Fermi-Dirac Research Articles

Fermionic steering in multi-event horizon spacetime

We investigate quantum steering of Dirac field for different types of Bell states in Schwarzschild–de Sitter (SdS) spacetime that has a black hole event horizon (BEH) and a cosmological event horizon (CEH). We find that fermionic steerability from Bob to Alice is greater than fermionic steerability from Alice to Bob, while bosonic steerability exhibits the opposite behavior in SdS spacetime. These different properties between fermionic and bosonic steering arise from the differences between Fermi–Dirac statistics and Bose–Einstein statistics. We also find that the Hawking effect of the black hole decreases fermionic steerability. However, the Hawking effect of the expanding universe can enhance fermionic steerability, which differs from the properties of quantum steering in single-event horizon spacetime. Interestingly, we can indirectly protect quantum steering by using appropriate types of Bell states in multi-event horizon spacetime. These conclusions are helpful to guide the task of processing relativistic quantum information for quantum steering in SdS spacetime.

Emergent quasicrystal in fermionic superradiance

Quasicrystal is state of matter with multiple crystalline orders, displaying a short-range density-wave order and a long-range disorder. As an exotic state lying in between crystals and Anderson insulators, its dynamical formation is little discussed. Here, we study the emergence of quasicrystalline order in fermionic superradiance, where Fermi statistics plays a crucial role, being distinct from its bosonic counterpart where interaction is the stabilizer. Owing to quasicrystalline orders, there exist multiple energy gaps opening at different quasicrystalline order strength, which can modify the density of states in excitation spectrum. As a result, the effective ground-state energy is strongly modified and the superradiant quasicrystal transition becomes first order and density dependent. This new mechanism leads to a linear V-shape kink of the fermionic superradiance transition line near a filling which uniquely relates to the quasicrystalline order. Our findings demonstrate that quasicrystal can be realized in fermionic superradiance as a result of Fermi statistics and be verified by characteristic density-dependent phenomena. Published by the American Physical Society 2025

Multi-fold fermionic and bosonic states in topologically non-trivial Ti3Pd.

The topological properties of the A15-type compound Ti3Pd reveal a complex landscape of multi-fold fermionic and bosonic states, as uncovered through ab initio calculations within the framework of density functional theory (DFT). The electronic band structure shows multi-fold degenerate crossings at the high-symmetry point R near the Fermi level, which evolves into 4-fold and 8-fold degenerate fermionic states upon the introduction of spin-orbit coupling (SOC). Likewise, the phononic band structure features multi-fold degenerate bosonic crossings at the same R point. Topological analysis, including the calculation of 2 invariant and surface states, confirms the non-trivial nature of Ti3Pd. Moreover, both fermionic and bosonic quasiparticles exhibit nodal line features, whose topological non-triviality is further substantiated by Berry phase calculation. This research illuminates the intricate topological framework of Ti3Pd, opening avenues for experimental exploration in the field of topological quantum materials.

In-situ gamma-ray measurement to estimate depth distribution of 137Cs in farmland in Fukushima Prefecture.

Radioactive cesium released into the atmosphere caused by the Fukushima Dai-ichi Nuclear Power Plant accident in March 2011 has contaminated the surrounding area. We confirmed the applicability of in-situ methods to evaluate the depth distribution of 137Cs by employing the ratio of Compton-scattering and photo-peak components (rC) obtained from measured gamma-ray spectra. In the present study, we applied the in-situ method to farmlands in Fukushima Prefecture whose sites were disturbed by decontamination and plowing operations. rC and the net count of the 662-keV photo-peak, npeak, were obtained from gamma-ray spectra measured using a portable CsI detector. Reasonable rC was obtained by removing the contribution of naturally occurring radioactive materials through a simple and versatile procedure. The depth distribution of 137Cs measured using the conventional sampling method was reproduced using the Fermi distribution function. The concentration of 137Cs on the ground surface, N(0), and the depth at which the concentration becomes half of N(0), d1/2, can be described by simple functions of npeak and rC, respectively. We also confirmed that the Monte Carlo simulation is useful to reproduce the present results, taking into account the contribution of 134Cs and the detection system properly.

