Negative Energy States Research Articles

Assessment of Zitterbewegung Interpretation for Free Particle Solution Using the Concept of Relativistic Wave

The Assessment of the interpretation of Zitterbewegung for free particle solution using various models has been carried out in this work where we firstly considered by using the free particle solution for which Dirac equation and projection operator were carried out.. ln this case, it was invariably revealed that the solution have two doubly degenerate eigenvalues representing positive and negative state that was further support by the analysis which was carried out using Heisenberg’s equation and the representation in relativistic velocity and semi-classical equation of motion for acceleration., but in this second case, the results obtained were observed to have two terms, first terms standing in for rapidly oscillatory motion and the second term representing average motion of the particle in x-direction. The first term in the expression is the one deemed to signify zitterbewegung which is one considered to be sas a result of the fluctuation resulting from the interference between negative and positive energy state while the other term is the normal state terms signifying the average motion of the particle. This therefore confirms the explicit nature of using Dirac equation in handling problems involving the behavior of free particles in field as compared to the use of semiclassical equation of motion.

Contribution of negative-energy states to multipolar polarizabilities of the Sr optical lattice clock

Contribution of negative-energy states to multipolar polarizabilities of the Sr optical lattice clock

Imprints of rastall gravity on particle dynamics

In this paper, we investigate the trajectories of test particle around the Kerr-Newman anti de-Sitter black hole enclosed by scalar field matter in the context of Rastall gravity. We limit our research to the equatorial plane and analyze the dynamics of both null as well as time-like geodesics. We explore the stable regions with respect to the event horizon, radius of photon orbit and the so called static radius for both null as well as time-like particles. We found that the stable point is always less than the cosmological horizon as well as the static radius. We also discuss the energy extraction as well as negative energy state via Penrose process. The efficiency of the process from Kerr-Newman anti de-Sitter black hole is also examined. We observe that the efficiency of the Penrose process increased with the spin parameter as well the intensity of the scalar field around the BH.

Extracting the energy and angular momentum of a Kerr black hole

It has been thought for decades that rotating black holes (BHs) power the energetic gamma-ray bursts (GRBs) and active galactic nuclei (AGNs), but the mechanism that extracts the BH energy has remained elusive. We here show that the solution to this problem arises when the BH is immersed in an external magnetic field and ionized low-density matter. For a magnetic field parallel to the BH spin, the induced electric field accelerates electrons outward and protons inward in a conical region, centered on the BH rotation axis, and of semi-aperture angle θ≈60∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta \\approx 60^\\circ $$\\end{document} from the BH rotation axis. For an antiparallel magnetic field, protons and electrons exchange their roles. The particles that are accelerated outward radiate off energy and angular momentum to infinity. The BH powers the process by reducing its energy and angular momentum by capturing polar protons and equatorial electrons with net negative energy and angular momentum. The electric potential allows for negative energy states outside the BH ergosphere, so the latter does not play any role in this electrodynamical BH energy extraction process.

Energy bands in a three dimension simple cubic lattice of contact potential

In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald’s summation method. In comparison with single point potential, the presence of lattice potential changes the existence condition of negative energy states near zero energy. It is found that the system always has negative energy states for an arbitrarily weak periodic potential. In addition, we prove that if an irreducible unitary representation is not a trivial representation of group of wave vector, the corresponding wave functions at lattice sites would be zero. With this theorem, the degeneracy of energy bands is explained with group theory. Furthermore, we find that there exists some energy bands which are not affected by the lattice potential. We call their corresponding eigenstates as dark states. The physical mechanism of the dark states is explained by explicitly constructing the standing wave-type Bloch wave functions.

Weyl Fermions and broken symmetry phases of laterally confined 3He films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D) 3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum, , for Cooper pairs. The power law suppression of the angular momentum, for , in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid 3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at . The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length . The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at , in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

Short communication: Predicting blood plasma non-esterified fatty acid and beta-hydroxybutyrate concentrations from cow milk-addressing systematic issues in modelling.

