Fermionic Solutions Research Articles

Rotational influence on fermions within negative curvature wormholes

In this research, we examine relativistic fermions within the rotating frame of negative curvature wormholes. Initially, as is typical in our context, we introduce the wormholes by embedding a curved surface into a higher-dimensional flat Minkowski spacetime. Subsequently, we derive the spacetime metric that characterizes the rotating frame of these wormholes. We then investigate analytical solutions of the generalized Dirac equation within this framework. Through exploring a second-order non-perturbative wave equation, we seek exact solutions for fermions within the rotating frame of hyperbolic and elliptic wormholes, also known as negative curvature wormholes. Our analysis provides closed-form energy expressions, and we generalize our findings to Weyl fermions. By considering the impact of the rotating frame and curvature radius of wormholes, we discuss how these factors affect the evolution of fermionic fields, offering valuable insights into their behavior.

Relativistic fermions and vector bosons in magnetized three-dimensional space-time with a cosmological constant

In this manuscript, we study the relativistic dynamics of fermions and vector bosons within a (2+1)-dimensional magnetized space-time. We consider the Bonnor-Melvin magnetic space-time, characterized by a homogeneous magnetic field aligned along the symmetry axis and a non-zero cosmological constant. This space-time background, featuring cylindrical symmetry, retains the invariance of quantum field dynamics under Lorentz boosts along the z-direction. This enables us to explore (2+1)-dimensional realms, where the associated 2+1-dimensional spacetime background is recognized as the Bonnor-Melvin magnetic 2+1+0-brane solution within the framework of gravity coupled with nonlinear electrodynamics. We seek exact solutions for relativistic fermions and vector bosons within this space-time background. We have managed to derive the radial wave equations in both instances, securing precise eigenvalue solutions devoid of any approximations. Our findings extend seamlessly to massless fermions and vector bosons, ensuring generality. Moreover, we observe that the ground state energy of massless vector bosons (photons) within the examined space-time background is unequivocally zero.

Spectral properties and exact solutions for Rabi-coupled noninteracting fermions in a spin-dependent anharmonic trapping potential

We investigate the effect of spin-motion coupling on the spectral properties of Rabi-coupled noninteracting fermions in a spin-dependent harmonic trapping potential plus an anharmonic term. It is shown that when the spin-motion coupling becomes strong, fermions tend to stay in one of the two components. In the limit of the strong spin-motion coupling, the entire energy spectrum exhibits a sequence of near degeneracy. In particular, in the case of the sextic anharmonic term, the system admits the exact analytical energies and wave functions of the bound states for an infinite number of the specific parameter conditions. The properties of the energy spectrum have also been discussed on basis of these obtained exact analytical solutions.

Rotationally invariant isospinning baby-skyrmions dressed by fermions

We couple Fermions to the isospinning (2+1) baby-skyrme model. We show that consistent rotationally invariant localised solutions can be found but the Fermionic solutions to the equations of motion are not in general eigenstates of the Hamiltonian. These do however become full eigenstates in a particular limit. We also find the corresponding Fermionic eigenstates of the Hamiltonian, for which our Fermion ansatz is also well suited. For localised Fermionic states, a novel constraint on the internal isospin frequency exists. Throughout our studies, we include the backreaction of the Fermions on the baby-skyrmion.

Stationary solutions for fermions in the fields of Schwarzschild and Reissner–Nordström quantum black holes

The problem of existence of fermion’s stationary states in the fields of quantum black holes [R. Casadio, Universe 7, 478 (2021), arXiv:2103.00183v4 [gr-qc]; R. Casadio, A. Giusti and J. Ovalle, Phys. Rev. D 105, 124026 (2022), arXiv:2203.03252v2 [gr-qc]] is considered. It is shown that in the domains, outside external event horizons, quantum black holes preserve qualitative characteristics typical for classical Schwarzschild and Reissner–Nordström black holes [V. P. Neznamov and I. I. Safronov, J. Exp. Theor. Phys. 127, 647 (2018); V. P. Neznamov, I. I. Safronov and V. E. Shemarulin, J. Exp. Theor. Phys. 127, 684 (2018)]. Quantitative differences are the dependence of the radii of the event horizons in quantum black holes on the maximum (cut-off) momentum of the gravitons [Formula: see text] and some distinctions in the effective potentials of the relativistic self-conjugate Schrödinger-type equation.

