Physics, Volume 5, Issue 4 (December 2023) – 14 articles

The paper provides an extended overview of recent results obtained by the authors in the process of studying the vacuum interaction of topological cosmic strings at short distances, taking into account their transverse size a and the mass m of the quantized field. We consider the case of a massive real-valued scalar field with minimal coupling. It is shown that at the interstring distances significantly larger than the Compton length, $l_c=1/m$, the Casimir effect is damped exponentially. On the other hand, at distances smaller than $l_c$ but much larger than the typical string width, the field-mass influence becomes insignificant. In this case, the partial contribution of a massive field to the Casimir energy is of the same order as the contribution of a massless one. At these distances, the string’s transverse size is insignificant also. However, at the interstring distances of the same order as a string radius, the energy of the vacuum interaction of thick strings may significantly surpass the one for two infinitely thin strings with the same mass per unit length. Full article

The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential. Full article

The theory of fluids is used to modify the integral equations of the reference interaction site model (RISM) approximation. Its applicability to the study of biomolecules solvation is evaluated. Unlike traditional RISM applications, the new integral equation contains an intramolecular correlation matrix that only needs to be calculated once. This allows us to bypass the effort of repeatedly solving RISM equations and the time-consuming averaging of values obtained for each time point of a molecular trajectory. The new approach allows for the assessment of the conformational transience of dissolved molecules while taking into account the effects of solvation. The free energy of oxytocin, which is a peptide hormone, as well as self-assembled ionic peptide complexes calculated using both the traditional RISM and the new RISM with average matrix (RISM-AM) approach are estimated. The free energy of oxytocin calculated using RISM-AM shows that the statistical error does not exceed the error obtained by standard averaging of solutions in the RISM equation. Despite the somewhat ambiguous results obtained for ionic peptide self-assembly using RISM-AM with Lennard–Jones repulsion correction, this method can still be considered applicable for fast molecular dynamics analysis. Since the required computational power can be reduced by at least two orders of magnitude, the medium-matrix RISM is indeed a highly applicable tool for studying macromolecular conformations as well as corresponding solvation effects. Full article

In this paper, we discuss quantum formalisms that do not use the axiom of choice. We also consider the fundamental problem that addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the København interpretation of quantum theory, and propose a new approach to this problem (based on the Lefschetz principle). Rather than a theorem–proof paper, this paper describes two new research programs on the foundational level, and focuses on basic open questions that arise in these programs. Full article

We study a graph-based generalization of the Galam opinion formation model. Consider a simple connected graph which represents a social network. Each node in the graph is colored either blue or white, which indicates a positive or negative opinion on a new product or a topic. In each discrete-time round, all nodes are assigned randomly to groups of different sizes, where the node(s) in each group form a clique in the underlying graph. All the nodes simultaneously update their color to the majority color in their group. If there is a tie, each node in the group chooses one of the two colors uniformly at random. Investigating the convergence time of the model, our experiments show that the convergence time is a logarithm function of the number of nodes for a complete graph and a quadratic function for a cycle graph. We also study the various strategies for selecting a set of seed nodes to maximize the final cascade of one of the two colors, motivated by viral marketing. We consider the algorithms where the seed nodes are selected based on the graph structure (nodes’ centrality measures such as degree, betweenness, and closeness) and the individual’s characteristics (activeness and stubbornness). We provide a comparison of such strategies by conducting experiments on different real-world and synthetic networks. Full article

Here, we investigate the actuation dynamics of a micro device with different intervening liquids between the actuating components under the influence of Casimir and dissipative hydrodynamic forces. This is enabled via phase space portraits, which demonstrate that by increasing the dielectric response of the intervening layer the autonomous device may not come into stiction due to the decreasing in magnitude Casmir force. Unlike the micro devices that are placed in vacuum with an intervening liquid, the phase portraits show only a spiral trajectory which eventually stops at a rest position due to the strong energy dissipation by the position dependent hydrodynamic drag forces, even when considering sufficiently strong restoring forces. Moreover, it is feasible to expand the area of motion using intervening liquids with lower dynamic viscosity or increasing the slip length of the intervening fluid. Finally, under the influence of an external driven force, which is the realistic case for possible applications, the system can reach stable oscillation at larger separations with an amplitude higher for the liquid that led to lower Casimir and hydrodynamic forces. Hence, the results presented in this study are essential for studying the dynamical behavior of MEMS and their design in liquid environments. Full article

We present first results of the analysis of optical spectra of two complementary samples of Seyfert galaxies (Seyferts). The first sample was extracted from a selection of the 4th Fermi Gamma-ray Large Area Telescope (4FGL) catalog and consists of 11 $\gamma$-ray-emitting jetted Seyfert galaxies. The second one was extracted from the Swift-BAT AGN Spectroscopic Survey (BASS) and is composed of 38 hard-X-ray-selected active galactic nuclei (AGN). These two samples are complementary, with the former being expected to have smaller viewing angles, while the latter may include objects with larger viewing angles. We measured emission-line ratios to investigate whether the behavior of these Seyferts can be explained in terms of obscuration, as suggested by the Unified Model (UM) of AGN, or if there are intrinsic differences due to the presence of jets or outflows, or due to evolution. We found no indications of intrinsic differences. The UM remains the most plausible interpretation for these classes of objects, even if some results can be challenging for this model. Full article

Absorptive corrections, which are known to suppress proton-neutron transitions with a large fractional momentum $z\to 1$ in $pp$ collisions, become dramatically strong on a nuclear target, and they push the partial cross sections of leading neutron production to the very periphery of the nucleus. The mechanism of the pion $\pi$ and axial vector meson $a_1$ interference, which successfully explains the observed single-spin asymmetry in a polarized $pp\to nX$, is extended to the collisions of polarized protons with nuclei. When corrected for nuclear effects, it explains the observed single-spin azimuthal asymmetry of neutrons that is produced in inelastic events, which is where the nucleus violently breaks up. This single-spin asymmetry is found to be negative and nearly atomic mass number A-independent. Full article

