Search Results (101)

In this investigation, we explore previously unknown relations between natural constants by taking the following steps: (1) We discard Dirac’s constant ℏ from the universal man-made constants of physics, which we redefine in terms of Planck’s constant h. (2) Working in the SI system of units, we determine Newton’s gravitational constant G from Boltzmann’s constant $k_{\mathrm{B}}$ and the elementary charge e, recognizing the entropy of matter as their common underlying characteristic. (3) By comparing the mass of 1 mole of electrons to the h-defined Planck mass $M_{\mathrm{P}}$, we deduce nature’s own molar constant ($\simeq$0.1 mol) that contains a ‘reduced Avogadro number’ ${\aleph }_{\mathrm{A}}=N_{\mathrm{A}}/f_{\mathrm{A}}$ of particles, where $N_{\mathrm{A}}$ is Avogadro’s number and $f_{\mathrm{A}}\simeq 10$ is the associated Avogadro factor. (4) From the new effective gravitational constant $G_{★}\equiv 4\pi {\epsilon }_{0}G$, where ${\epsilon }_0$ is the vacuum permittivity, we obtain MOND’s universal constant ${\mathcal{A}}_0$ and its critical acceleration $a_0$, recognizing the Newtonian source of gravity as the common underlying characteristic and repudiating the need for a principle of equivalence of masses. (5) We derive the gravitational coupling constant ${\mathsf{\alpha }}_{\mathrm{g}}$ solely from ${\aleph }_{\mathrm{A}}$. (6) We adopt the measured value of the h-defined fine-structure constant (FSC) $\mathsf{\alpha }$ and the value of ${\mathsf{\alpha }}_{\mathrm{g}}$ (or, equivalently, nature’s ${\aleph }_{\mathrm{A}}$), and we determine the relative ratio ${\mathsf{\beta }}_{\mathrm{g}}={\mathsf{\alpha }}_{\mathrm{g}}/\mathsf{\alpha }$ precise to 10 significant digits. (7) We derive the relative strong ratio ${\mathsf{\beta }}_{\mathrm{s}}={\mathsf{\alpha }}_{\mathrm{s}}/\mathsf{\alpha }$ directly from the Avogadro factor $f_{\mathrm{A}}$. (8) We determine the coupling constants of weak and strong interactions (${\mathsf{\alpha }}_{\mathrm{w}}$ and ${\mathsf{\alpha }}_{\mathrm{s}}$, respectively) in terms of the FSC $\mathsf{\alpha }$. (9) The relation ${\mathsf{\alpha }}_{\mathrm{w}}=\sqrt{\mathsf{\alpha }}$ leads to a determination of the mass of the W boson $m_{\mathrm{W}}$ from the measured values of $\mathsf{\alpha }$ and the reduced Fermi constant $G_{\mathrm{F}}^0$. (10) Using the Planck mass as a principal constant ($M_{\mathrm{P}}={\aleph }_{\mathrm{A}}{m}_{\mathrm{e}}$, where $m_{\mathrm{e}}$ is the electron mass), we obtain new classical definitions of $h,\mathsf{\alpha }$, and the Compton radius $r_{\mathrm{c}}$; and we reformulate in a transparent, geometrically clear way several important QED equations, as well as the extended Planck system of units itself. We discuss the implications of these results, and we pave a way forward in exploring the unification of the fundamental forces of nature. Full article

Based on first-principles calculations and linear-response time-dependent density functional theory within the random phase approximation (LR-TDDFT-RPA), this work systematically investigates the modulation of Dirac plasmons in germanene via carrier doping, biaxial strain, and substrate effects. The results demonstrate that carrier doping induces highly tunable Dirac plasmons whose excitation energy follows the ω ∝ n^1/4 scaling relation, leading to a sublinear increase with doping concentration. Furthermore, biaxial strain effectively modulates the Fermi velocity, and the established ω ∝ √V_F relationship directly explains the observed linear tuning of plasmon energy with strain. More importantly, the combined modulation of carrier density and strain enables a significantly broader plasmon energy range (0.16–0.61 eV) than achievable through individual parameter control. When supported on hBN substrates, germanene maintains the characteristic √q plasmon dispersion despite band hybridization and a redshift in energy, a behavior well explained by the 2D free electron gas model. This study provides important theoretical insights into the multi-parameter control of Dirac plasmons and supports the design of germanene-based tunable nanophotonic devices. Full article