Search for additional Higgs bosons in fermionic final states with the CMS experiment

Search for additional Higgs bosons in fermionic final states with the CMS experiment

Resurgence for the nonconformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics

We consider resurgence for the nonconformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics in the extended relaxation-time approximation. First, we examine the full formal transseries expanded around the equilibrium and then construct the resurgent relation by looking at the structure of Borel-transformed ordinary differential equations. We form a conjecture of the resurgent relation based on the consideration that the Stokes constants constituting the resurgent relation originate only from singularities of dissipative variables on the Borel plane and that the other variables such as temperature and chemical potential become Borel nonsummable through nonlinear terms with the dissipative variables. We numerically check the conjecture for fundamental variables by explicitly evaluating the values of the dominant Stokes constant depending on the initial conditions and the particle mass. We also comment on some issues related to transseries structure and resurgence, such as the case of broken U(1) symmetry, the massless case, generalized relaxation time, and attractor solutions. Published by the American Physical Society 2024

Torsional four-fermion interaction and the Raychaudhuri equation

Intrinsic spin of fermions can generate torsion in spacetime. This torsion is a non-propagating field that can be integrated out, leaving an effective non-universal four-fermion interaction. This geometrical interaction affects fermions inside a matter distribution and can be expected to become stronger as the density grows. We investigate the role of this interaction in a gravitationally collapsing fermionic distribution, by considering a statistical average of the interaction term which incorporates the effect of mixed vector and axial currents. We consider a gravitationally collapsing distribution of massive fermions, ignoring other interactions. Using simplified yet reasonable assumptions, we establish that the contribution can be attractive or repulsive depending on how torsion couples with different chiralities. Also, the interaction starts to dominate as the collapse proceeds, accelerating or decelerating the collapse depending on the relative signs of the geometrical interaction between different species of fermions.

Exact eigenstates of multicomponent Hubbard models: SU( N ) magnetic η pairing, weak ergodicity breaking, and partial integrability

We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η-pairing mechanism. Our models include the SU(N) Hubbard model as a special case. Unlike the conventional two-component case, the generalized η-pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent η pairs. While the η-pairing states in the SU(2) Hubbard model are based on the η-pairing symmetry, the exact eigenstates in the N-component system with N≥3 arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized η-pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the N-component Hubbard models for N≥3. Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a noninteracting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of nonthermalization caused by dissipation. This work establishes the coexistence of off-diagonal long-range order and SU(N) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators. Published by the American Physical Society 2024

Thermal quasiparticle theory.

The widely used thermal Hartree-Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi-Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi-Dirac or thermal HF theory. The theory thus stipulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green's function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperatures, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperatures by including additional electron-correlation effects through orbital energies. A physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak's theorem.

Past-performance-driven strategy updating promote cooperation in the spatial prisoner's dilemma game

Strategy update rules play an important role in repeated Prisoner's Dilemma games. This work proposes a modified strategy update rule based on the traditional Fermi function, in which individual past performance is taken into account in strategy update. Then, the consistency aspiration α serves as a benchmark to measure an individual's past performance, and the past performance score is dynamically adjusted during the evolution process according to the BM reinforcement learning rules. The computational results indicate that the proposed modified strategy update rules can significantly improve system cooperation t than the traditional version, and the network reciprocity effect is enhanced as the result of past performance is coupled into the strategy update rule. Moreover, different temptation to defection b exist a corresponding aspiration α result in maximizing system cooperation. Furthermore, an optimal sensitivity level β can also result in a maximizing system cooperation. As a whole, for α − β phase diagram, different a will correspond to an optimal value β that allows the system to achieve the maximum cooperation. Finally, the proposed mechanism is robust. Hopefully this can help to inspire further research on how to deal with social dilemmas.

Study of the structure of atomics by the method of electron scattering in the distorted-wave approximation: Atomic energy

Using distorted-wave approximation obtained the differential cross-section (DCS) of elastic scattering at energy of 80 eV of electrons on 49In, 31Ga, 34Se and 70Yb atoms, and calculated accordingly on the proposed mathematical method. The electron density distribution in the atom is chosen as a function calculated in the Dirac-Hartree-Fock-Slater approximation, which is a superposition of the spherically symmetric Yukawa potential. In addition, the DCSs were calculated for the electron density in the 49 In and 20 Ca atoms expressed as a three-parameter Fermi function at incident electron energy of 100 eV. The obtained theoretical calculations of the cross sections were compared with the experimental data. Besides, the proposed mathematical method simplifies the calculation of integral expressions and makes it possible to obtain a convenient and simple expression for the atomic form factor. Data on the scattering cross sections of electrons on atoms are of considerable interest both in the field of fundamental science for in-depth study of interaction processes and in practical applications, and are necessary in many areas of research, such as modeling low-temperature plasma, astrophysics phenomena, laser physics, and atmospheric effects etc. In addition to natural phenomena, the processes of collision of electrons with matter play an essential role in plasma technologies, such as, for example, microelectronics and biomedicine. Atomic physics, plasma physics and optics - fields directly related to electron-atom make a significant contribution to the fundamental understanding of the world. Despite the long study of the effects of electron scattering on atoms, and the results obtained in the physics of atomic collisions, this area still requires theoretical and experimental research, there is a significant lack of data on collision cross sections for their subsequent use in modeling and calculations. In particular, there are no systematized data on the cross sections for elastic scattering of high energy electrons by atomic.