The study of opinion formation and dynamics is one of the core topics in sociophysics. In this paper, the results of computer simulation of opinion dynamics based on social impact theory are presented. The simulations are based on Latané theory in its computerised version proposed by Nowak, Szamrej and Latané. The active parameters of the model describe the volatility of the actors (social temperature T) and the effective range of interaction (governed by an exponent $\alpha$ in a scaling function of distance between actors). Initially, every actor i has his/her own opinion. Our results indicate that ultimately at least 90% of the initial opinions available are removed from the society. For a low social temperature and a long range of interaction, only one opinion survives. Also, a rough sketch of the system phase diagram is presented. It indicates a set of ($\alpha ,T$) leading either to (1) the dominance of the unanimity of the opinions or (2) mixtures of unanimity and polarisation, or (3) taking random opinions by actors, or (4) a mixture of the final fates of the systems. The drastic reduction of finally observed opinions vs. their initial variety may be generic for many sociophysical models of opinions formation but masked by assuming an initially small pool of available opinions (in the worst case, in models with only binary opinions). Full article

We consider the Casimir pressure between two graphene sheets and contributions to it determined by evanescent and propagating waves with different polarizations. For this purpose, the derivation of the 2-dimensional (2D) Fresnel reflection coefficients on a graphene sheet is presented in terms of the transverse and longitudinal dielectric permittivities of graphene with due account of the spatial dispersion. The explicit expressions for both dielectric permittivities as the functions of the 2D wave vector, frequency, and temperature are written along the real frequency axis in the regions of propagating and evanescent waves and at the pure imaginary Matsubara frequencies using the polarization tensor of graphene. It is shown that in the application region of the Dirac model nearly the total value of the Casimir pressure between two graphene sheets is determined by the electromagnetic field with transverse magnetic (TM) polarization. By using the Lifshitz formula written along the real frequency axis, the contributions of the TM-polarized propagating and evanescent waves into the total pressure are determined. By confronting these results with the analogous results found for plates made of real metals, the way for bringing the Lifshitz theory using the realistic response functions in agreement with measurements of the Casimir force between metallic test bodies is pointed out. Full article

Using the formulation of the electromagnetic Green’s function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir–Polder interaction energy of a cone with a polarizable particle. We introduce this formalism by first reviewing the analogous approach for a perfectly conducting wedge, and then demonstrate the calculation through numerical evaluation of the resulting integrals. Full article

The minimal length conjecture is merged with a generalized quantum uncertainty formula, where we identify the minimal uncertainty in a particle’s position as the minimal measurable length scale. Thus, we obtain a quantum-induced deformation parameter that directly depends on the chosen minimal length scale. This quantum-induced deformation is conjectured to require the generalization of Riemannian spacetime geometry underlying the classical theory of general relativity to an eight-dimensional spacetime fiber bundle, which dictates the deformation of the line element, metric tensor, Levi-Civita connection, Riemann curvature tensor, etc. We calculate the deformation thus produced in the Levi-Civita connection and find it to explicitly and exclusively depend on the product of the minimum measurable length and the particle’s spacelike four-acceleration vector, $L^2{\ddot{x}}^2$. We find that the deformed Levi-Civita connection preserves all properties of its undeformed counterpart, such as torsion freedom and metric compatibility. Accordingly, we have constructed a deformed version of the Riemann curvature tensor whose expression can be factorized in all its terms with different functions of $L^2{\ddot{x}}^2$. We also show that the classical four-manifold status of being Riemannian is preserved when the quantum-induced deformation is negligible. We study the dependence of a parallel-transported tangent vector on the spacelike four-acceleration. We illustrate the impact of the minimal-length-induced quantum deformation on the classical geometrical objects of the general theory of relativity using the unit radius two-sphere example. We conclude that the minimal length deformation implies a correction to the spacetime curvature and its contractions, which is manifest in the additional curvature terms of the corrected Riemann tensor. Accordingly, quantum-induced effects endow an additional spacetime curvature and geometrical structure. Full article

We analyze the correlations functions across the horizon in Hawking black hole radiation to reveal the correlations between Hawking particles and their partners. The effects of the underlying space–time on this are shown in various examples ranging from acoustic black holes to regular black holes. Full article

We consider the Casimir pressure between two metallic plates and calculate the four contributions to it determined by the propagating and evanescent waves and by the transverse magnetic and transverse electric polarizations of the electromagnetic field. The range of interplate separations is considered where nearly the whole pressure has its origin in the electromagnetic response of conduction electrons. In the Casimir physics, this response is described either by the dissipative Drude model resulting in contradictions with the measurement data or by the experimentally consistent but dissipationless plasma model. It is shown that the total transverse magnetic contribution to the Casimir pressure due to both the propagating and evanescent waves and the transverse electric contribution due to only the propagating waves, computed by means of the Drude model, correlate well with the corresponding results obtained using the plasma model. We conclude that the disagreement between the theoretical predictions obtained using the Drude model and precision measurements of the Casimir force is not caused by the account of dissipation in itself, but arises from an incorrect description of the response of metals to the low-frequency transverse electric evanescent waves by this model. It is demonstrated that the Drude model has no supporting experimental evidence in the range of transverse electric evanescent waves, so that the above conclusion is consistent with all available information. The alternative test of the Drude model for the transverse electric evanescent waves suggested in the framework of classical electrodynamics is discussed. Full article