This study investigates the effect of temperature on the performance of the single-walled carbon nanotube (SWCNT) film/Si photodetector. Specifically, the photocurrent across a SWCNT/Si heterojunction when illuminated with light of 632.8 nm wavelength of different powers was studied in detail in a wide temperature range, from 20 to 300 K. The objective was to determine the parameters of the heterojunction, which is inherently inhomogeneous, and to identify the main ones that determine the optoelectronic figures of merit of a photodetector based on it. The barrier height and its temperature dependence were determined within the framework of the theory of thermionic emission, taking into account the non-uniform distribution of the barrier height over the heterojunction area. The parameters of the heterojunction and SWCNT/Si interface and their temperature dependences were calculated based on the known temperature dependences of the concentration of charge carriers and ionized impurities in Si using the Poisson equation based on Fermi–Dirac statistics. The obtained results indicate the importance of interplay between the effects of reducing the barrier height and the processes of decreasing the separation efficiency of nonequilibrium charge carriers and increasing the rate of their recombination. Full article

Ru₃Sn₇ crystallizes in the cubic Ir₃Ge₇-type structure (space group Im3m), a class of intermetallic compounds. Previous studies focused primarily on its crystal structure, band calculations, and basic transport properties. Here, we report a systematic investigation of high-quality single crystals via electrical resistivity, Hall effect, specific heat, and thermal transport measurements. The T₃X₇ intermetallic family—with its diverse electronic ground states—provides an ideal platform for exploring such topology–property relationships. Ru₃Sn₇ exhibits metallic behavior, with consistent Hall effect and Seebeck coefficient data indicating a compensated electron-hole two-band system. Temperature-dependent modulation of electronic states near the Fermi surface alters charge carrier transport, which may imply the presence of a Lifshitz transition in Ru₃Sn₇. More importantly, magnetic quantum oscillations are observed for the first time, confirming the presence of two Dirac points in its band structure. Full article

The Thomas–Fermi model and its quantum and exchange corrections with mathematic manipulations and numerical approaches are primarily investigated. The reduced ideal electron chemical potential is adopted as the initial value for the iterative solution of the Thomas–Fermi model. A new transformation for the quantum and exchange equations is proposed to apply the boundary conditions easily. Both the Thomas–Fermi equation and correction equations are solved with the Runge–Kutta algorithm. The mathematical difficulties in controlling the computing accuracy of the equations containing the Fermi–Dirac integral are settled. The equation of state, based on the Thomas–Fermi model with its quantum and exchange corrections, is constructed and compared with relevant data. Full article

The paper outlines the hybrid framework of spin hydrodynamics, combining classical kinetic theory with the Israel–Stewart method of introducing dissipation. The local equilibrium expressions for the baryon current, the energy–momentum tensor, and the spin tensor of particles with spin 1/2 following the Fermi–Dirac statistics are obtained and compared with the earlier derived versions where the Boltzmann approximation was used. The expressions in the two cases are found to have the same form, but the coefficients are shown to be governed by different functions. The relative differences between the tensor coefficients in the Fermi–Dirac and Boltzmann cases are found to grow exponentially with the baryon chemical potential. In the proposed formalism, nonequilibrium processes are studied including mathematically possible dissipative corrections. Standard conservation laws are applied, and the condition of positive entropy production is shown to allow for the transfer between the spin and orbital parts of angular momentum. Full article

