Fermi-Dirac Research Articles

Van der waals equation of state

Van der Waals (vdW) invented his equation of state about 150 year ago. This equation described the liquidgas phase transition and predicted an existence of the critical point. The vdW equation of state remains today the most familiar and one of the most successful model in molecular physics. It is presented in all text books on statistical physics. However, several important questions concerning the vdW model had no answers. Only very recently these questions were discussed in the literature, and several important extensions of the vdW equation of state were developed. These new results presented in this article correspond to the grand canonical ensemble formulation, the effects of quantum statistics, and applications of the vdW model to nuclear matter taking into account Fermi statistics for interacting protons and neutrons. A special attention is also paid to the particle number fluctuations in a vicinity of the vdW critical point.

Spin-1/2 “bosons” with mass dimension 3/2 and fermions with mass dimension 1 cannot represent physical particle states

We delve into the first principles of quantum field theory to prove that the so-called spin-1/2 “bosons” and the fermions with mass dimension 1, including ELKO, cannot represent physical particle states with spin 1/2. Specifically, we first demonstrate that both aforementioned fields are not invariant under rotational symmetry, which implies that the particles created for these fields are not eigenstates of the spin operator in the (frac{1}{2},0)oplus (0,frac{1}{2}) representation of the Lorentz group, nor is it possible to construct a Hamiltonian density scalar under the rotational group from them. Furthermore, following Weinberg’s approach to local causal fields, we prove that regardless of any discrete symmetry or adjoint structure, the relativistic fields in the (frac{1}{2}, 0) oplus (0,frac{1}{2}) representation satisfy the Fermi-Dirac statistics in complete agreement with the well-established spin-statistics theorem and experimental results.

Revealing the simultaneous increase in transient transmission and reflectivity in InN

The ultrafast transient behavior of InN under intensive laser irradiation remains unclear. The simultaneous measurements of pump–probe transient transmission and reflectivity are reported in this study. The irradiation-induced change in the dielectric constant of InN films due to the generation of thermalized carriers gives rise to complex transient behavior, and simultaneous increase in both transient transmission and reflectivity are observed at certain wavelengths. Herein, transient transmission is interpreted as the occupation probability of thermalized electrons at the probing level originating from a hot Fermi–Dirac distribution, and our calculation results are in good agreement with the experiments. Likewise, the Drude-like response due to the collective motion of thermalized carriers causes the increase in transient reflectivity, which depends on the change of dielectric constant caused by the collective motion of thermalized carriers. The ultrafast carrier dynamics is modeled by calculating the temporal evolution of the occupation probability of thermalized electrons in the conduction band. On the basis of the two-temperature model, the electron–phonon scattering time is extrapolated to be ∼300 fs in InN, which dominates the cooling of excited electrons.

One-particle entanglement for one-dimensional spinless fermions after an interaction quantum quench

Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large scale exact diagonalization and time dependent density matrix renormalization group calculations, we numerically compute the one body reduced density matrix for the J-V model, as well as its post-quench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.

A steep switching WSe2 impact ionization field-effect transistor

The Fermi-Dirac distribution of carriers and the drift-diffusion mode of transport represent two fundamental barriers towards the reduction of the subthreshold slope (SS) and the optimization of the energy consumption of field-effect transistors. In this study, we report the realization of steep-slope impact ionization field-effect transistors (I2FETs) based on a gate-controlled homogeneous WSe2 lateral junction. The devices showed average SS down to 2.73 mV/dec over three decades of source-drain current and an on/off ratio of ~106 at room temperature and low bias voltages (<1 V). We determined that the lucky-drift mechanism of carriers is valid in WSe2, allowing our I2FETs to have high impact ionization coefficients and low SS at room temperature. Moreover, we fabricated a logic inverter based on a WSe2 I2FET and a MoS2 FET, exhibiting an inverter gain of 73 and almost ideal noise margin for high- and low-logic states. Our results provide a promising approach for developing functional devices as front runners for energy-efficient electronic device technology.

