Fermi-Dirac Research Articles

Creation of bound half-fermion pairs by solitons

In the presence of topologically nontrivial bosonic field configurations, the fermion number operator may take on fractional eigenvalues, because of the existence of zero-energy fermion modes. The simplest examples of this occur in 1+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+1$$\\end{document} dimensions, with zero modes attached to kink-type solitons. In the presence of a kink-antikink pair, the two associated zero modes bifurcate into positive and negative energy levels with energies ±ge-gΔ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm ge^{-g\\Delta }$$\\end{document}, in terms of the Yukawa coupling g≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g\\ll 1$$\\end{document} and the distance Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document} between the kink and antikink centers. When the kink and antikink are moving, it seems that there could be Landau–Zener-like transitions between these two fermionic modes, which would be interpretable as the creation or annihilation of fermion-antifermion pairs; however, with only two solitons in relative motion, this does not occur. If a third solitary wave is introduced farther away to perturb the kink-antikink system, a movement of the faraway kink can induce transitions between the discrete fermion modes bound to the solitons. These state changes can be interpreted globally as creation or destruction of a novel type of pair: a half-fermion and a half-antifermion. The production of the half-integral pairs will dominate over other particle production channels as long as the solitary waves remain well separated, so that there is a manifold of discrete fermion states whose energies are either zero or exponentially close to zero.

Pandemic Equation and COVID-19 Evolution

The Pandemic Equation describes multiple pandemic waves and has been applied to describe the COVID-19 pandemic. Using the generalized approaches of solid-state physics, we derive the Pandemic Equation, which accounts for the effects of pandemic mitigation measures and multiple pandemic waves. The Pandemic Equation uses slow and fast time scales for “curve flattening” and describing vaccination and mitigation measures and the Scaled Fermi–Dirac distribution functions for describing transitions between pandemic waves. The Pandemic Equation parameters extracted from the pandemic curves can be used for comparing different scenarios of the pandemic evolution and for extrapolating the pandemic evolution curves for the periods of time on the order of the instantaneous Pandemic Equation characteristic time constant. The parameter extraction for multiple locations could also allow for uncertainty quantification for such pandemic evolution predictions.

Beyond Conventional Charge Density Wave for Strongly Enhanced 2D Superconductivity in 1H-TaS2 Superlattices.

Noncentrosymmetric transition metal dichalcogenide (TMD) monolayers offer a fertile platform for exploring unconventional Ising superconductivity (SC) and charge density waves (CDWs). However, the vulnerability of isolated monolayers to structural disorder and environmental oxidation often degrade their electronic coherence. Herein, an alternative approach is reported for fabricating stable and intrinsic monolayers of 1H-TaS2 sandwiched between SnS blocks in a (SnS)1.15TaS2 van der Waals (vdW) superlattice. The SnS block layers not only decouple individual 1H-TaS2 sublayers to endow them with monolayer-like electronic characteristics, but also protect the 1H-TaS2 layers from electronic degradation. The results reveal the characteristic 3 × 3 CDW order in 1H-TaS2 sublayers associated with electronic rearrangement in the low-lying sulfur p band, which uncovers a previously undiscovered CDW mechanism rather than the conventional Fermi surface-related framework. Additionally, the (SnS)1.15TaS2 superlattice exhibits a strongly enhanced Ising-like SC with a layer-independent Tc of ≈3.0 K, comparable to that of the isolated monolayer 1H-TaS2 sample, presumably attributed to their monolayer-like characteristics and retained Fermi states. These results provide new insights into the long-debated CDW order and enhanced SC of monolayer 1H-TaS2, establishing bulk vdW superlattices as promising platforms for investigating exotic collective quantum phases in the 2D limit.

Charge Critical Phenomena in a Field Heterostructure with Two-Dimensional Crystal

The charge properties and regularities of mutual influence of the electro-physical parameters in a metal (M)/insulator (I)/two-dimensional crystal heterostructure were studied. In one case, the transition metal dichalcogenide (TMD) MoS2 was considered as a two-dimensional crystal, and in another the Weyl semi-metal (WSM) ZrTe5, representative of a quasi-two-dimensional crystal was chosen for this purpose. By self-consistently solving the electrostatic equations of the heterostructures under consideration and the Fermi–Dirac distribution, the relationship between such parameters as the concentration of charge carriers, chemical potential, and quantum capacitance of the TMD (WSM), as well as the capacitance of the I layer and the interface capacitance I–TMD (WSM), and their dependence on the field electrode potential, have been derived. The conditions for the emergence of charge instability and the critical phenomena caused by it are also determined.

Thermodynamic geometry of a system with unified quantum statistics.

