Physics

This paper presents a two-qubit model derived from an SU(2)-symmetric 4×4 Hamiltonian. The resulting model is physically significant and, due to the SU(2) symmetry, is exactly solvable in both time-independent and time-dependent cases. Using the formal, general form of the related time evolution operator, the time dependence of the entanglement level for certain initial conditions is examined within the Rabi and Landau–Majorana–Stückelberg–Zener scenarios. The potential for applying this approach to higher-dimensional Hamiltonians to develop more complex exactly solvable models of interacting qubits is also highlighted. Full article

The elastic and inelastic scattering of deuterons on ¹⁰B nuclei and the ¹⁰B(d, t)⁹B reaction were studied at a deuteron energy of 14.5 MeV. In inelastic scattering, differential cross-sections for transitions to ¹⁰B states at excitation energies, E_x, of 0.718 MeV (1⁺), 2.154 MeV (1⁺), and 3.59 MeV (2⁺) were measured. The cross-sections of the (d, t) reaction were measured for the ground (3/2⁻) and excited states of the ⁹B nucleus at E_x = 2.361 MeV (5/2⁻) and 2.79 MeV (5/2⁺). An analysis of the corresponding angular distributions was carried out using the coupled channel method. As a result of the calculations, the values of the quadrupole deformation parameters (β₂ ≈ 0.7 ± 0.1) for various transitions in the ¹⁰B nucleus in inelastic scattering were extracted. From the analysis of the (d, t) reaction, the values of spectroscopic amplitudes (SA = 0.67 and SA = 0.94) for transitions to the states of the ⁹B nucleus were extracted. The results obtained here, taking into account possible measurement errors, are in good agreement with the previously obtained data and the theoretical predictions. Full article

Ferroelectric charged domain walls offer a revolutionary path for next-generation ferroelectric devices due to their exceptional conductivity within an otherwise insulating matrix. However, quantitative understanding of this “giant conductivity” has remained elusive due to the lack of robust models describing carrier behavior within CDWs. The current paper bridges this critical knowledge gap by employing a first-principles approach that incorporates Boltzmann transport theory and the relaxation time approximation. This strategy enables the calculation of carrier concentration, mobility, and conductivity for both head-to-head and tail-to-tail domain wall configurations within a stabilized periodic structure. The comprehensive transport analysis given here reveals that the accumulation of charge carriers, particularly their concentration, is the dominant factor governing domain wall conductance. Interestingly, observed conductance differences between head-to-head and tail-to-tail walls primarily arise from variations in carrier mobility. Additionally, this study demonstrates a significantly reduced domain wall width compared to previous reports. This miniaturization is attributed to the presence of compressive strain, which lowers the energy barrier for electron–hole pair generation. Furthermore, the findings here suggest that reducing the band gap presents a viable strategy for stabilizing charged domain walls. These results pave the way for the optimization and development of domain wall devices across a spectrum of ferroelectric materials. Full article

In the present introductory to the Special Issue “75 Years of the Casimir Effect: Advances and Prospects”, we summarize the state of the art in this field of physics, briefly describe the topics of the contributing papers, formulate several unresolved problems, and outline possible pathways towards their resolution. Special attention is given to experiments on measuring the Casimir force, to the known problem of the dissipation of conduction electrons when one compares experiment with theory, and to the Casimir effect in novel materials and non-traditional situations. We conclude that in the future, this multidisciplinary quantum effect will continue to play a crucial role in both fundamental physics and its applications. Full article

In this paper, we review some recent findings related to the Casimir effect. Initially, the thermal corrections to the vacuum Casimir energy density are calculated, for a quantum scalar field, whose modes propagate in the (3+1)-dimensional Euclidean spacetime, subject to a nontrivial compact boundary condition. Next, we analyze the Casimir effect induced by two parallel plates placed in a weak gravitational field background. Finally, we review the three-dimensional wormhole solutions sourced by the Casimir density and pressures associated with the quantum vacuum fluctuations of the Yang-Mills field. Full article