Thin-walled Higgs assisted Q-balls from pseudo-Nambu-Goldstone bosons

We consider the question of whether Q-balls can exist in a chiral Lagrangian truncated at leading order when, in addition, the Standard Model Higgs boson couples to the pseudo-Nambu-Golstone bosons (pNGBs). In particular, we consider the so-called thin-wall limit where volume energy dominates over surface energy. It is known that the leading order chiral Lagrangian alone does not support such multi-field solutions. Augmented by the Higgs, however, we do indeed find that such solutions exist. We then study their properties numerically and, in various limits, analytically. Furthermore, since we consider a mirror-world-like model where the pNGBs are composite states of fundamental fermions, the question of Fermi repulsion in the high density bulk of the Q-ball plays a central role in determining its properties. The main effect is that when the parameter controlling the Fermi repulsion increases beyond a critical value, the radius of the Q-ball increases and continues to increase while the Q-ball becomes more weakly bound. As a result, there are Q-ball solutions with radii well exceeding a femtometer which would interact with nuclei in direct detection experiments via momentum-dependent form factors making their signatures striking. We leave the question of the production and direct detection of these Q-balls to a future study.

Fermion-axion stars: Static solutions and dynamical stability

We construct spherically symmetric static solutions of the Einstein-Klein-Gordon-Euler system involving a complex scalar field governed by a periodic potential that emerges in models of axionlike particles and fermionic matter modeled by a perfect fluid with a polytropic equation of state. Such solutions describe gravitationally bound composites of fermions and axions, which we dub fermion-axion stars. Sequences of pure axion stars in the existence domain may show the presence of multiple stable branches depending on the value of the decay constant parameter in the potential; this reflects in the appearance of multiple islands of stability in the two-dimensional parameter space of fermion-axion configurations. We investigate the domain of existence for three different values of the decay constant, identifying one or more regions of linear stability, making use of a method we already employed in previous works. We confirm the results from the linear analysis performing fully nonlinear numerical relativity evolutions. In this context, we perform several numerical simulations to identify regions in the parameter space where unstable models face different fates: the collapse to a Schwarzschild black hole, the migration to a stable model, and finally the dispersion of the scalar field together with the dilution of the fermionic matter, which approaches a static fermion star model with very low mass. This latter scenario was never observed in previous models without the periodic potential.

Evolutionary prisoner’s dilemma game on signed networks based on structural balance theory

Evolutionary game has applications in many fields, from engineering to economics and social sciences. Applying evolutionary games to complex networks has become a hot research field. In real society, due to different personalities or interests, friendship or hostility will be established between people, and the alienation or closeness of the relationship will have a greater impact on the game. However, the existing evolutionary game studies on networks rarely comprehensively involve the multiplicity of this relationship. Trying to fill this gap, in this paper, we propose a new Signed-PD (prisoners’ dilemma) game model and derive the fixation probability formula. In our model, we introduce a trust factor and a modified Fermi function to characterize the impact of different relationships on the payoff matrix and strategy imitation respectively. Moreover, the theory of structural balance is extended by taking into account the nodes’ strategy, and a new structural balance rate calculated from energy functions is introduced to reflect structural balance changes. We explore the effect of trust factors on network game and study the impact of game parameters as well as network parameters on evolution, and investigate the impact of monotonic structural balance increasing on the evolution of cooperation in signed networks. Simulation results show that if the temptation value is below a certain threshold, the Game structural balance will change its qualitative dynamics. Furthermore, when the classical structural balance has a monotonic growth control beginning at 0, it can successfully boost the cooperator’s survival.

Concealing Dirac neutrinos from cosmic microwave background

The existence of prolonged radiation domination prior to the Big Bang Nucleosynthesis (BBN), starting just after the inflationary epoch, is not yet established unanimously. If instead, the universe undergoes a non-standard cosmological phase, it will alter the Hubble expansion rate significantly and may also generate substantial entropy through non-adiabatic evolution. This leads to a thumping impact on the properties of relic species decoupled from the thermal bath before the revival of the standard radiation domination in the vicinity of the BBN. In this work, considering the Dirac nature of neutrinos, we have studied decoupling of ultra-relativistic right-handed neutrinos (νR s) in presence of two possible non-standard cosmological phases. While in both cases we have modified Hubble parameters causing faster expansions in the early universe, one of the situations predicts a non-adiabatic evolution and thereby a slower redshift of the photon temperature due to the expansion. Considering the most general form of the collision term with Fermi-Dirac distribution and Pauli blocking factors, we have solved the Boltzmann equation numerically to obtain ΔNeff for the three right-handed neutrinos. We have found that for a large portion of parameter space, the combined effect of early decoupling of νR as well as the slower redshift of photon bath can easily hide the signature of right-handed neutrinos, in spite of precise measurement of ΔNeff, at the next generation CMB experiments like CMB-S4, SPT-3G etc. This however will not be applicable for the scenarios with only fast expansion.

