representation and elucidation of optical interactions with matter. Its history spans nearly a century of significant advances in its detailed theory and applications, and in its wider appreciation. To fully appreciate the development of the subject into its modern form invites a perspective on progressive technical progress in the theory, noting a growth in applications that closely mirrors advances in optical experimentation. The challenges and deficiencies of alternative approaches to theory are also taken into consideration. Full article

This paper for the first time derives some properties of the hydrogen atom inside a box with an impenetrable wall. Scaling of the Hamiltonian operator proves to be practical for the derivation of some general properties of the eigenvalues. The radial part of the Schrödinger equation is conditionally solvable and the exact polynomial solutions provide helpful information. There are accidental degeneracies that take place at particular values of the box radius, some of which can be determined from the conditionally-solvable condition. Some of the roots stemming from the conditionally-solvable condition appear to converge towards the critical values of the model parameter. This analysis is facilitated by the Rayleigh–Ritz method that provides accurate eigenvalues. Full article

The steady-state quantum dynamics of a compound sample consisting of a semiconductor double-quantum-dot (DQD) system, non-linearly coupled with a leaking superconducting transmission line resonator, is theoretically investigated. Particularly, the transition frequency of the DQD is taken to be equal to the doubled resonator frequency, whereas the inter-dot Coulomb interaction is considered weak. As a consequence, the steady-state quantum dynamics of this complex non-linear system exhibit sudden changes in its features, occurring at a critical DQD-cavity coupling strength, suggesting perspectives for designing on-chip microwave quantum switches. Furthermore, we show that, above the threshold, the electrical current through the double-quantum dot follows the mean photon number into the microwave mode inside the resonator. This might not be the case any more below that critical coupling strength. Lastly, the photon quantum correlations vary from super-Poissonian to Poissonian photon statistics, i.e., towards single-qubit lasing phenomena at microwave frequencies. Full article

In this study, a nonlinear dynamic model is developed to examine the stability and vibration behavior of a self-balancing electric Segway operating over irregular stochastic terrains. The Segway is treated as a three-degrees-of-freedom cart–inverted pendulum system, incorporating elastic and damping effects at the wheel–ground interface. Road irregularities are generated in accordance with international standard using high-order filtered noise, allowing for representation of surface classes from smooth to highly degraded. The governing equations, formulated via Lagrange’s method, are transformed into a Lorenz-like state-space form for nonlinear analysis. Numerical simulations employ the fourth-order Runge–Kutta scheme to compute translational and angular responses under varying speeds and terrain conditions. Frequency-domain analysis using Fast Fourier Transform (FFT) identifies resonant excitation bands linked to road spectral content, while Kernel Density Estimation (KDE) maps the probability distribution of displacement states to distinguish stable from variable regimes. The Lyapunov stability assessment and bifurcation analysis reveal critical velocity thresholds and parameter regions marking transitions from stable operation to chaotic motion. The study quantifies the influence of the gravity–damping ratio, mass–damping coupling, control torque ratio, and vertical excitation on dynamic stability. The results provide a methodology for designing stability control systems that ensure safe and comfortable Segway operation across diverse terrains. Full article

In special relativity, particle trajectories, whether mass-bearing or not, can be traced on the Minkowski spacetime manifold in (3+1)D. Meantime, in quantum mechanics, trajectories in the phase space are not strictly outlined because coordinate and linear momentum cannot be measured simultaneously with arbitrary precision since they do not commute within the Hilbert space formalism. However, from the density matrix representing a quantum system, the extracted information still produces an imperative description of its properties and, furthermore, by appropriately reordering the matrix entries, additional information can be obtained from the same content. Adhering to this line of work, the paper investigates the definition and the meaning of velocity and speed in a typical quantum phenomenon, the disentanglement for a bipartite system when dynamical evolution is displayed in a (3+1)D pseudo-spacetime whose coordinates are constructed from combinations of entries to the density matrix. The formalism is based on the definition of a Minkowski manifold with compact support, where trajectories are defined following the same reasoning and formalism present in the Minkowski manifold of special relativity. The space-like and time-like regions acquire different significations referred to entangled-like and separable-like, respectively. The definition and the sense of speed and velocities of disentanglement follow naturally from the formalism. Depending on the dynamics of the physical state of the system, trajectories may meander between regions of entanglement and separability in the space of new coordinates defined on the Minkowski manifold. Full article

We review and as well obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to the calculation of both the equilibrium and nonequilibrium Casimir and Casimir–Polder forces. After a brief summary of the properties of the polarization tensor of graphene obtained within the Dirac model in the framework of quantum field theory, we derive the expressions for the longitudinal and transverse dielectric functions. The behavior of these functions at different temperatures is investigated in the regions below and above the threshold. Special attention is paid to the double pole at zero frequency, which is present in the transverse response function of graphene. An application of the response functions of graphene to the calculation of the equilibrium Casimir force between two graphene sheets and the Casimir–Polder forces between an atom (nanoparticle) and a graphene sheet is considered with due attention to the role of a nonzero energy gap, chemical potential and a material substrate underlying the graphene sheet. The same subject is discussed for out-of-thermal-equilibrium Casimir and Casimir–Polder forces. The role of the obtained and presented results for fundamental science and nanotechnology is outlined. Full article