Negative energy status in early lactation is linked to a variety of metabolic disorders, reduced fertility, and decreased milk production. To improve the energy status of cows by breeding and management, the identification of negative energy status is crucial. While biomarkers such as non-esterified fatty acid (NEFA) concentration and beta-hydroxybutyrate (BHB) in blood plasma could be used to identify a negative energy state, measuring them directly from blood is both invasive and expensive. In this work, we developed prediction equations for blood plasma NEFA and BHB levels based on mid-IR spectral measurements of milk. The models were fitted using partial least squares regression and evaluated using both cross-validation and independent-herd validation. A total of 3183 spectral records from 606 lactations originating from three different herds were utilised. R2 values of 0.53 (RMSE=0.206mmol/l, RMSE of cross-validation (RMSECV) 0.217mmol/l) for NEFA and 0.63 (RMSE=0.326mmol/l, RMSECV=0.353mmol/l) for BHB were obtained. Furthermore, relatively similar prediction accuracies were found for BHB (RMSE of prediction (RMSEP) 0.411mmol/l and 0.422mmol/l) and NEFA (RMSEP=0.186mmol/l and 0.221mmol/l) when model training was done using two herds and validated on the third herd. The results from the model fits confirm that it is possible to build blood plasma BHB and NEFA models based on mid-IR spectra that are sufficiently accurate for practical use.

State-dependent risky choices in primates: Variation in energy budget does not affect tufted capuchin monkeys' (Sapajus spp.) risky choices.

Economic models predict that rational decision makers' choices between a constant, "safe" option and a variable, "risky" option leading, on average, to the same payoff, should be random. However, a wealth of research has revealed that, when faced with risky decisions, both human and nonhuman animals deviate from economic rationality. According to the risk-sensitivity theory, individuals should prefer a safe option when they are in a positive energy state and a risky option when they are in a negative energy state. The abundance/risk hypothesis proposes that individuals should prefer risky options when diet quality exceeds their nutritional requirements. We tested how energy budget affects decision making under risk by presenting 22 capuchins belonging to two colonies (IT: N = 12, US: N = 10) with a risky choice task. Capuchins had to choose between a constant option (always four food items) and a variable option (one or seven food items with a 50% probability) in two conditions. In the Low-energy condition capuchins were tested before their main meal, whereas in the High-energy condition they were tested following a high-caloric meal. In neither colony did we find a significant difference between conditions, suggesting that the energy budget did not affect risk preferences. However, we found differences between colonies in their general response to risky choices: US capuchins were more risk-prone after selecting a safe option than a risky option and after selecting a bad (one food item) than a good (seven food items) risky option, whereas this did not hold true in IT capuchins. Furthermore, in the IT colony, males were more risk-prone under the High-energy condition compared to the Low-energy condition. Subtle differences in individual characteristics, management conditions, or stochastic founder effects may be implied, with relevant consequences for the outcomes of research on risky decision-making across laboratories.

Deep anharmonicity on the relativistic spin-0 particles within the spherical regime

We present an oscillator model of relativistic spin-0 charges moving in quantum states with minimal electromagnetic field coupling. Rather than using a perturbative approach, we implemented anharmonicity directly under the integer-dependent levels. In this way, the rest mass energy is kept at 280[Formula: see text]MeV. Within the extended Pekeris approximation, we have also improved the deep approximation to the third and fourth orders near equilibrium at 7.5[Formula: see text]fm with a width range of [Formula: see text]. By taking into account the Morse potential energy, the improved approximation provides a model for the relativistic quantum states of the spatially independent rest mass without an external magnetic field. We considered an extra-energy addition that results in shifted Morse potentials in the depth range of 80–100[Formula: see text]MeV, yielding positive and negative values for particles and antiparticles, respectively. As a result of the shift, it has been concluded that the potential depth of the charged particle affects the relativistic energy levels, where we have found about 200[Formula: see text]MeV for particles and nearly [Formula: see text]10[Formula: see text]MeV for antiparticles. In addition to the negative energy states, the wave functions ([Formula: see text], [Formula: see text]) and ([Formula: see text], [Formula: see text]), which correspond to the energy levels, have been followed by the typical probability form, which shows charge distribution.

Energy extraction from Janis-Newman-Winicour naked singularity

In general, energy extraction methods such as the Penrose process and the magnetic Penrose process are thought to be reliant on the existence of an ergoregion. Inside an ergoregion, there are negative energy states that allow a particle to extract energy and escape to an observer at infinity. In this paper, we considered the electromagnetic field in the rotating Janis-Newman-Winicour (JNW) spacetime. This concept is feasible because an accretion disc forms an electromagnetic field around compact objects. After that, we briefly examine negative energy orbits and their significance in energy extraction. The ergoregion is absent in a rotating JNW geometry, but we show that the effective ergoregion is there. The change in a negative energy orbit concerning the magnetic field ($B$), spin parameter ($a$), and electric charge ($Q$) is analyzed. We find that the total energy extraction efficiency within this process can be around 60% for the rotating JNW naked singularity.

