Physics

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

Measurement uncertainty limits how precisely information can be extracted from quantum systems due to inherent quantum indeterminacy. On the other hand, dense coding capacity quantifies the amount of classical information that can be sent using shared entanglement, thereby enhancing communication efficiency beyond classical limits. In this paper, we investigate these two concepts for a spin-star network under an external magnetic field under a thermal regime, considering both homogeneous and inhomogeneous models. We reveal that under certain conditions, dense coding capacity not only becomes valid but is also optimized, implying that measurement uncertainty is significantly suppressed. Furthermore, we analyze the local quantum uncertainty of the thermal state under the influence of decoherence channels to assess the effectiveness of the approach studied. Full article

We compare the semiclassical and quantum predictions for the unitary dynamics of a two-level atom interacting with a single-mode electromagnetic field under parametric modulation of the atomic parameters in the regime of multiphoton atom–field resonances. We derive approximate analytic solutions for the semiclassical Rabi model when the atomic transition frequency and the atom–field coupling strength undergo harmonic external modulations. These solutions are compared to the predictions of the quantum Rabi model, which we solve numerically for an initial coherent state with a large average photon number (on the order of ${10}^4$), in the regime of three-photon resonance. We show that, for short enough times and sufficiently intense coherent states, the semiclassical dynamics agrees quite well with the quantum dynamics, although it inevitably fails at longer times due to the absence of collapse–revival behavior. Furthermore, we describe how the field state evolves throughout the interaction, presenting numerical results for the average photon number, entropies (related to atom–field entanglement), and other quantities characterizing the photon number statistics of the electromagnetic field. Full article

The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be implemented in two ways: resonant and nonresonant. Under resonant excitation, several coherent modes are generated by external alternating fields with the frequencies been tuned to resonance with some transition frequencies of the trapped system. A Bose system of trapped atoms with Bose–Einstein condensate can display two types of the Josephson effect, the standard one, when the system is separated into two or more parts in different locations, or the internal Josephson effect, when there are no any separation barriers but the system becomes nonuniform due to the coexistence of several coherent modes interacting one with another. The mathematics in both these cases is similar. We focus on the internal Josephson effect. Systems with nonlinear coherent modes demonstrate rich dynamics, including Rabi oscillations, the Josephson effect, and chaotic motion. Under the Josephson effect, there exist dynamic transitions that are similar to phase transitions in equilibrium systems. The bosonic Josephson effect is shown to be implementable not only for quite weakly interacting systems, but also in superfluids with not necessarily as weak interactions. Sufficiently strong nonresonant excitation can generate several types of nonequilibrium states comprising vortex germs, vortex rings, vortex lines, vortex turbulence, droplet turbulence, and wave turbulence. Nonequilibrium states are shown to be characterized and distinguished by effective temperature, effective Fresnel number, and dynamic scaling laws. Full article

We demonstrate the possibility of generation of zonal (shear) flows in a rotating self-gravitating fluid. A set of equations describing the nonlinear interaction between a large-scale zonal flow (ZF) and a small-scale drift-gravity wave is derived. A nonlinear dispersion relation is obtained, from which the possible instability of the ZF follows. The necessary condition for instability in the space of wave numbers of the drift-gravity wave, as well as the instability threshold for the wave amplitude, are obtained. The growth rate of the modulation instability of ZF is found. The generation of ZFs is due to the Reynolds stresses produced by finite amplitude drift-gravity waves. Full article

The production rate of charm quarks in strongly interacting matter is investigated under various conditions, employing the effective quasiparticle framework. This phenomenological approach treats quarks and gluons as quasiparticles with dynamically generated self-energies linked to the medium. This paper studies thermal production of charm quarks in hot deconfined matter when those quarks are treated as impurities with a constant mass or as dynamical quarks dressed by the effective mass. When charm quarks are considered quasiparticles, their large (compared to the bare value) mass generates a significant decrease in the production rate in the crossover region. Various initial conditions for the evolution of the system are applied, showing that lower initial temperature leads to the continual suppression of the charm quark production rate, which appears in line with the previously reported estimate at certain values of the initial parameters. Full article