We investigate the thermodynamic characteristics of unified quantum statistics, a framework exhibiting a crossover between Bose-Einstein and Fermi-Dirac statistics by varying a generalization parameter δ. An intrinsic statistical interaction becomes attractive for δ≤0.5, maintaining positive thermodynamic curvature across the entire physical range. In the range 0.5<δ<1, the system predominantly displays Fermi-like behavior at high temperatures. Conversely, at low temperatures, the thermodynamic curvature is positive, resembling bosonic behavior. Further temperature reduction induces a transition into the condensate phase. We introduce a critical fugacity (z=Z^{*}) at which the thermodynamic curvature changes sign. Below (z<Z^{*}) and above (z>Z^{*}) this critical point, the statistical behavior mimics fermions and bosons, respectively. We explore the system's statistical behavior for various δ values with respect to temperature, determining the critical fugacity and temperature-dependent condensation. Finally, we analyze specific heat as a function of temperature and condensation phase transition temperature for different δ values in various dimensions.

Random Green’s Function Method for Large-Scale Electronic Structure Calculation

We report a linear-scaling random Green’s function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi–Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi–Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H2O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H2O clusters at T = 0 K can reach an error of ∼ 1 meV per H2O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.

Theoretical Advances in Beta and Double-Beta Decay

Weak interaction processes continue to be hot topics in fundamental physics research. In this paper, we briefly review some recent advances in the theoretical study of beta and double-beta decays that include both the nuclear and atomic part of these processes. On the nuclear side, we present a statistical approach for the computation of the nuclear matrix elements (NME) for neutrinoless double-beta (0νββ). A range of NME values, the most probable value for NME, and the associated theoretical uncertainty are given. Correlations with other related observables are shown as well. On the atomic side, we first briefly review the methods used to obtain the electrons’ wave functions. Further, we use them for the computation of some relevant kinematic quantities such as Fermi functions, electron spectra, and angular correlation between the emitted electrons. Then, we present applications of these calculations to the experimental data analysis related to the search of the Lorentz invariance violation in two-neutrino double-beta (2νββ) decay and description of the decay rates and decay rate ratios for allowed and unique forbidden electron capture (EC) processes.

Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

Out-of-equilibrium states of many-body systems tend to evade a description by standard statistical mechanics, and their uniqueness is epitomized by the possibility of certain long-range correlations that cannot occur in equilibrium. In quantum many-body systems, coherent correlations of this sort may lead to the emergence of remarkable entanglement structures. In this work, we analytically study the asymptotic scaling of quantum correlation measures—the mutual information (MI) and the fermionic negativity—within the zero-temperature steady state of voltage-biased free fermions on a one-dimensional lattice containing a non-interacting impurity. Previously, we have shown that two subsystems on opposite sides of the impurity exhibit volume-law entanglement, which is independent of the absolute distances of the subsystems from the impurity. Here, we go beyond that result and derive the exact form of the subleading logarithmic corrections to the extensive terms of correlation measures, in excellent agreement with numerical calculations. In particular, the logarithmic term of the MI asymptotics can be encapsulated in a concise formula, depending only on simple four-point ratios of subsystem length scales and on the impurity scattering probabilities at the Fermi energies. This echoes the case of equilibrium states, where such logarithmic terms may convey universal information about the physical system. To compute these exact results, we devise a hybrid method that relies on Toeplitz determinant asymptotics for correlation matrices in both real space and momentum space, successfully circumventing the inhomogeneity of the system. This method could potentially find wider use for analytical calculations of entanglement measures in similar scenarios.

Extracting Kinetic Freeze-Out Properties in High-Energy Collisions Using a Multisource Thermal Model

We study the transverse momentum (pT) spectra of neutral pions and identified charged hadrons produced in proton–proton (pp), deuteron–gold (d–Au), and gold–gold (Au–Au) collisions at the center of mass energy sNN=200 GeV. The study is made in the framework of a multisource thermal model used in the partonic level. It is assumed that the contribution to the pT-value of any hadron comes from two or three partons with an isotropic distribution of the azimuthal angle. The contribution of each parton to the pT-value of a given hadron is assumed to obey any one of the standard (Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein) distributions with the kinetic freeze-out temperature and average transverse flow velocity. The pT spectra of the final-state hadrons can be fitted by the superposition of two or three components. The results obtained from our Monte Carlo method are used to fit the experimental results of the PHENIX and STAR Collaborations. The results of the present work serve as a suitable reference baseline for other experiments and simulation studies.

Variational Tensor Wave Functions for the Interacting Quantum Spin Hall Phase.