Influence of quantum particles on self-gravitational magnetic dust acoustic double layers

The impact of Fermi–Dirac distributed electrons and ions on the features of dust acoustic double layers in a four-component magnetized dusty plasma was investigated. In this model, the plasma consists of Fermi–Dirac distributed electrons and ions and negative and positive dust particles. The plasma species experience electrical, magnetical, and self-gravitational forces as well as the degeneracy pressure force that is caused by the Pauli exclusion law and the quantum tunneling force due to Bohm force. Employing a reductive perturbation method, the quantum extended Korteweg-de Vries equation was extracted from the set of fluid equations. The results show that the energy of generated dust acoustic double layers is extremely smaller than that in similar classical plasmas. The ratio of the Fermi temperature of ions to electrons is an effective parameter in the structure of double layers. With the variation of this parameter, the structure of double layers changes from compressive to rarefactive, and its polarity switches from negative to positive.

Prediction of Ground State Structures and Robust Weyl Fermionic States in MnRhP

Prediction of Ground State Structures and Robust Weyl Fermionic States in MnRhP

Thermodynamic Limit of the Pieces’ Model

We study the ground states of the pieces’ model in the Fermi-Dirac statistics in the thermodynamic limit. In other words, we consider the minimizing configurations of n interacting fermions in an interval [0, L] divided into pieces by a Poisson point process, when $$ \frac{n}{L}\rightarrow \rho >0 $$ as $$ L \rightarrow \infty $$ . We notice that a decomposition into groups of pieces arises from the hypothesis of finite-range pairwise interaction. Under assumptions of convexity and non-degeneracy of the subsystems, we get an almost complete factorization of any ground state. This method applies at least for groups comprising one or two particles. It improves the expansion of the thermodynamic limit of the ground state energy per particle up to the error $$ O(\rho ^{2-\delta }) $$ , with $$ 0<\delta <1 $$ [see Klopp and Veniaminov (in: Frontiers in Analysis and Probability, Springer, Cham, 2020)]. It also provides an approximate ground state for the pieces’ model.

Trie-based ranking of quantum many-body states

Ranking bit patterns -- finding the index of a given pattern in an ordered sequence -- is a major bottleneck scaling up numerical quantum many-body calculations, as fermionic and hard-core bosonic states translate naturally to bit patterns. Traditionally, ranking is done by bisectioning search, which has poor cache performance on modern machines. We instead propose to use tries (prefix trees), thereby achieving a two- to ten-fold speed-up in numerical experiments with only moderate memory overhead. For the important problem of ranking permutations, the corresponding tries can be compressed. These compressed "staggered" lookups allow for a considerable speed-up while retaining the memory requirements of prior algorithms based on the combinatorial number system.

Dissipation and geometry in nonlinear quantum transports of multiband electronic systems

Nonlinear responses in condensed matters attract recent intensive interest because they provide rich information about the materials and hold the possibility of being applied in diodes or high-frequency optical devices. Nonlinear responses are often closely related to the multiband nature of the system which can be taken into account by the geometric quantities such as the Berry curvature as shown in the nonlinear Hall effect. Theoretically, the semi-classical Boltzmann treatment or the reduced density matrix method have been often employed, in which the effect of dissipation is included through the relaxation time approximation. In the diagrammatic method, the relaxation is treated through the imaginary part of the self-energy of the Green function and the consequent broadening of the spectral function for the integration over the real frequency. Therefore, the poles of the Green function do not play explicit pole when there is finite dissipation. In this paper, in stark contrast to this conventional picture, we show that the poles of the Green function determine mostly the nonlinear response functions with dissipation, which leads to the terms with the Fermi distribution function of complex argument and results in the dissipation-induced geometric term. We elucidate the geometric origin of the nonreciprocal conductivity, which is related to the Berry curvature generalized to the higher derivative. Finally, we derive the analytical results on the geometric terms of the nonlinear conductivities in the type-I and type-II Weyl Hamiltonian to demonstrate their crucial roles.