We introduce a modern methodology for constructing global analytical approximations of special functions over their entire domains. By integrating the traditional method of matching asymptotic expansions—enhanced with Padé approximants—with differential evolution optimization, a modern machine learning technique, we achieve high-accuracy approximations using elegantly simple expressions. This method transforms non-elementary functions, which lack closed-form expressions and are often defined by integrals or infinite series, into simple analytical forms. This transformation enables deeper qualitative analysis and offers an efficient alternative to existing computational techniques. We demonstrate the effectiveness of our method by deriving an analytical expression for the Fermi gas pressure that has not been previously reported. Additionally, we apply our approach to the one-loop correction in thermal field theory, the synchrotron functions, common Fermi–Dirac integrals, and the error function, showcasing superior range and accuracy over prior studies. Full article

We consider the macroscopic motion of the normal component of superfluid ³He-A in global thermodynamic equilibrium within the context of the Zubarev statistical operator method. We formulate the corresponding effective theory in the language of the functional integral. The effective Lagrangian comprising macroscopic motion of fermionic excitations is calculated explicitly for the emergent relativistic fermions of the superfluid ³He-A phase immersed in a non-trivial bosonic background due to a space- and time-dependent matrix-valued vierbein featuring nonzero torsion as well as the Nieh–Yan anomaly. We do not consider the dynamics of the superfluid component itself and thereby its backreaction effects due to normal component macroscopic flow. It is treated as an external background within which the emergent relativistic fermions of the normal component move. The matrix-valued vierbein formulation comprises an additional two-dimensional internal spin space for the two axially charged Weyl fermions living at the Fermi points, which may be replaced by one featuring a Dirac fermion doublet with a real-valued vierbein, an axial Abelian gauge field, and a spin connection gauge field mixing the Dirac and internal spin spaces. We carry out this change of description in detail and determine the constraints on the superfluid background as well as the the normal component motion as determined from the Zubarev statistical operator formalism in global thermodynamic equilibrium. As an application of the developed theory, we consider macroscopic rotation around the axis of pure integer mass vortices. The corresponding thermodynamic quantities of the normal component are analyzed. Our formulation incorporates both superfluid background flow and macroscopic motion flow of the normal component and thereby enables an analysis of their interrelation. Full article

Accurately controlling the mechanical properties of silicon is essential for developing high-performance micro-devices and systems. In this study, we investigate the influence of phosphorus doping on the elastic constants of silicon across a wide temperature range using a combination of tight-binding simulations and deformation potential theory. The mechanical properties were derived using Keyes’s framework integrated with Fermi–Dirac statistics. The Goodwin–Skinner–Pettifor functional form was applied to estimate dopant-induced stress potentials and their effect on lattice stiffness. In particular, we investigated the change in elastic constants and their temperature dependence under ultra-high doping concentrations. The results show a monotonic decrease in c₁₁ and a non-monotonic increase in c₁₂ with both temperature and doping, while c₄₄ remains relatively unaffected, consistent with experimental and theoretical studies. These changes are attributed to anisotropic carrier redistribution among conduction band valleys and strain-modulated interactions between valleys. The novelty of this work lies in the explicit, atomistically informed calculation of deformation potential constants using tight-binding parameters specific to phosphorus doping in silicon, enabling the accurate prediction of temperature-dependent elastic constants and anisotropic mechanical behaviour in emerging microsystem applications. Full article

This paper elaborates on the proposal of a new analytical model for a non-ballistic transport scenario for Schottky barrier carbon nanotube field effect transistors (SB-CNTFETs). The non-ballistic transport scenario depends on incorporating the effects of acoustic phonon (A-Ph) and optical phonon (O-Ph) electron scattering mechanisms. The analytical model is rooted in the solution of the Landauer integral equation, which is modified to account for non-ballistic transport through a set of approximations applied to the Wentzel–Kramers–Brillouin (WKB) transmission probability and the Fermi–Dirac distribution function. Our proposed model was simulated to evaluate the total current and transconductance, considering scenarios both with and without the electron–phonon scattering effect. The simulation results revealed a substantial decrease of approximately 78.6% in both total current and transconductance due to electron–phonon scattering. In addition, we investigated the impact of acoustic phonon (A-Ph) and optical phonon (O-Ph) scattering on the drain current under various conditions, including different temperatures, gate lengths, and nanotube chiralities. This comprehensive analysis helps in understanding how these parameters influence device performance. Compared with experimental data, the model’s simulation results demonstrate a high degree of agreement. Furthermore, our fully analytical model achieves a significantly faster runtime, clocking in at around 2.726 s. This validation underscores the model’s accuracy and reliability in predicting the behavior of SB-CNTFETs under non-ballistic conditions. Full article