Quantum real-time evolution of entanglement and hadronization in jet production: Lessons from the massive Schwinger model

The possible link between entanglement and thermalization, and the dynamics of hadronization are addressed by studying the real-time response of the massive Schwinger model coupled to external sources. This setup mimics the production and fragmentation of quark jets, as the Schwinger model and quantum chromodynamics (QCD) share the properties of confinement and chiral symmetry breaking. By using simulations of quantum dynamics on classical hardware, we study the entanglement between the produced jets, and observe the growth of the corresponding entanglement entropy in time. This growth arises from the increased number of contributing eigenstates of the reduced density matrix with sufficiently large and close eigenvalues. We also investigate the physical nature of these eigenstates, and find that at early times they correspond to fermionic Fock states. We then observe the transition from these fermionic Fock states to mesonlike bound states as a function of time. In other words, we observe how hadronization develops in real time. At late times, the local observables at midrapidity (such as the fermion density and the electric field) approach approximately constant values, suggesting the onset of equilibrium and approach to thermalization. Published by the American Physical Society 2024

Majorana representation for topological edge states of massless Dirac fermion with nonquantized Berry phase

We study the bulk-boundary correspondences for zigzag ribbons (ZRs) of massless Dirac fermion in the two-dimensional α−T3 lattice. By tuning the hopping parameter α∈[0,1], the α−T3 lattice interpolates between pseudospin S=1/2 (graphene) and S=1 (T3 or dice lattice), for α=0 and 1, respectively, which is followed by a continuous change of the Berry phase from π to 0. The range of existence for edge states in the momentum space is determined by solving tight-binding equations at the boundaries of the ZRs. We find that the transitions of in-gap bands from bulk to edge states in the momentum space do not only occur at the positions of the Dirac cones but also at additional points depending on α∈(0,1). The α−T3 ZRs are mapped onto stub Su-Schrieffer-Heeger chains by performing unitary transformations of the bulk Hamiltonian. The nontrivial topology of the bulk bands is revealed by the Majorana representation of the eigenstates, where the topological invariant is manifested by winding numbers on the complex plane and the Bloch sphere. Published by the American Physical Society 2024

Floquet engineering of anomalous Hall effects in monolayer MoS2

Light-matter interactions have emerged as a new research focus recently offering promises of unveiling novel physics and leading to applications under nonequilibrium conditions. The quantized Hall conductivities predicted by Floquet theory assuming a Fermi-Dirac distribution however deviate from experimental observations. To resolve these puzzles, we consider the effect of nonequilibrium electron occupation to study the anomalous, valley, and spin Hall effects of a prototype monolayer transition metal dichalcogenide MoS2. We find that spin Hall conductivity can be effectively suppressed approaching zero value by linearly polarized light under near resonant excitations. In contrast, it is substantially enhanced by circularly polarized light, originating from optical selection rules and topological phase transitions. Besides, the quantized anomalous Hall conductivity is much reduced if nonequilibrium occupations of Floquet bands are considered. Our study provides a novel avenue for engineering various Hall effects in two-dimensional materials using light, holding great promises for future device applications.

Wave functions of multiquark hadrons from representations of the symmetry groups Sn

Construction of the wave functions of multiquark hadrons by a traditional method based on the tensor products of colors, flavors, spins (and orbital) parts becomes quite complex when quark numbers grow n=5,6…12, as it gets difficult to satisfy the requirements of Fermi statistics. Our novel approach is focused directly on representations of the permutation symmetry generators. After showing how C3 is manifested in the wave functions of (excited) baryons, we use it to construct the wave functions for a set of pentaquarks and hexaquarks (n=5,6). We also have some partial results for larger systems, with n=9 and 12, and even beyond that as far as n=24. Published by the American Physical Society 2024