On the measurement uncertainty of microdosimetric quantities using diamond and silicon microdosimeters in carbon-ion beams.

The purpose of this paper is to compare the response of two different types of solid-state microdosimeters, that is, silicon and diamond, and their uncertainties. A study of the conversion of silicon microdosimetric spectra to the diamond equivalent for microdosimeters with different geometry of the sensitive volumes is performed, including the use of different stopping power databases. Diamond and silicon microdosimeters were irradiated under the same conditions, aligned at the same depth in a carbon-ion beam at the MedAustron ion therapy center. In order to estimate the microdosimetric quantities, the readout electronic linearity was investigated with three different methods, that is, the first being a single linear regression, the second consisting of a double linear regression with a channel transition and last a multiple linear regression by splitting the data into odd and even groups. The uncertainty related to each of these methods was estimated as well. The edge calibration was performed using the intercept with the horizontal axis of the tangent through the inflection point of the Fermi function approximation multi-channel analyzer spectrum. It was assumed that this point corresponds to the maximum energy difference of particle traversing the sensitive volume (SV) for which the residual range difference in the continuous slowing down approximation is equal to the thickness of the SV of the microdosimeter. Four material conversion methods were explored, the edge method, the density method, the maximum-deposition energy method and the bin-by-bin transformation method. The uncertainties of the microdosimetric quantities resulting from the linearization, the edge calibration and the detectors thickness were also estimated. It was found that the double linear regression had the lowest uncertainty for both microdosimeters. The propagated standard (k = 1) uncertainties on the frequency-mean lineal energy and the dose-mean lineal energy values from the marker point, in the spectra, in the plateau were 0.1% and 0.2%, respectively, for the diamond microdosimeter, whilst for the silicon microdosimeter data converted to diamond, the uncertainty was estimated to be 0.1%. In the range corresponding to the 90% of the amplitude of the Bragg Peak at the distal part of the Bragg curve (R90 ) the uncertainty was found to be 0.1%. The uncertainty propagation from the stopping power tables was estimated to be between 5% and 7% depending on the method. The uncertainty on the and coming from the thickness of the detectors varied between 0.3% and 0.5%. This article demonstrate that the linearity of the readout electronics affects the microdosimetric spectra with a difference in values between the different linearization methods of up to 17.5%. The combined uncertainty was dominated by the uncertainty of stopping power on the edge.

Models with two Higgs doublets and a light pseudoscalar: A portal to dark matter and the possible (g−2)μ excess

In the context of a two-Higgs doublet model, supplemented by an additional light pseudoscalar Higgs boson and a stable isosinglet fermion, we consider the possibility of addressing simultaneously the discrepancy from the standard expectation of the anomalous magnetic moment of the muon recently measured at Fermilab and the longstanding problem of the dark matter in the universe which can be accounted for by a thermal weakly interacting massive particle. We show that it is indeed possible, for a range of masses and couplings of the new light pseudoscalar and the fermionic states, to explain at the same time the two features while satisfying all other constraints from astroparticle physics and collider searches, including the constraints from flavor physics.

Topological triplet-superconductivity in spin-1 semimetal

Superconductivity in topological semimetals gives a new paradigm of unconventional superconductors. Their exotic gap structures and topological properties have fascinated searching for material realizations and applications. In this work, we focus on a triple point semimetal where quasiparticle excitations, triple point fermions, carry the effective integer spin-1 in two distinct valleys. Our work demonstrates that the triple point fermion stabilizes inter-valley s-wave spin-triplet pairing. This is due to Fermi statistics, which strictly forbids the formation of inter-valley s-wave spin-singlet pairings. This feature is clearly distinct from the BCS and other multi-band superconductors. We find that two distinct inter-valley s-wave spin-triplet superconductors are allowed which in principle can be controlled by tuning the chemical potential: time-reversal symmetric (sz) state with topologically protected nodal lines and time-reversal broken (sx + isy) state with topologically protected Bogoliubov Fermi surfaces. Our study provides guidance in searching for spin-triplet superconductivity.