Layered perovskites have been actively studied due to their outstanding electronic and optical properties as well as kinetic stability. Layered perovskites with hexagonal symmetry have special electronic properties, such as the Dirac cone in the band structure, similar to graphene. In the presented study, the heterostructure of single-layer all-inorganic lead-free hexagonal perovskite of the A₃B₂X₉ type (A = Cs, Rb, K; B = In, Sb; X = Cl, Br) and graphene (Gr) was studied. The structural and electronic characteristics of A₃B₂X₉ and the A₃B₂X₉/Gr composite were calculated using density functional theory. It was found that graphene is not deformed, while the main deformation is observed only in perovskite. B-X bonds have different sensitivities to stretching or compression. The Fermi level of the A₃In₂X₉/Gr composite can be shifted down from the Dirac point, which can be used to create optoelectronic devices or as spacer layers for graphene-based resonant tunneling nanostructures. Full article

An electric field applied to the Bernal-stacked bilayer graphene opens an energy gap; its reversal in some regions creates domain walls and leads to the appearance of one-dimensional chiral gapless states localized at the walls. Here, we investigate the energy structure of bilayer graphene with superlattice potential defined by an external electric field. The calculations are performed within an atomistic π-electron tight-binding approximation. We study one-dimensional and two-dimensional superlattices formed by arrays of electric-field walls in the zigzag and armchair directions and investigate different field polarizations. Chiral gapless states discretize due to the superlattice potential and transform into minibands in the energy gap. As the main result, we show that the minibands can cross at the Fermi level for some field polarizations. This leads to a new kind of two-dimensional gapless states of topological character that form Dirac-like cones at the crossing points. This also has application potential: changing the field polarization can close the energy gap and change the character of the superlattice from semiconducting to metallic. Full article

This study proposes a novel theoretical approach to understanding the statistical–mechanical similarities between nuclear fission phenomena and semiconductor physics. Using the Hill–Wheeler formula as a quantum mechanical distribution function and establishing its correspondence with the Fermi–Dirac distribution function, we analyzed nuclear fission processes for nine nuclides (²³²Th, ²³³U, ²³⁵U, ²³⁸U, ²³⁷Np, ²³⁹Pu, ²⁴⁰Pu, ²⁴²Pu, ²⁴¹Am) using JENDL-5.0 data. Full article

We explore the equivalence between the low-energy dynamics of strained graphene and a quantum mechanical framework for the 2D Dirac equation in flat space with a deformed momentum operator. By considering some common forms of the anisotropic Fermi velocity tensor emerging from the elasticity theory, we associate such tensor forms with a deformation of the momentum operator. We first explore the bound states of charge carriers in a background uniform magnetic field in this framework and quantify the impact of strain in the energy spectrum. Then, we use a quadrature algebra formula as a mathematical tool to analyze the impact of the deformation attached to the momentum operator and identify physical consequences of such deformation in terms of energy modifications due to the applied strain. Full article

We introduce a novel entropy minimization approach for the solution of constrained linear regression problems. Rather than minimizing the quadratic error, our method minimizes the Fermi–Dirac entropy, with the problem data incorporated as constraints. In addition to providing a solution to the linear regression problem, this approach also estimates the measurement error. The only prior assumption made about the errors is analogous to the assumption made about the unknown regression coefficients: specifically, the size of the interval within which they are expected to lie. We compare the results of our approach with those obtained using the disciplined convex optimization methodology. Furthermore, we address consistency issues and present examples to illustrate the effectiveness of our method. Full article