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There are several well-established methods for computing thermodynamics in single-horizon spacetimes. However, understanding thermodynamics becomes particularly important when dealing with spacetimes with multiple horizons. Multiple horizons raise questions about the existence of a global temperature for such spacetimes. Recent studies highlight the significant role played by the contribution of all the horizons in determining Hawking's temperature. Here we explore the Hawking temperature of a rotating and charged black hole in four spacetime dimensions and a rotating BTZ black hole. We also find that each horizon of those black holes contributes to the Hawking temperature. The effective Hawking temperature for a four-dimensional rotating and charged black hole depends only on its mass. This temperature is the same as the Hawking temperature of a Schwarzschild's black hole. In contrast, the effective Hawking temperature depends on the black hole's mass and angular momentum for a rotating BTZ hole. [ABSTRACT FROM AUTHOR]

Dirac’s theory is not the unique theory consistent with the physical principles specific of a free spin-one-half particle. In fact, we derive classes of theories of an elementary free particle from the principle of Poincaré’s invariance and from the principle of the covariance of the position. The theory of Dirac is just one of these theories, characterized by singular predictions, namely, the zitterbewegung. Yet, the class here derived contains families of consistent theories without singular predictions. For the time being, the experimental verifiability of these alternative theories is restricted to the predictions of free-particle theories for ideal experiments.

Dirac's theory is not the unique theory consistent with the physical principles specific of a free spin-one-half particle. In fact, we derive classes of theories of an elementary free particle from the principle of Poincaré's invariance and from the principle of the covariance of the position. The theory of Dirac is just one of these theories, characterized by singular predictions, namely, the zitterbewegung. Yet, the class here derived contains families of consistent theories without singular predictions. For the time being, the experimental verifiability of these alternative theories is restricted to the predictions of free-particle theories for ideal experiments. [ABSTRACT FROM AUTHOR]

According to Lorentz-violating theory, the dynamical equation of Dirac particles in the Kinnersley black hole with variably accelerated linear motion is modified. The Hawking quantum tunneling radiation characteristics of Kinnersley black hole are obtained by solving the modified equation. The expression of the Hawking temperature of Kinnersley black hole has been updated.

We analyse the behaviour of the Dirac field under the effects of the violation of the Lorentz symmetry determined by a fixed time-like vector background and azimuthal electric fields. We show, from the interaction of the Dirac particle with an azimuthal electric field (proportional to the inverse of the radial distance) and the fixed time-like vector field, that analogues of the Aharonov-Bohm effect can be obtained. Besides, from the interaction of the Dirac field with an azimuthal electric field (proportional to the radial distance) and the fixed time-like vector field, therefore, a relativistic analogue of the Landau quantization can be achieved. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the influence of the Aharonov-Casher (AC) effect on the relativistic and nonrelativistic energy spectra of a neutral Dirac particle with position-dependent mass (PDM). To exactly solve our system, we use the projection operators left-handed and right-handed. Next, we explicitly determine the energy spectra for the bound states of the particle. As a result, we verify that the relativistic spectrum depends on the quantum numbers n and ml, AC quantum phase ΦAC generated by AC effect and of the parameter κ that characterize the PDM. In addition, this spectrum is a periodic function and increase in absolute values with the increase of ΦAC. We also verify that the energies of the particle are minors that of the antiparticle, and in the limit of the constant mass (κ → 0) the rest energy is recovered. However, in the absence of the AC effect (ΦAC → 0), the spectrum still remains quantized in terms of n and ml. Finally, we analyze the nonrelativistic limit of our work, where we obtain an energy spectrum with some characteristics similar to the relativistic case. Making an analogy with some works of the literature, in particular with the hydrogen atom, we note that our nonrelativistic spectrum provides the so-called binding energies, while that its absolute values provides the so-called ionization energies. [ABSTRACT FROM AUTHOR]

It is shown that the paper "Energy spectrum of a Dirac particle with position-dependent mass under the influence of the Aharonov-Casher effect," by Oliveira et al. (Braz. J. Phys. 49, 801 2019), is based on a series of ingredients clearly incorrect. [ABSTRACT FROM AUTHOR]

Berry phase is a very general concept. It is applied here to families of solutions of the Dirac equation with different values of spin. The value of the Berry phase in the spin space is given by the same expression as was found before in the momentum space. [ABSTRACT FROM AUTHOR]

The semiclassical Boltzmann transport equation of charged, massive fermions in a rotating frame of reference, in the presence of external electromagnetic fields is solved in the relaxation time approach to establish the distribution function up to linear order in the electric field in rotating coordinates, centrifugal force and the derivatives. The spin and spin current densities are calculated by means of this distribution function at zero temperature up to the first order. It is shown that the nonequilibrium part of the distribution function yields the spin Hall effect for fermions constrained to move in a plane perpendicular to the angular velocity and magnetic field. Moreover it yields an analogue of Ohm’s law for spin currents whose resistivity depends on the external magnetic field and the angular velocity of the rotating frame. Spin current densities in three-dimensional systems are also established. [ABSTRACT FROM AUTHOR]

