Search Results (19)

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 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 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

The sun is a fundamental element of the natural environment, and kinetic equations are crucial mathematical models for determining how quickly the chemical composition of a star like the sun is changing. Taking motivation from these facts, we develop and solve a novel fractional kinetic equation containing Fermi–Dirac (FD) and Bose–Einstein (BE) functions. Several distributional properties of these functions and their proposed new generalizations are investigated in this article. In fact, it is proved that these functions belong to distribution space ${\mathcal{D}}^{\prime }$ while their Fourier transforms belong to ${\mathcal{Z}}^{\prime }.$ Fourier and Laplace transforms of these functions are computed by using their distributional representation. Thanks to them, we can compute various new fractional calculus formulae and a new relation involving the Fox–Wright function. Some fractional kinetic equations containing the FD and BE functions are also formulated and solved. Full article

The Fermi–Dirac and Bose–Einstein statistics are considered to be key concepts in quantum mechanics, and they are used to explain the occupancy limit of electron orbitals. We investigate the physical origin of these two statistics and uncover that the key determining factor is whether an individual electron spin is measurable or not. Microscopically, a system with individually measurable electron spins corresponds to the presence of Larmor spin precession in electron–electron interactions, while the non-measurability of individual electron spins corresponds to the absence of Larmor spin precession. Both interaction types are possible, and the favored interaction type is thermodynamically determined. The absence of Larmor spin precession is realized in coherent electron states, and coherent electrons therefore obey Bose–Einstein statistics. Full article

In this paper, a gallium nitride (GaN) magnetic Hall effect current sensor is simulated in 2D and 3D using the TCAD Sentaurus simulation toolbox. The model takes into account the piezoelectric polarization effect and the Shockley–Read–Hall (SRH) and Fermi–Dirac statistics for all simulations. The galvanic transport model of TCAD Sentaurus is used to model the Lorentz force and magnetic behaviour of the sensor. The current difference, total current, and sensitivity simulations are systematically calibrated against experimental data. The sensor is optimised using varying geometrical and biasing parameters for various ambient temperatures. This unintentionally doped ungated current sensor has enhanced sensitivity to 16.5 %${\mathrm{T}}^{-1}$ when reducing the spacing between the drains to 1 μm and increasing the source to drain spacing to 76 μm. It is demonstrated that the sensitivity degrades at 448 K (S = 12 %T⁻¹), 373 K (S = 14.1 %T⁻¹) compared to 300 K (S = 16.5 %T⁻¹). The simulation results demonstrate a high sensitivity of GaN sensors at elevated temperatures, outperforming silicon counterparts. Full article

Can we accurately model the spin state of a quantum particle? If so, we should be able to make identical copies of such a state and also obtain its mirror image. In quantum mechanics, many subatomic particles can form entangled pairs that are mirror images of each other, although the state of an individual particle cannot be duplicated or cloned as experimentally demonstrated by Aspect, Clauser and Zeilinger, the winners of the Nobel Prize in Physics 2022. We show that there is a higher-order symmetry associated with the SL(2,C) group that underlies the singlet state, which means that the singlet pairing preserves Lorentz transformations independently of the metric used. The Pauli exclusion principle can be derived from this symmetry. Full article

A present summary is assigned to present the transport characteristics of the free randomly moving (RM) electrons in silicon at any doping level by phosphorous donors. The application of the Fermi-Dirac statistics and stochastic description of the free RM electrons lead to obtaining the general expressions of conductivity, the effective density of the free RM electrons, their diffusion coefficient and the drift mobility, which are valid for silicon with any doping level. It is shown that drift mobility of the free RM electrons considerably exceeds the Hall mobility at heavy doping, and that the Einstein relation is fundamental and is conserved at any level of degeneracy. It is estimated what part of electrons in the conduction band of heavily doped silicon is not free and is coupled with phosphorous ions. The main conclusions and formulations can be applicable for holes in acceptor-doped silicon, and other homogeneous materials with one type of the free RM charge carriers as well. Full article

We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statistical mechanics of very long walks may be used to quantify the structural properties important for the dynamics of processes defined in networks. Networks open to random structural modifications are characterized by a Fermi–Dirac distribution of node’s fugacity in the framework of grand canonical ensemble of walks. The same distribution appears as the unique stationary solution of a discrete Fokker–Planck equation describing the time evolution of probability distribution of stochastic processes in networks. Nodes of inferior centrality are the most likely candidates for the future structural changes in the network. Full article