Chaos classification in forced fermionic instanton solutions by the Generalized Alignment Index (GALI) and the largest Lyapunov exponent

Instantons play an important role in particle physics and cosmology. Fermion-like instanton solutions are obtained in the two-dimensional Thirring model via Heisenberg ansatz. In this study, chaotic behavior of the fermion-like instanton solutions with an external periodic force is investigated. The chaotic behavior is analyzed by performing a comparative numerical study of the time evolution of the largest Lyapunov exponent (LLE) and the Generalized Alignment Index of order 2 (GALI2) method. Diagram of the LLE and GALI2 time (TG) (the time TG needed for the GALI2 to become <10−12) of the system of two nonlinear ordinary differential equations corresponding the forced fermion like instanton solutions with respect to varying the parameters at different time units are plotted comparatively. Moreover, color plots of the LLEs and GALI2 time (TG) of the system in the phase space are analyzed with different initial conditions for different parameters. As a result of these analyzes, the fermionic instanton solutions with an external periodic force are regular, chaotic and weakly chaotic states for some parameters and initial conditions. In addition, using diagram and color plot of the GALI2 time (TG), which is considered as an indicator of the system's chaoticity strength, by adjusting the needed time for the GALI2 to become <10−12 can be an alternative method to the diagram and color plot of the LLE of system with respect to varying the parameters.

Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux

Scattering of charged fermion with (1+2)-dimensional wormhole in the presence of constant axial magnetic flux is explored. By extending the class of fermionic solutions of the Dirac equation in the curved space of wormhole surface to include normal modes with real energy and momentum, we found a quantum selection rule for the scattering of fermion waves to the wormhole. The newly found momentum–angular momentum relation implies that only fermion with the quantized momentum k=m'/asqrt{q} can be transmitted through the hole. The allowed momentum is proportional to an effective angular momentum quantum number m' and inversely proportional to the radius of the throat of the wormhole a. Flux dependence of the effective angular momentum quantum number permits us to select fermions that can pass through according to their momenta. A conservation law is also naturally enforced in terms of the unitarity condition among the incident, reflected, and transmitted waves. The scattering involving quasinormal modes (QNMs) of fermionic states in the wormhole is subsequently explored. It is found that the transmitted waves through the wormhole for all scenarios involving QNMs are mostly suppressed and decaying in time. In the case of QNMs scattering, the unitarity condition is violated but a more generic relation of the scattering coefficients is established. When the magnetic flux phi =mhc/e, i.e., quantized in units of the magnetic flux quantum hc/e, the fermion will tunnel through the wormhole with zero reflection.

Thermodynamic instabilities in holographic neutron stars at finite temperature

We study the thermodynamics of a self-gravitating system of neutral fermions at finite temperature and analyze its backreaction in an asymptotically AdS space. We evaluate numerically the free entropy as a function of temperature, and perform a stability analysis applying the simpler and powerful graphical method referred as the Katz criterion. We found that for highly-enough degenerate fermionic solutions, the onset of thermodynamic instability arises, though prior to the turning point on the mass as a function of the central density. Our results for finite temperature fermions provide a novel and more general way to study the confinement to deconfinement phase transition in the holographic field theory, generalizing former conclusions developed for systems at zero temperature.

Continuous quantum phase transition in the fermionic mass solutions of the Nambu–Jona-Lasinio model

Recently, quantum simulators have been constructed to investigate experimentally the most prominent theoretical four-point many-body system described by the Hubbard model. By varying the coupling strength of the four-point interaction in relation to the kinetic term, it is possible to analyze the phase structure of the model. This intriguing fact leads us to ask the question as to whether similar Hamiltonians with four-point interactions can also be studied as a function of their four-point coupling strength. In this paper, we reexamine the Nambu--Jona-Lasinio model, regarding it generally beyond the context of quantum chromodynamics. Essentially, it is a model in which particle-antiparticle pairing leads to a Bardeen-Cooper-Schrieffer-like condensate, with the result that chiral symmetry is broken dynamically in the strong-coupling regime, where $G{\mathrm{\ensuremath{\Lambda}}}^{2}$ is larger than a critical value, i.e., $G{\mathrm{\ensuremath{\Lambda}}}^{2}&gt;{G}_{c}{\mathrm{\ensuremath{\Lambda}}}^{2}$. To study the behavior of the system, it is necessary to move from this regime to a hypothetical regime of weak coupling, altering the coupling strength of the interaction arbitrarily. In order to do this, the gap equation must be regarded as complex and its Riemann surface structure must be known. We do this and obtain a continuous quantum phase transition characterized by the development of a complex order parameter (the dynamically generated mass) from the second sheet of the Riemann surface associated with the gap equation, as we move into the weak-coupling regime. The power-law behavior of the order parameter in the vicinity of the phase transition point is demonstrated to be independent of the choice of the regularization scheme with the critical exponent as $\ensuremath{\beta}\ensuremath{\approx}0.55$. At the same time, the isovector pseudoscalar modes retain their feature as Goldstone modes and still have zero mass, while the isoscalar scalar meson follows the behavior of the order parameter and gains a width. Energetically, this mode is not favored over the normal, uncondensed mode but would have to be accessed through an excitation process.