A system of multiple spacelike separated Dirac particles is considered and a method for constructing polynomial invariants under the spinor representations of the local proper orthochronous Lorentz groups is described. The method is a generalization of the method used in Johansson (2022) for the case of two Dirac particles. All polynomials constructed by this method are identically zero for product states. The behaviour of the polynomials under local unitary evolution that acts unitarily on any subspace defined by fixed particle momenta is described. By design all of the polynomials have invariant absolute values on this kind of subspaces if the evolution is locally generated by zero-mass Dirac Hamiltonians. Depending on construction some polynomials have invariant absolute values also for the case of nonzero-mass or additional couplings. Because of these properties the polynomials are considered potential candidates for describing the spinor entanglement of multiple Dirac particles, with either zero or arbitrary mass or additional couplings. Polynomials of degree 2 and 4 are derived for the cases of three and four Dirac spinors. For three spinors no non-zero degree 2 polynomials are found but 67 linearly independent polynomials of degree 4 are identified. For four spinors 16 linearly independent polynomials of degree 2 are constructed as well as 26 polynomials of degree 4 selected from a much larger number. The relations of these polynomials to the polynomial spin entanglement invariants of three and four non-relativistic spin- 1 2 particles are described. Moreover, it is described how degree 4 polynomials for five spinors can be constructed and how degree 2 polynomials can be constructed for any even number of spinors. • Method for constructing local Lorentz invariants for multiple Dirac spinors • Locally Lorentz invariant polynomials constructed from skew-symmetric bilinear forms • Constructed polynomials identically zero for all product states • Constructed polynomials invariant up to U(1) phase under different local evolutions [ABSTRACT FROM AUTHOR]

One-dimensional discrete-time quantum walks (DTQWs) can simulate various quantum and classical dynamics and have already been implemented in several physical systems. This implementation needs a well-controlled quantum dynamical system, which is the same requirement for implementing quantum information processing tasks. Here, we consider how to realize DTQWs by Dirac particles toward a solid-state implementation of DTQWs. [ABSTRACT FROM AUTHOR]

As a follow-up to a recent study in the spin-0 case (Bunao and Galapon, 2015), we construct a one-particle Time of Arrival (TOA) operator conjugate to a Hamiltonian describing a free relativistic spin- 1 / 2 particle in one spatial dimension. Upon transformation in a representation where the Hamiltonian is diagonal, it turns out that the constructed operator consists of an operator term T ˆ whose action is the same as in the spin-0 case, and another operator term T ˆ 0 which commutes with the Hamiltonian but breaks invariance under parity inversion. If we must impose this symmetry on our TOA operator, then we can throw away T ˆ 0 so that the TOA operator is just T ˆ . [ABSTRACT FROM AUTHOR]

The tunneling of the Dirac particle through the strained graphene stripes driven by the static and dynamic potentials has been investigated. The central and neighboring sidebands transmissions have been obtained and compared under the different incident angles, the strength of time-periodic potentials and the strains exerted along respectively the armchair and zigzag directions. The detailed numerical results show that the well-known normal-incidence Klein tunneling can be realized through the superposition of the transmissions from each sideband channels. The increase of the strength of time-periodic potentials can usually lead to the suppression of the transmission from the central band, but the enhancement of the transmission from the side channels, when the strain is exerted along the zigzag direction. [ABSTRACT FROM AUTHOR]

We consider the Duffin-Kemmer-Petiau (DKP) equation in the presence of a spatially one-dimensional Woods-Saxon (WS) potential and we show by graphics how the zero-reflection condition on the Klein interval depends on the shape of the potential. [ABSTRACT FROM AUTHOR]

In this contribution, we discuss the influence of noninertial effects on a Dirac particle in the Minkowski spacetime by showing that the geometry of the manifold can play the role of a hard-wall confining potential. Thus, we discuss a limit case where the relativistic bound states can be achieved in analogous way to having a Dirac particle confined to a quantum dot. We discuss the application of this mathematical model in studies of noninertial effects on condensed matter systems described by the Dirac equation, and compare the nonrelativistic limit of the energy levels with the spectrum of energy of a spin-½ particle confined to a quantum dot [E. Tsitsishvili et al., Phys. Rev. B 70 (2004) 115316]. [ABSTRACT FROM AUTHOR]

Abstract: We study the nonperturbative effects of the minimal length on the energy spectrum of a relativistic particle in the context of the generalized uncertainty principle (GUP). This form of GUP is consistent with various candidates of quantum gravity such as string theory, loop quantum gravity, and black-hole physics and predicts a minimum measurable length proportional to the Planck length. Using a recently proposed formally self-adjoint representation, we solve the generalized Dirac and Klein–Gordon equations in various situations and find the corresponding exact energy eigenvalues and eigenfunctions. We show that for the Dirac particle in a box, the number of the solutions renders to be finite as a manifestation of both the minimal length and the theory of relativity. For the case of the Dirac oscillator and the wave equations with scalar and vector linear potentials, we indicate that the solutions can be obtained in a more simpler manner through the self-adjoint representation. It is also shown that, in the ultrahigh frequency regime, the partition function and the thermodynamical variables of the Dirac oscillator can be expressed in a closed analytical form. The Lorentz violating nature of the GUP-corrected relativistic wave equations is discussed finally. [Copyright &y& Elsevier]

Abstract: We consider a quantum system of a Dirac particle interacting with the quantum radiation field, where the Dirac particle is in a -Hermitian matrix-valued potential V. Under the assumption that the total Hamiltonian is essentially self-adjoint (we denote its closure by ), we investigate properties of the Heisenberg operator () of the j-th position operator of the Dirac particle at time and its strong derivative (the j-th velocity operator), where is the multiplication operator by the j-th coordinate variable (the j-th position operator at time ). We prove that , the domain of the position operator , is invariant under the action of the unitary operator for all and establish a mathematically rigorous formula for . Moreover, we derive asymptotic expansions of Heisenberg operators in the coupling constant (the electric charge of the Dirac particle). [Copyright &y& Elsevier]