A note on stellar ionization

In this paper, we examine the thermal ionization in the core of a main-sequence stable star with the assumption that the main-sequence stellar core behaves like an ideal 3-Dimensional (D) Fermi gas. This assumption is based on the fact that the stellar core persists as a region of very high temperature, typically in a range between 15×106 K and density near 150 gcm−3, like that of our Sun where the classical gas description fails and Fermi–Dirac (F–D) distribution become important. Finally, we compare our ionization equation with Saha’s thermal ionization equation based on classical Maxwell–Boltzmann (M–B) distribution. The mathematical analysis provides us with the result that the ionization fraction is proportional to the probability-distribution function and also exponentially proportional to the Fermi energy and has volume dependency under the 3-D ideal Fermi gas consideration, thus inducing an extensive nature for the equation of state.

Equivalence between two charged black holes in dynamics of orbits outside the event horizons

Using the Fermi–Dirac distribution function, Balart and Vagenas gave a charged spherically symmetric regular black hole, which is a solution of Einstein field equations coupled to a nonlinear electrodynamics. In fact, the regular black hole is a Reissner–Nordström (RN) black hole when a metric function is given a Taylor expansion to first order approximations. It does not have a curvature singularity at the origin, but the RN black hole does. Both black hole metrics have horizons and similar asymptotic behaviors, and satisfy the weak energy conditions everywhere. They are almost the same in photon effective potentials, photon circular orbits and photon spheres outside the event horizons. Due to the approximately same photon spheres, the two black holes have no explicit differences in the black hole shadows and constraints of the black hole charges based on the First Image of Sagittarius A $$^{*}$$ . There are relatively minor differences between effective potentials, stable circular orbits and innermost stable circular orbits of charged particles outside the event horizons of the two black holes immersed in external magnetic fields. Although the two magnetized black holes allow different construction methods of explicit symplectic integrators, they exhibit approximately consistent results in the regular and chaotic dynamics of charged particles outside the event horizons. Chaos gets strong as the magnetic field parameter or the magnitude of negative Coulomb parameter increases, but becomes weak when the black hole charge or the positive Coulomb parameter increases. A variation of dynamical properties is not sensitive dependence on an appropriate increase of the black hole charge. The basic equivalence between the two black hole gravitational systems in the dynamics of orbits outside the event horizons is due to the two metric functions having an extremely small difference. This implies that the RN black hole is reasonably replaced by the regular black hole without curvature singularity in many situations.

Invariant quadratic operators associated with linear canonical transformations and their eigenstates

The main purpose of this work is to identify invariant quadratic operators associated with Linear Canonical Transformations (LCTs) which could play important roles in physics. In quantum physics, LCTs are the linear transformations which keep invariant the Canonical Commutation Relations (CCRs). In this work, LCTs corresponding to a general pseudo-Euclidian space are considered and related to a phase space representation of quantum theory. Explicit calculations are firstly performed for the monodimensional case to identify the corresponding LCT-invariant quadratic operators then multidimensional generalizations of the obtained results are deduced. The eigenstates of these operators are also identified. A first kind of LCT-invariant operator is a second order polynomial of the coordinates and momenta operators. The coefficients of this polynomial depend on the mean values and the statistical variances-covariances of the coordinates and momenta operators themselves. It is shown that these statistical variances-covariances can be related with thermodynamic variables. In this context, new quantum corrections to the ideal gas state equation are deduced from correction to the Hamiltonian operator of non-relativistic free quantum particles that is suggested by LCT-covariance. Two other LCT-invariant quadratic operators, which can be considered as the number operators of some quasiparticles, are also identified: the first one is a number operator of bosonic type quasiparticles and the second one corresponds to fermionic type. This fermionic LCT-invariant quadratic operator is directly related to a spin representation of LCTs. It is shown explicitly, in the case of a relativistic pentadimensional theory, that the eigenstates of this operator can be considered as basic quantum states of elementary fermions. A classification of the fundamental fermions, compatible with the Standard Model of particle physics, is established from a classification of these states.