Nodal structures of few electron atoms

In this paper, the nodal structure for simple atomic systems is revisited and a procedure for identifying the symmetry properties and nodal structure of the time and spin independent Schrodinger equation will be presented. Application is made to the few electron atom, and explicit new nodal surface equations are given for states of various symmetries. In the construction of trial functions for variational calculations in quantum mechanics and in the choice of nodal surfaces needed in Monte Carlo calculations to obtain fermion solutions to Schrodinger’s equation for spin independent Hamiltonians, the accuracy of the calculations can be strongly influenced by the initial choice of the trial functions. We incorporated these newly found nodal conditions in the trial functions, and energy eigenvalues were calculated with better accuracy for different symmetries.

Axially symmetric exact solutions for flagpole fermions with gravity

The Lounesto classification splits spinors in six classes: I, II, III are those for which at least one among scalar and pseudo-scalar bi-linear spinor quantities is non-zero, its spinors are called regular, and among them we find the usual Dirac spinor. IV, V, VI are those for which the scalar and pseudo-scalar bi-linear spinor quantities are identically zero, its spinors are called singular, and they are split in further sub-classes: IV has no further restrictions, its spinors are called flag-dipole; V is the one for which the spin axial-vector vanishes, its spinors are called flagpole, and among them we find the Majorana spinor; VI is the one for which the momentum antisymmetric-tensor vanishes, its spinors are called dipole, and among them we find the Weyl spinor. In the quest for exact solutions of fully-coupled systems of spinor fields in their own gravity, we have already given examples in the case of Dirac fields and Weyl fields but never in the case of Majorana or more generally flagpole spinor fields. Flagpole spinor fields in interaction with their own gravitational field, in the case of axial symmetry, will be considered. Exact solutions of the field equations will be given.

Triplet leptogenesis, type-II seesaw dominance, intrinsic dark matter, vacuum stability and proton decay in minimal SO(10) breakings

We implement type-II seesaw dominance for neutrino mass and baryogenesis through heavy scalar triplet leptogenesis in a class of minimal non-supersymmetric SO(10) models where matter parity as stabilising discrete symmetry as well as WIMP dark matter (DM) candidates are intrinsic predictions of the GUT symmetry. We also find modifications of relevant CP-asymmetry formulas in such models. Baryon asymmetry of the universe as solutions of Boltzmann equations is further shown to be realized for both normal and inverted mass orderings in concordance with cosmological bound and best fit values of the neutrino oscillation data including θ23 in the second octant and large values of leptonic Dirac CP-phases. Type-II seesaw dominance is at first successfully implemented in two cases of spontaneous SO(10) breakings through SU(5) route where the presence of only one non-standard Higgs scalar of intermediate mass ∼ 109−1010 GeV achieves unification. Lower values of the SU(5) unification scales ∼ 1015 GeV are predicted to bring proton lifetimes to the accessible ranges of Super-Kamiokande and Hyper-Kamiokande experiments. Our prediction of WIMP DM relic density in each model is due to a ∼ \U0001d4aa (1) TeV mass matter-parity odd real scalar singlet (⊂ 16H ⊂ SO(10)) verifiable by LUX and XENON1T experiments. This DM is also noted to resolve the vacuum stability issue of the standard scalar potential. When applied to the unification framework of M. Frigerio and T. Hambye, in addition to the minimal fermionic triplet DM solution of 2.7 TeV, our mechanism of type-II seesaw dominance and triplet leptogenesis is also found to make an alternative prediction of the triplet fermion plus the real scalar singlet DM near the TeV scale.