We review the formalism of center-of-mass tomograms, which allows us to describe quantum states in terms of probability distribution functions. We introduce the concept of separable and entangled probability distributions for center-of-mass tomography. We obtain the time evolution of center-of-mass tomograms of entangled states of the inverted oscillator. Full article

Traditional models of opinion dynamics provide a simplified approach to understanding human behavior in basic social scenarios. However, when it comes to issues such as polarization and extremism, a more nuanced understanding of human biases and cognitive tendencies are required. This paper proposes an approach to modeling opinion dynamics by integrating mental models and assumptions of individuals agents using Bayesian-inspired methods. By exploring the relationship between human rationality and Bayesian theory, this paper demonstrates the usefulness of these methods in describing how opinions evolve. The analysis here builds upon the basic idea in the Continuous Opinions and Discrete Actions (CODA) model, by applying Bayesian-inspired rules to account for key human behaviors such as confirmation bias, motivated reasoning, and human reluctance to change opinions. Through this, This paper updates rules that are compatible with known human biases. The current work sheds light on the role of human biases in shaping opinion dynamics. I hope that by making the model more realistic this might lead to more accurate predictions of real-world scenarios. Full article

Magnetic quantum oscillations (MQOs) are traditionally applied to investigate the electronic structure of metals. In layered quasi-two-dimensional (Q2D) materials, the MQOs have several qualitative features, offering additional helpful information, provided their theoretical description is developed. Within the framework of the Kubo formula and the self-consistent Born approximation, we reconsider the phase of the beats in the amplitude of the Shubnikov oscillations of the interlayer conductivity in Q2D metals. We show that the phase shift of the beats of the Shubnikov (conductivity) oscillations relative to the de Haas–van Alphen (magnetization) oscillations is larger than woud be expected and, under certain conditions, can reach the value of $\pi /2$, as observed experimentally. We explain the phase inversion of the MQOs during the 3D–2D crossover and predict the decrease in the relative MQO amplitude of the interlayer magnetoresistance in a strong magnetic field, larger than the beat frequency. Full article

An approach to derive the below-bandgap absorption in GaSb/GaAs self-assembled quantum dot devices using room-temperature external quantum efficiency measurement results is presented. Devices with five layers of delta-doped quantum dots placed in the intrinsic, n- and p-regions of a GaAs solar cell are studied. The importance of incorporating an extended Urbach tail absorption in analyzing the absorption strength of quantum dots and the transition states is demonstrated. The theoretically integrated absorbance via quantum dot ground states is calculated as 1.04 × 10¹⁵ cm⁻¹s⁻¹, which is in reasonable agreement with the experimentally derived value 8.1 × 10¹⁵ cm⁻¹s⁻¹. The wetting layer and quantum dot absorption contributions are separated from the tail absorption and their transition energies are calculated. Using these transition energies and the GaAs energy gap of 1.42 eV, the heavy hole confinement energies for the quantum dots (320 meV) and for the wetting layer (120 meV) are estimated. Full article

On 17 October 1947, Niels Bohr was made a knight of the Order of the Elephant by the King of Denmark in view of his outstanding achievements and contributions to science. Bohr designed his own coat of arms that featured a pattern of Yin and Yang (Tai Chi symbol) to symbolize the wave–particle complementarity. However, Bohr’s Yin-Yang diagram (YYD) was neither drawn based on the principles of quantum mechanics, nor did it originate from the traditional Taoist YYD. Scientists still have doubts about the legitimacy of using YYD as the icon of the wave–particle complementarity, because the YYD belonging to quantum mechanics itself is unknown so far. This paper reports the YYDs existing in quantum mechanics and justifies the role of YYD in the wave–particle duality by showing that any system, whether classical or quantum, has an ideal YYD as long as it satisfies Bohr’s principle of complementarity (BPC). The deviation of a deformed YYD from the ideal YYD indicates the extent to which a real system satisfies BPC. This paper constructs the quantum YYD by the complex quantum trajectory of a particle tunneling via a step barrier, which displays the continuous transition between the wave behavior and the particle behavior. It appears that the YYD designed by Bohr in his coat of arms resembles the YYD generated by tunneling motion, not only in appearance but also in the governing equation. Full article