It is difficult to imagine an isolated classical object which possess different moments of inertia when it is uniformly rotated about the same axis with the same angular frequency in opposite, clockwise and counterclockwise, directions. We argue that due to quantum effects, certain (semi-) conductors should exhibit asymmetry in their mechanical and conducting properties with respect to the opposite rotations. We show that a cylinder made of a suitably chosen semiconductor, coated in a metallic film and placed in the magnetic-field background, can serve as a “rotational diode”, which conducts electricity only at a specific range of angular frequencies. The critical angular frequency and the direction of rotation can be tuned with the magnetic field’s strength. Mechanically, the rotational diode possesses different moments of inertia when rotated in clockwise and counterclockwise directions. These effects emerge as a particularity of the Fermi-Dirac statistics of electrons in rotating conductors. Full article

In this work, we develop the general theory for analyzing the thermodynamic consistency of the Richardson–Duhmann model for vacuum thermionic energy converters. In addition to the electron fluxes from emitter to collector and vice versa, we calculate the energy and entropy fluxes associated to them. The calculation of the entropy fluxes is what allows us to conclude that the model is consistent by verifying that both at the emitter and at the collector the entropy generation rate is positive. In the process, we review the Richardson–Duhmann model in order to assure that the assumptions we make for calculating the energy and entropy fluxes are consistent. We also generalize the Richardson–Duhmann model in order to consider Fermi–Dirac statistics. Full article

We describe society as an out-of-equilibrium probabilistic system: in it, $N$ individuals occupy $W$ resource states and produce entropy $S$ over definite time periods. The resulting thermodynamics are however unusual, because a second entropy, $H$ , measures inequality or diversity―a typically social feature―in the distribution of available resources. A symmetry phase transition takes place at Gini values $1/3$ , where realistic distributions become asymmetric. Four constraints act on $S$ : $N$ and $W$ , and new ones, diversity and interactions between individuals; the latter are determined by the coordinates of a single point in the data, the peak. The occupation number of a job is either zero or one, suggesting Fermi–Dirac statistics for employment. Contrariwise, an indefinite number of individuals can occupy a state defined as a quantile of income or of age, so Bose–Einstein statistics may be required. Indistinguishability rather than anonymity of individuals and resources is thus needed. Interactions between individuals define classes of equivalence that happen to coincide with acceptable definitions of social classes or periods in human life. The entropy $S$ is non-extensive and obtainable from data. Theoretical laws are compared to empirical data in four different cases of economic or physiological diversity. Acceptable fits are found for all of them. Full article

To study the kinetic properties of dense quantum plasma, a new quantum dynamics method in the Wigner representation of quantum mechanics has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. This method combines the Feynman and Wigner formulation of quantum mechanics and uses for calculation the path integral Monte-Carlo (WPIMC) in phase space and quantum generalization of the classical molecular dynamics methods (WMD) allowing to solve the quantum Wigner–Liouville-like equation. The Fermi–Dirac statistical effects are accounted for by the effective pair pseudopotential depending on coordinates and momenta and allowing to avoid the famous “sign problem” due to realization of the Pauli blocking of fermions. Significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions have been observed. According to the quantum Kubo formula, we also study the electron conductivity of dense plasma media. Full article

Modified entropies have been extensively considered by several authors in articles published almost anywhere. Among the most well known are the Rényi entropy and the Havdra-Charvtá and Tsallis entropy. All these depend on one or several parameters. By means of a modification to Superstatistics, one of the authors (Obregón) has proposed generalized entropies that depend only on the probability. There are three entropies: $S_I=k\sum _{l=1}^{\Omega }(1-p_l^{p_l})$ , $S_{II}=k\sum _{l=1}^{\Omega }(p_l^{-p_l}-1)$ and their linear combination $S_{III}=k\sum _{l=1}^{\Omega }\frac{p_l^{-p_l}-p_l^{p_l}}{2}$ . It is interesting to notice that the expansion in series of these entropies having as a first term $S=-k\sum _{l=1}^{\Omega }{p}_{l}ln{p}_l$ in the parameter $x_{{}_l}\equiv p_{l}ln{p}_l\le 1$ cover, up to the first terms, any other expansion of any other possible function in $x_{{}_l}$ , one would want to propose as another entropy. The three proposed entropies by Obregón are then the only possible generalizations of the Boltzmann-Gibbs (BG) or Shannon entropies that depend only of the probability. One obtains a superposition of two statistics (that of $\beta$ and that of $p_l$ ), hence the name superstatistics. One may define an averaged Boltzmann factor as $B\left(E\right)={\int }_0^{\infty }f\left(\beta \right)e^{\beta E}d\beta$ where $f\left(\beta \right)$ is the distribution of $\beta$ . This work will deal with the analysis of the first two generalized entropies and will propose and deduce their associated quantum statistics; namely Bose-Einstein and Fermi-Dirac. The results will be compared with the standard ones and those due to the entropies by Tsallis. It will be seen in both cases that the BEO (the Bose-Einstein statistics corresponding to the entropies proposed by Obregón) statistic differs slightly from the usual BE statistic and in the same way for FDO the difference is small from the usual FD. Full article