Second-Order Stationary Solutions for Fermions in an External Coulomb Field

We have studied self-conjugate second-order equations with spinor wavefunctions for fermions moving in an external Coulomb field. For stationary states, the equations are characterized by separated states with positive and negative energies, which render probabilistic interpretation possible. For the Coulomb field of attraction, the energy spectrum of the second-order equation coincides with the spectrum of the Dirac equation, while the probability densities of states are slightly different. For a Coulomb field of repulsion, there exists an impermeable potential barrier with radius depending on the classical electron radius and on the electron energy. The existence of the impermeable barrier does not contradict the results of experiment for determining the inner electron structure and does not affect (in the lowest order of perturbation theory) the Coulomb electron scattering cross section. The existence of the impermeable barrier can lead to positron confinement in supercritical nuclei with $Z \geq 170$ in case of realization of spontaneous emission of vacuum electron-positron pairs.

The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices

We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in two regimes. The first corresponds to functionals that annihilate the generalized free fermion spectrum. In this case, we analytically find both OPE and gap maximization functionals proving the extremality of the generalized free fermion solution to crossing. Secondly, we consider a scaling limit where all conformal dimensions become large, equivalent to the large AdS radius limit of gapped theories in AdS2. In this regime we demonstrate analytically that optimal bounds on OPE coefficients lead to extremal solutions to crossing arising from integrable field theories placed in large AdS2. In the process, we uncover a close connection between asymptotic extremal functionals and S-matrices of integrable field theories in flat space and explain how 2D S-matrix bootstrap results can be derived from the 1D conformal bootstrap equations. These points illustrate that our formalism is capable of capturing non-trivial solutions of CFT crossing.

N=2 Supersymmetry with Central Charge: A Twofold Implementation

In this work, we analyze an extended N=2 supersymmetry with central charge and develop its superspace formulation under two distinct viewpoints. Initially, in the context of classical mechanics, we discuss the introduction of deformed supersymmetric derivatives and their consequence on the deformation of one-dimensional nonlinear sigma model. After that, considering a field-theoretical framework, we present an implementation of this superalgebra in two dimensions, such that one of the coordinates is related to the central charge. As an application, in this two-dimensional scenario, we consider topological (bosonic) configurations of a special self-coupled matter model and present a nontrivial fermionic solution.

The emergence of flagpole and flag-dipole fermions in fluid/gravity correspondence

The emergence of flagpole and flag-dipole singular spinor fields is explored, in the context of fermionic sectors of fluid/gravity correspondence, arising from the duality between the gravitino, in supergravity, and the phonino, in supersymmetric hydrodynamics. Generalized black branes, whose particular case consists of the AdS–Schwarzschild black brane, are regarded. The correspondence between hydrodynamic transport coefficients, and the universal absorption cross sections of the generalized black branes, is extended to fermionic sectors, including supersound diffusion constants. A free parameter, in the generalized black brane solution, is shown to control the flipping between regular and singular fermionic solutions of the equations of motion for the gravitino.

Study of the stability of the fermionic instanton solutions by the scale index method

In the last years, there has been great interest to the formulation and application of wavelet transformation in variety of fields to investigate the characteristics of dynamical systems. Recently, a method based on the scalogram analysis of the continuous wavelet transform, the scale index has been proposed to measure aperiodicity and determine the transitions from aperiodic behaviour to periodic behaviour in nonlinear dynamical systems. In this work we test the scale index method by performing the analysis of the deterministic behaviour of the fermion-like two-dimensional Akdeniz–Smailagic instanton solution in Thirring Model. We show that the scale index method can also be considered to detect the periodic behaviours of the fermion-like instanton solutions.

Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions

The exactly solvable model of two indistinguishable quantum particles (bosons or fermions) confined in a one-dimensional harmonic trap and interacting via finite-range soft-core interaction is presented and many properties of the system are examined. Particularly, it is shown that independently on the potential range, in the strong interaction limit bosonic and fermionic solutions become degenerate. For sufficiently large ranges a specific crystallization appears in the system. The results are compared to predictions of the celebrated Busch et al. model and those obtained in the Tonks-Girardeau limit. The assumed inter-particle potential is very similar to the potential between ultra-cold dressed Rydberg atoms. Therefore, the model can be examined experimentally.

Analytical solutions for fermions on a thick brane with a piecewise and smooth warp factor

In this paper, we study analytical solutions for fermion localization in Randall–Sundrum (RS) models. We show that there exist special couplings between scalar fields and fermions giving us discrete massive localizable modes. Besides this we obtain resonances in some models by analytical methods.

Generalized relativistic harmonic oscillator in minimal length quantum mechanics

We solve the generalized relativistic harmonic oscillator in 1 + 1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. Furthermore, we also find an isolated solution from the Sturm–Liouville scheme. All cases already analyzed in the literature are obtained as particular cases.