Based on the position and momentum of noncommutative relations with a noncanonical map, we study the Dirac equation and analyze its parity and time reversal symmetries in a noncommutative phase space. Noncommutative parameters can be endowed with the Planck length and cosmological constant such that the noncommutative effect can be interpreted as an effective gauge potential or a $(0,2)$-type curvature associated with the Plank constant and cosmological constant. This provides a natural coupling between dynamics and spacetime geometry. We find that a free Dirac particle carries an intrinsic velocity and force induced by the noncommutative algebra. These properties provide a novel insight into the Zitterbewegung oscillation and the physical scenario of dark energy. Using perturbation theory, we derive the perturbed and nonrelativistic solutions of the Dirac equation. The asymmetric vacuum gaps of particles and antiparticles reveal the particle–antiparticle symmetry breaking in the noncommutative phase space, which provides a clue to understanding the physical mechanisms of particle–antiparticle asymmetry and quantum decoherence through quantum spacetime fluctuation. Full article

There are numerous instabilities present in charged particle beams that undergo exponential growth and reach saturation. In various applications, such as free-electron lasers or micro-bunching light sources, achieving saturation is desirable. Conversely, there are applications where these instabilities are utilized as linear broad-band amplifiers for signals embedded in the charged beam. In the latter scenario, the saturation of an instability induces non-linear distortions in the imprinted signal, thereby limiting the useful range of such amplifiers. Accurate evaluation of these instabilities necessitates a complete and comprehensive modeling approach that includes shot noise within the beam. Unfortunately, such modeling is not always feasible or practical. In this paper, we introduce a methodology utilizing the frequency and bandwidth of the instability as key parameters. Through this, we derive an estimation for the range of linear instability growth. Our derivation is conducted in a model-independent manner, making it applicable to a broad spectrum of instabilities. To validate our approach, we employ established and thoroughly benchmarked simulations with a free electron laser (FEL) code as well as self-consistent 3-dimensional simulation of plasma-cascade instability using code SPACE. Full article

We investigate the effects of the electromagnetic vacuum field on a harmonically bound electron. We show that in the electric-dipole approximation the model atom couples only to an effective one-dimensional electric field. In a simplified form, in which the problem is reduced to a single spatial dimension, we determine, analytically, the form of the ground state and discuss the significance of this state. Full article

Here, we review recent advances in precision Casimir force measurements with both non-magnetic and magnetic materials. In addition, the measurement of the geometric dependence of the Casimir force, both lateral and normal, using uniformly corrugated surfaces is briefly presented. Finally, the measurement of the thermal Casimir force in graphene is discussed. Full article

The mass $m_{{\mu }^{-}}$ of the negative muon is one of the parameters of the elementary particle Standard Model and it allows us to verify the CPT (charge–parity–time) symmetry theorem by comparing $m_{{\mu }^{-}}$ value with the mass $m_{{\mu }^{+}}$ of the positive muon. However, the experimental determination precision of $m_{{\mu }^{-}}$ is $3.1\mathrm{ppm}$, which is an order of magnitude lower than the determination precision of $m_{{\mu }^{+}}$ at $120\mathrm{ppb}$. The authors aim to determine $m_{{\mu }^{-}}$ and the magnetic moment ${\mu }_{{\mu }^{-}}$ with a precision of $\mathcal{O}\left(10\mathrm{ppb}\right)$ through spectroscopy of the hyperfine structure (HFS) of muonic helium-4 atom ${(}^4\mathrm{He}{\mu }^{-}{e}^{-})$ under high magnetic fields. ${}^4\mathrm{He}{\mu }^{-}{e}^{-}$ is an exotic atom where one of the two electrons of the ${}^4\mathrm{He}$ atom is replaced by a negative muon. To achieve the goal, it is necessary to determine the HFS of ${}^4\mathrm{He}{\mu }^{-}{e}^{-}$ with a precision of $\mathcal{O}\left(1\mathrm{ppb}\right)$. This paper describes the determination procedure of the HFS of ${}^4\mathrm{He}{\mu }^{-}{e}^{-}$ in weak magnetic fields reported recently, and the work towards achieving the goal of higher precision measurement. Full article

