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Register a new userSemiclassical dynamics of Dirac and Weyl particles in rotating coordinates
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The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in spin indices is proposed. The particle number and current densities for the Dirac particles are acquired in the helicity basis. Following a similar procedure, semiclassical kinetic theory of the Weyl particles is accomplished. It is shown that the phase-space dynamics of the Weyl and Dirac particles is directly linked. The anomalous chiral effects due to the external electromagnetic fields and angular velocity of the frame are calculated.
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Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact in equations of motion it eliminates the terms arising from the Berry gauge fields.
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 Ohms 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.
We establish covariant semiclassical transport equations of massive spin-1/2 particles which are generated by the quantum kinetic equation modified by enthalpy current dependent terms. The purpose of modification is to take into account the noninertial properties due to the angular velocity of rotating frame which is equivalent to the fluid vorticity in hydrodynamical approach. We present the equations satisfied by the Wigner function components and by studying their solution in the semiclassical approximation we accomplish the transport equations. To acquire a three-dimensional kinetic theory, the relativistic kinetic equations in the comoving frame are integrated over the zeroth component of four-momentum. The resulting vector and axial-vector currents are calculated at zero temperature. There exists another three-dimensional formulation of Dirac particles which correctly addresses the noninertial features of rotating coordinates. We review it briefly and obtain the mass corrections to the chiral vector and axial-vector currents produced by this formulation.
Hawking radiation from black holes has been studied as a phenomenon of quantum tunneling of particles through their horizons. We have extended this approach to study the tunneling of Dirac particles from a large class of black holes which includes those with acceleration and rotation as well. We have calculated the tunneling probability of incoming and outgoing particles, and recovered the correct Hawking temperature by this method.
The nonlinear transport features of inhomogeneous chiral plasma in the presence of electromagnetic fields, in rotating coordinates are studied within the relaxation time approach. The chiral distribution functions up to second order in the electric field in rotating coordinates and the derivatives of chemical potentials are established by solving the Boltzmann transport equation. First, the vector and axial current densities in the weakly ionized chiral plasma for vanishing magnetic field are calculated. They involve the rotational analogues of the Hall effect as well as several new terms arising from the Coriolis and fictitious centrifugal forces. Then in the short relaxation time regime the angular velocity and electromagnetic fields are treated as perturbations. The current densities are obtained by retaining the terms up to second order in perturbations. The time evolution equations of the inhomogeneous chemical potentials are derived by demanding that collisions conserve the particle number densities.
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