We consider a multi-species mixture of interacting bosons, $N_1$ bosons of mass $m_1$, $N_2$ bosons of mass $m_2$, and $N_3$ bosons of mass $m_3$, in a harmonic trap with frequency $\omega$. The corresponding intra-species interaction strengths are ${\lambda }_{11}$, ${\lambda }_{22}$, and ${\lambda }_{33}$, and the inter-species interaction strengths are ${\lambda }_{12}$, ${\lambda }_{13}$, and ${\lambda }_{23}$. When the shape of all interactions is harmonic, the system corresponds to the generic multi-species harmonic-interaction model, which is exactly solvable. We start by solving the many-particle Hamiltonian and concisely discussing the ground-state wavefunction and energy in explicit forms as functions of all parameters, the masses, numbers of particles, and the intra-species and inter-species interaction strengths. We then explicitly compute the reduced one-particle density matrices for all the species and diagonalize them, thus generalizing the treatment by the authors earlier. The respective eigenvalues determine the degree of fragmentation of each species. As an application, we focus on phenomena that do not arise in the corresponding single-species or two-species systems. For instance, we consider a mixture of two kinds of bosons in a bath made by a third kind, controlling the fragmentation of the former by coupling to the latter. Another example exploits the possibility of different connectivities (i.e., which species interacts with which species) in the mixture, and demonstrates how the fragmentation of species 3 can be manipulated by the interaction between species 1 and species 2, when species 3 and 1 do not interact with each other. We highlight the properties of fragmentation that only appear in the multi-species mixture. Further applications are briefly discussed. Full article

The Planck constant is a fundamental parameter of nature that appears in the description of phenomena on a microscopic scale. Its origin is associated with an explanation of the distribution of the blackbody spectrum performed by Max Planck. This constant stands the basis for the definition of the International System of Units (SI), and, in particular, the new mass definition. This paper presents different methods for determining the Planck constant based on phenomena such as blackbody radiation, light diffraction through a single slit, the current–voltage characteristics of a light-emitting diode, the photoelectric phenomenon, and the hydrogen atom spectrum in the visible range. The Planck constant was measured using instruments in a stationary laboratory and via remote access. The influence of various factors on the accuracy of the measurements was determined, and the consistency of the obtained results with the accepted value of the Planck constant are examined and discussed. Full article

A new conformally invariant gravitational generalization of the Born–Infeld (BI) model is proposed and analyzed from the point of view of symmetries. Taking a geometric identity involving the determinant functions det$f\left(B_{\mu \nu },F_{\mu \nu }\right)$ with the Bach $B_{\mu \nu }$ and the electromagnetic field $F_{\mu \nu }$ tensors (with the 4-dimensional Greek letter indexes), two characteristic geometrical Lagrangian densities (Lagrangians) are derived: the first Lagrangian being the square root of the determinant function $\sqrt{\left|det\left(B_{\mu \nu }+F_{\mu \nu }\right)\right|}$ (reminiscent of the standard BI model) and the second Lagrangian being the fourth root $\sqrt[4]{gdet\left(B_{\alpha \gamma }{B}_{\beta }^{\gamma }+F_{\alpha \gamma }{F}_{\beta }^{\gamma }\right)}$. It is shown, after explicit computation of the gravitational equations, that the square-root model is incompatible with the inclusion of the electromagnetic tensor, consequently forcing the nullity of $F_{\mu \nu }$. In sharp contrast, the traceless fourth-root model is fully compatible and a natural ansatz of the type $B_{\mu \rho }{B}_{\nu }^{\rho }\propto \mathrm{\Omega }\left(x\right)g_{\mu \nu }$ (conformal-Killing), with $\mathrm{\Omega }$ the conformal factor and x the 4-coordinate, can be considered. Among other essential properties, the geometrical conformal Lagrangian of the fourth-root type is self-similar with respect to the determinant g of the metric tensor $g_{\mu \nu }$ and can be extended to non-Abelian fields in a way similar to the model developed by the author earlier. This self-similarity is related to the conformal properties of the model, such as the Bach currents or flows presumably of a topological origin. Possible applications and comparisons with other models are briefly discussed. Full article

Semiclassical (SC) approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in the phase space but such surface is not available for chaotic systems. An analogous evolution surface underlies SC representations of the evolution operator, albeit in a doubled phase space. Here, it is shown that corresponding to the Fourier transform on a unitary operator, represented as a Green function or spectral Wigner function, a Legendre transform generates a resolvent surface as the classical basis for SC representations of the resolvent operator in the double-phase space, independently of the integrable or chaotic nature of the system. This surface coincides with derivatives of action functions (or generating functions) depending on the choice of appropriate coordinates, and its growth departs from the energy shell following trajectories in the double-phase space. In an initial study of the resolvent surface based on its caustics, its complex nature is revealed to be analogous to a multidimensional sponge. Resummation of the trace of the resolvent in terms of linear combinations of periodic orbits, known as pseudo orbits or composite orbits, provides a cutoff to the SC sum at the Heisenberg time. Here, it is shown that the corresponding actions for higher times can be approximately included within true secondary periodic orbits, in which heteroclinic orbits join multiple windings of relatively short periodic orbits into larger circuits. Full article