Direct Observation of Ultrafast Relaxation Dynamics of a Mixed Excimer State in Perylene Monoimide Dimer by Femtosecond Transient Absorption.

A J-type dimer PMI-2, two perylene monoimides linked by butadiynylene bridger was prepared, and its excited-state dynamics was studied using ultrafast femtosecond transient absorption spectroscopy, along with steady-state spectroscopy and quantum chemical calculations. It is evidently demonstrated that the symmetry-breaking charge separation (SB-CS) process in PMI-2 is positively mediated by an excimer, which is mixed by localized Frenkel excitation (LE) and an interunit charge transfer (CT) state. Kinetic studies show that, with the polarity increasing of the solvent, the transformation of excimer from a mixture to the CT state (SB-CS) is accelerated, and the recombination time of the CT state is reduced obviously. Theoretical calculations indicate that these are due to PMI-2 obtaining more negative free energy (ΔGcs) and lower CT state energy levels in highly polar solvents. Our work suggests that the mixed excimer can be formed in a J-type dimer with suitable structure, in which the charge separation the process is sensitive to the solvent environment.

Relativistic Brueckner-Hartree-Fock Theory: an ab initio Approach for Nuclear Matter and for Finite Nuclei

Recent years have seen considerable progress with ab-initio calculations of the nuclear structure by non-relativistic many-body methods. Dirac-Brueckner-Hartree-Fock Theory provides a relativistic ab-intio approach, which is able to reproduce saturation properties of symmetric nuclear matter without three-body forces. However, so far, the corresponding equations have been solved only for positive energy states. Negative energy states have been included for forty years in various approximations, leading to differences in the isospin dependence. This problem has been solved only recently by a complete solution of the self-consistent relativistic Brueckner-Hartree-Fock equations in asymmetric nuclear matter. Due to its numerical complexity, however, it is very difficult to extend the Relativistic Brueckner-Hartree-Fock theory to the study of finite nuclear systems. Recent efforts will be discussed to overcome this problem.

Evaluating the spin-0 particle in Gurses rainbow universe

In this study, we solved the Klein–Gordon’s oscillator equation in Gurses rainbow universe. Subsequently, the energy quantization and associated wave function are obtained with the help of the Nikiforov–Uvarov technique. In the final stage, we compare graphically the rainbow effect with General Relativity(GR) one. According to the obtained result, the occurrence of asymmetrical breaking between positive and negative energy states has been observed in the rainbow scenario.

Quantum tunneling decay due to a resonance state of negative energy and a decaying width

By using an exact analytical formalism for quantum tunneling decay we show the existence of a regime of purely nonexponential decay for the survival probability in the full time interval and a propagating probability density along the external interaction region that evolves as a spreading process having no wavefront. This decaying regime follows from a complex pole of the propagator which in the wave number plane possesses an imaginary part larger than the corresponding real part, which implies a negative resonance energy and a decaying width, together with a dominant large overlap of the initial decaying state with the corresponding resonant state of the problem.

A new perspective on quantum field theory revealing possible existence of another kind of fermions forming dark matter

Quantum fields are considered as generators of infinite-dimensional Clifford algebra [Formula: see text], which can be either orthogonal (in the case of fermions) or symplectic (in the case of bosons). A generic quantum state can be expressed as a superposition of the basis elements of [Formula: see text], with the superposition coefficients being multiparticle complex-valued wavefunctions. The basis elements, that are products of the generators of [Formula: see text] in the Witt basis, act as creation and annihilation operators. They create positive and negative energy states that include the bare and the Dirac vacuum as special cases. It is shown that the nonvanishing electric charge arises from an extra dimension or from doubling the number of creation and annihilation operators, which brings an extra imaginary unit [Formula: see text] into the description. A further extension is to consider [Formula: see text] as one of the quaternionic imaginary units and consider a generic state as having values in the quaternionic algebra or, equivalently, in the complexified two-dimensional Clifford algebra, [Formula: see text]. It contains two distinct fundamental representations of [Formula: see text], one associated with the weak isospin doublet [Formula: see text] and the other one with the doublet of new leptons, denoted by [Formula: see text], that together with the new quarks [Formula: see text] can be identified with dark matter.