III–V heterostructure tunnel field-effect transistor operation at different temperature regimes

Tunnel field-effect transistors (TFETs) are a potential alternative to MOSFETs for low-temperature electronics. We provide an in-depth experimental characterization of TFETs analyzing the fundamental physical behavior at different temperature regimes. TFET characteristics from 13 to 300 K both in forward and reverse bias are discussed by employing a variation in InAs/InGaAsSb/GaSb heterojunction vertical nanowire devices. Evaluation of the TFET Negative Differential Resistance (NDR) characteristics at different temperatures is established as a technique to probe the dopant incorporation. It is observed that the temperature dependence of the Fermi degeneracy and Fermi-Dirac distribution largely influences the transistor performance at each operating temperature. Our investigation reveals that the TFETs demonstrate lower subthreshold swing than the physical limit of MOSFETs above 125 K. For low-temperature applications, the devices can be operated down to a low operating bias of 0.1 V, while for high temperature, a larger bias of 0.3 V is preferred.

Self-consistent Strong Screening Applied to Thermonuclear Reactions

Self-consistent strong plasma screening around light nuclei is implemented in the Big Bang nucleosynthesis (BBN) epoch to determine the short-range screening potential, e ϕ(r)/T ≥ 1, relevant for thermonuclear reactions. We numerically solve the nonlinear Poisson–Boltzmann equation incorporating Fermi–Dirac statistics, adopting a generalized screening mass to find the electric potential in the cosmic BBN electron–positron plasma for finite-sized α particles (4He++) as an example. Although the plasma follows Boltzmann statistics at large distances, Fermi–Dirac statistics is necessary when work performed by ions on electrons is comparable to their rest-mass energy. While self-consistent strong screening effects are generally minor owing to the high BBN temperatures, they can enhance the fusion rates of high-Z (Z > 2) elements while leaving fusion rates of lower-Z (Z ≤ 2) elements relatively unaffected. Our results also reveal a pronounced spatial dependence of the self-consistent strong screening potential near the nuclear surface. These findings about the electron–positron plasma’s role refine BBN theory predictions and offer broader applications for studying weakly coupled plasmas in diverse cosmic and laboratory settings.

Semiclassical Scattering by Edge Imperfections in Topological Insulators in a Magnetic Field

We study the scattering of edge states of 2D topological insulator in the uniform external magnetic field due to edge imperfections, common in realistic 2D topological insulator samples. The external magnetic field breaks time-reversal symmetry, opening the possibility of the scattering of otherwise topologically protected fermionic edge states. The scattering happens to be always an over-barrier event, irrespective of the shape of the edge deformation and magnitude of the magnetic field. We use the advanced Pokrovsky–Khalatnikov semiclassical approach, which allows us to obtain analytically both the main exponential and pre-exponential factors of the scattering amplitude for wide classes of analytic deformation profiles.

On a drift‐diffusion model for perovskite solar cells

AbstractWe introduce a vacancy‐assisted charge transport model for perovskite solar cells. This instationary drift‐diffusion system describes the motion of electrons, holes, and ionic vacancies and takes into account Fermi–Dirac statistics for electrons and holes and the Fermi–Dirac integral of order for the mobile ionic vacancies in the perovskite. The free energy functional we work with corresponds to that choice of the statistical relations. To verify the existence of weak solutions, we consider a problem with regularized state equations and reaction terms on any arbitrarily chosen finite time interval. We motivate its solvability by time discretization and passage to the time‐continuous limit. A priori estimates for the chemical potentials that are independent of the regularization level ensure the existence of solutions to the original problem. These types of estimates rely on Moser iteration techniques and can also be obtained for solutions to the original problem.

Topological edge states of massless fermions with nonquantized and zero Berry phases

We investigate the bulk-boundary correspondence for massless Dirac fermions in α−T3 lattice where the Berry phase can be continuously tuned from π (graphene) to 0 (T3 or dice lattice) without modifying the energy dispersion. The topological origin of edge states is revealed by the unitary transformation of the Hamiltonian, which maps an α−T3 zigzag ribbon (ZR) onto a stub Su-Schrieffer-Heeger (SSH) chain. In the Majorana representation of the eigenstates, the topological invariant is manifested by the azimuthal winding number on the Bloch sphere. Particularly, T3 ZR exemplifies a topologically nontrivial system with zero Berry phase. Contrary to conventional topological insulators, the gap closing in the corresponding stub SSH chain is not accompanied by a topological phase transition. Published by the American Physical Society 2024