The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed as band insulators, this phase can also manifest in strongly correlated systems where conventional band theory fails. To overcome the challenge of simulating this phase in realistic correlated models, we propose a novel framework utilizing fermionic tensor network states. Our approach involves constructing a tensor representation of the fixed-point wave function based on an exact solvable model, enabling us to derive a set of tensor equations governing the transformation rules of local tensors under symmetry operations. These tensor equations lead to the anomalous edge theory, which provides a comprehensive description of the QSH phase. By solving these tensor equations, we obtain variational ansatz for the QSH phase, which we subsequently verify its topological properties through numerical calculations. This method serves as an initial step toward employing tensor algorithms to simulate the QSH phase in strongly correlated systems, opening new avenues for investigating and understanding topological phenomena in complex materials.

Krylov Complexity of Fermionic and Bosonic Gaussian States

AbstractThe concept of complexity has become pivotal in multiple disciplines, including quantum information, where it serves as an alternative metric for gauging the chaotic evolution of a quantum state. This paper focuses on Krylov complexity, a specialized form of quantum complexity that offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible orthogonal bases. This study is situated in the context of Gaussian quantum states, which are fundamental to both Bosonic and Fermionic systems and can be fully described by a covariance matrix. While the covariance matrix is essential, it is insufficient alone for calculating Krylov complexity due to its lack of relative phase information is shown. The relative covariance matrix can provide an upper bound for Krylov complexity for Gaussian quantum states is suggested. The implications of Krylov complexity for theories proposing complexity as a candidate for holographic duality by computing Krylov complexity for the thermofield double States (TFD) and Dirac field are also explored.

Ab initio calculation of nonequilibrium quasiparticle-phonon dynamics in superconductors

Phonon-induced Cooper pair breaking, inciting nonequilibrium quasiparticle (QP) bursts, is known to deteriorate the performance of superconducting devices. However, a detailed understanding of QP-phonon dynamics is lacking due to the absence of a well-established theoretical framework. This paper presents a fully ab initio scheme of calculating nonequilibrium, polarization-dependent QP-phonon dynamics in superconductors. The authors find that with only an 8% deviation from the equilibrium phonon Bose–Einstein distribution, the resulting nonequilibrium QP population is 83 times larger than the equilibrium Fermi–Dirac distribution, and the longitudinal acoustic (LA) phonon polarization is most responsible for QP generation. The authors demonstrated that the qubit transition rate in Josephson junction-based transmon qubits is increased by orders of magnitude when taking these nonequilibrium distributions into account, compared to equilibrium distributions. This framework allows an in-depth exploration of nonequilibrium QP-phonon dynamics in various Josephson-junction-based superconducting devices. It paves the way for formulating advanced phonon shielding strategies to target the LA polarization, potentially leading to enhanced device performance, such as increased coherence time of transmon qubits or reduced thermal noise in cryogenics.

Iron-bearing mining reject as an alternative and effective catalyst for photo-Fenton oxidation of phenol in water.

In this work, iron-bearing mining reject was employed as an alternative and potential low-cost catalyst to degrade phenol in water by photo-Fenton strategy. Various techniques, including SEM-EDS, BET, FTIR, and XRD, were applied to evaluate the material's properties. Process parameters such as hydrogen peroxide concentration, catalyst dosage, and pH were studied to determine the optimum reaction conditions ([catalyst] = 0.75g L-1, [H2O2] = 7.5mM, and pH = 3). Phenol degradation and mineralization efficiencies at 180 and 300min were 96.5 and 78%, respectively. These satisfactory results can be associated with the iron amount present in the waste sample. Furthermore, the material showed high catalytic activity and negligible iron leaching even after the fourth reuse cycle. The degradation behavior of phenol in water was well represented by a kinetic model based on the Fermi function. The iron-bearing mining reject can be considered a potential photo-Fenton catalyst for phenol degradation in wastewater.

The Use of Computer Mathematics Systems for Solving Some Problems of Thermodynamics and Statistical Physics

With the help of the MathCAD mathematical package, solutions to problems using the heat balance equation were obtained, in which the heat capacity was calculated according to Debye theory, and spline interpolation of experimental data on heat capacity from the reference book was also used. The degree of helium ionization at a given temperature is calculated. An example of the influence of lithium impurity on the degree of hydrogen ionization is considered. The energy and pressure of neon in the region of multiple ionization are calculated. Isotherms of an ideal fermi gas are con structed. A graph of the Fermi-Dirac distribution function for various temperatures is constructed. The concentration of electrons and positrons at temperatures corresponding to the rest energy of electrons is calculated. These examples can be used in the educational process.