Investigation of electrical and magnetical multipoles contributions to the total longitudinal and transverse form factors in some positive and negative 27Al states using different interactions

The shell model and Skyrme interaction calculations were used to study the nuclear structure of the 27Al nucleus. In particular, inelastic electron scattering form factors, energy levels, and transition probabilities for positive and some negative parity low energy states have been calculated. The sd shell model was used with SKX parameters for positive parity cases. The calculations were performed on sd space interactions and the best results were obtained from HBUMSD, HBUSD, CWH, PW, and W interactions. For negative parity cases, the zbm model space with SKXcsb parameters has been used with zwm interactions. The excitation energies and transitions probabilities to the ground state 5/2+ for positive parity states have been also calculated. The calculated form factors, energy level diagrams, and transition probabilities were compared with the available experimental data. It was confirmed that the Skyrme interaction is suitable with the shell model to study the nuclear structure.

Most probable distributions and distributions of extremes for particle systems with hierarchical structures

The problem of the most probable distributions on energy is studied in a combinatorial formulation, under the natural hypotheses regarding conservation laws, such as conservation of the total number of particles, total energy, etc. The particle distributions on the maximum and minimum energies are obtained and coincide with those found in the framework of the original combinatorial treatment. Two types of energy distributions for delimited particles are obtained. The results can be interpreted as sorting of particles based on their statistical mechanics behavior observed in various experiments. An effective Pauli principle arises in a non-contradictory way in one-particle observations both for once- and twice-delimited systems in the combinatorial formulation as well as in the problem of distributions on maximum and minimum energies. Many of the distributions obtained describe particles that do not have negative energy states.

Nuclear Matter and Neutron Stars from Relativistic Brueckner–Hartree–Fock Theory

The momentum and isospin dependence of the single-particle potential for the in-medium nucleon are the key quantities in the Relativistic Brueckner–Hartree–Fock (RBHF) theory. It depends on how to extract the scalar and the vector components of the single-particle potential inside nuclear matter. In contrast to the RBHF calculations in the Dirac space with the positive-energy states (PESs) only, the single-particle potential can be determined in a unique way by the RBHF theory together with the negative-energy states, i.e., the RBHF theory in the full Dirac space. The saturation properties of symmetric and asymmetric nuclear matter in the full Dirac space are systematically investigated based on the realistic Bonn nucleon–nucleon potentials. In order to further specify the importance of the calculations in the full Dirac space, the neutron star properties are investigated. The direct URCA process in neutron star cooling will happen at density ρ DURCA = 0.43, 0.48, 0.52 fm−3 with proton fractions of Y p,DURCA = 0.13. The radii of a 1.4M ⊙ neutron star are predicated as km, and their tidal deformabilities are for potential Bonn A, B, C. Compared with the results obtained in the Dirac space with PESs only, the full-Dirac-space RBHF calculation predicts the softest symmetry energy, which would be more favored by the gravitational wave detection of GW170817. Furthermore, the results from the full-Dirac-space RBHF theory are consistent with the recent astronomical observations of massive neutron stars and simultaneous mass–radius measurement.

Using zero-energy states to explore how external boundaries affect the number of bound states in a quantum well

We use the condition for the existence of zero-energy eigenstates to examine how the number of bound (negative energy) states in a finite-width one-dimensional quantum well is altered by the introduction of boundaries outside of the well. We consider a variety of quantum wells including a finite square well, a triangular well, and sets of two to five Dirac delta wells. Each of these quantum wells is placed at the center of an infinite square well with variable width and the conditions for the existence of zero-energy eigenstates are determined analytically. The zero-energy conditions (ZEC) form curves in the parameter space that separate regions with different numbers of bound states. Moving across one of these curves changes the number of bound states by one. We find that, for the systems studied, introducing external boundaries changes the number of bound states by at most two. This work illustrates the usefulness of the ZEC as a tool for studying how the number of bound states in a quantum well depends on the system parameters.

Circular motion around a regular rotating Hayward black hole

In this paper, we explore the geodesics motion of neutral test particles and the process of energy extraction from a regular rotating Hayward black hole (BH). We analyze the effect of spin as well as deviation parameter [Formula: see text], on ergoregion, event horizon and static limit of the said BH. By making use of geodesic equations on the equatorial plane, we determine the innermost stable circular and photon orbits. Moreover, we investigate the effective potentials and effective force to have information on motion and the stability of circular orbits. On studying the negative energy states, we figure out the energy limits of Penrose mechanism. Using Penrose mechanism, we found expression for the efficiency of energy extraction and observed that both spin and deviation parameters contribute to the efficiency of energy extraction. Finally, the obtained results are compared with that acquired from Kerr and braneworld Kerr BHs.