To curb the spread of fake news, I propose an alternative to the current trend of implementing coercive measures. This approach would preserve freedom of speech while neutralizing the social impact of fake news. The proposal relies on creating an environment to naturally sequestrate fake news within quite small networks of people. I illustrate the process using a stylized model of opinion dynamics. In particular, I explore the effect of a simultaneous activation of prejudice tie breaking and contrarian behavior, on the spread of fake news. The results show that indeed most pieces of fake news do not propagate beyond quite small groups of people and thus pose no global threat. However, some peculiar sets of parameters are found to boost fake news so that it “naturally” invades an entire community with no resistance, even if initially shared by only a handful of agents. These findings identify the modifications of the parameters required to reverse the boosting effect into a sequestration effect by an appropriate reshaping of the social geometry of the opinion dynamics landscape. Then, all fake news items become “naturally” trapped inside limited networks of people. No prohibition is required. The next significant challenge is implementing this groundbreaking scheme within social media. Full article

The International System of Units (SI), the current form of the metric system and the world’s most used system of units, has been continuously updated and refined since the Metre Convention of 1875 to ensure that it remains up to date with the latest scientific and technological advances. The General Conference on Weights and Measures, at its 26th meeting in 2018, decided to adopt stipulated values of seven physical constants linked to seven measurement units (the second, meter, kilogram, ampere, kelvin, mole, and candela). This paper reviews the technologies developed, in intense and long-standing work, to determine the Avogadro and Planck constants, which are now integral to realising the kilogram. Full article

The mutual influences of the electric field, rotation, and heat transmission find applications in controlled drug delivery systems, precise microfluidic manipulation, and advanced materials’ processing techniques due to their ability to tailor fluid behavior and surface morphology with enhanced precision and efficiency. Capillary instability has widespread relevance in various natural and industrial processes, ranging from the breakup of liquid jets and the formation of droplets in inkjet printing to the dynamics of thin liquid films and the behavior of liquid bridges in microgravity environments. This study examines the swirling impact on the instability arising from the capillary effects at the boundary of Rivlin–Ericksen and viscous liquids, influenced by an axial electric field, heat, and mass transmission. Capillary instability arises when the cohesive forces at the interface between two fluids are disrupted by perturbations, leading to the formation of characteristic patterns such as waves or droplets. The influence of gravity and fluid flow velocity is disregarded in the context of capillary instability analyses. The annular region is formed by two cylinders: one containing a viscous fluid and the other a Rivlin–Ericksen viscoelastic fluid. The Rivlin–Ericksen model is pivotal for comprehending the characteristics of viscoelastic fluids, widely utilized in industrial and biological contexts. It precisely characterizes their rheological complexities, encompassing elasticity and viscosity, critical for forecasting flow dynamics in polymer processing, food production, and drug delivery. Moreover, its applications extend to biomedical engineering, offering insights crucial for medical device design and understanding biological phenomena like blood flow. The inside cylinder remains stationary, and the outside cylinder rotates at a steady pace. A numerically analyzed quadratic growth rate is obtained from perturbed equations using potential flow theory and the Rivlin–Ericksen fluid model. The findings demonstrate enhanced stability due to the heat and mass transfer and increased stability from swirling. Notably, the heat transfer stabilizes the interface, while the density ratio and centrifuge number also impact stability. An axial electric field exhibits a dual effect, with certain permittivity and conductivity ratios causing perturbation growth decay or expansion. Full article