Evidence of hot carrier extraction in metal halide perovskite solar cells

AbstractThe presence of hot carriers is presented in the operational properties of an (FA,Cs)Pb(I, Br, Cl)3 solar cell at ambient temperatures and under practical solar concentration. Albeit, in a device architecture that is not suitably designed as a functional hot carrier solar cell. At 100 K, clear evidence of hot carriers is observed in both the high energy tail of the photoluminescence spectra and from the appearance of a nonequilibrium photocurrent at higher fluence in light J–V measurements. At room temperature, however, the presence of hot carriers in the emission at elevated laser fluence is shown to compete with a gradual red shift in the PL peak energy as photoinduced halide segregation begins to occur at higher lattice temperature. The effects of thermionic emission of hot carriers and the presence of a nonequilibrium carrier distribution are also shown to be distinct from simple lattice heating. This results in large unsaturated photocurrents at high powers as the Fermi distribution exceeds that of the heterointerface controlling carrier transport and rectification.

Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU (3) quark mean field model

In the present study, we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3) quark mean field model. Within this model, the properties of the quark matter were modified through the scalar fields , vector fields , ϕ, and Polyakov fields Φ and at finite temperature and chemical potential. Non-extensive effects were introduced through a dimensionless parameter q, and the results were compared to those of the extensive case ( ). In the non-extensive case, the exponential in the Fermi-Dirac (FD) function was modified to a q-exponential form. The influence of the q parameter on the thermodynamic properties, pressure, energy, and entropy density, as well as trace anomaly, was investigated. The speed of sound and specific heat with non-extensive effects were also studied. Furthermore, the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of and s quarks was explored. We found that the critical end point (CEP), which defines the point in the phase diagram where the order of the phase transition changes, shifts to a lower value of temperature, , and a higher value of chemical potential, , as the non-extensivity is increased, that is, 1.

Chiral spin liquids with projected Gaussian fermionic entangled pair states

Chiral spin liquids with projected Gaussian fermionic entangled pair states

Effects of spin polarization on the propagation of surface waves on a quantum plasma half-space

The study explores the wave propagation characteristics of surface plasma waves in a semi-bounded plasma, incorporating the influence of spin polarization arising from spin mismatch. The formulated plasma model integrates the density correlation effect via Bohm's potential force, Fermi pressure employing Fermi-Dirac statistics, and the exchange potential. These factors are considered in spin-polarized form and interconnected through the spin polarization index κ. We derive a dispersion relation for surface plasma waves, delineating the propagation features of the configured wave mode. Our findings indicate that an increase in spin polarization among electron populations results in a decrease in the phase velocity of surface plasma waves compared to the usual electron-ion quantum plasma. Moreover, an increase in the exchange potential contributes to a decrease in the phase speed. However, the ratio of plasmon to Fermi energy leads to an increase in the phase velocity of surface plasma waves in a spin-polarized quantum plasma. We provide a comparative analysis of our work with an earlier model based on the gold–air interface, revealing that our model facilitates the propagation of surface plasma waves with higher frequencies across the wave vector. This study highlights the significance of quantum effects for electrostatic surface plasma waves in dense metallic plasmas at room temperature, with implications for signal transmission in metallic waveguides observed in a recent study [Guo et al., “Excitation of graphene magneto-plasmons in terahertz range and giant Kerr rotation,” J. Appl. Phys. 125(1), 013102 (2019)] and some of the references therein.

Modeling Fermi energy, free-carrier density, and resistivity in degenerate n-Ge

A new expression for Fermi energy vs doping is derived using the standard model for free carriers in n-type semiconductors. The new expression is composed of the Fermi energy in non-degenerate semiconductors, a doping function for bandgap narrowing (BGN), and an adjustable energy variation. In non-degenerate semiconductors, the new expression is equivalent to the standard Boltzmann expression. Calculated curves of Fermi energy are assigned in the Fermi–Dirac expression for the donor ionization ratio, and reported data of electron density and resistivity measured in heavily doped n-Ge layers are fitted. Five reported doping functions for BGN are used. One of the BGN functions allows modeling frustrated incomplete ionization. Another allows modeling bandgap widening.

The Compressible Euler and Acoustic Limits from Quantum Boltzmann Equation with Fermi–Dirac Statistics

This paper justifies the compressible Euler and acoustic limits from quantum Boltzmann equation with Fermi–Dirac statistics rigorously. By employing Hilbert expansion, in particular analyzing the nonlinear implicit transformation between the classical form of compressible Euler equations and the one obtained directly from BFD, and some new type of Grad–Caflisch type decay estimate of the linearized collision operator, we establish the compressible Euler limit from scaled BFD equation, which was formally derived by Zakrevskiy in (Kinetic models in the near-equilibrium regime. Thesis at Polytechnique, 2015) by moment method. Consequently, the acoustic limit is obtained in optimal scaling with respect to Knudsen number.