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Register a new userA Semiclassical Kinetic Theory of Dirac Particles and Thomas Precession
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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.
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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.
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.
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical scheme. It is demonstrated that the chiral currents and energy-momentum tensor computed by means of them are consistent with the hydrodynamical results. A new semiclassical covariant chiral transport equation is established by inspecting the equations satisfied by the chiral vector fields. It uniquely provides a new three-dimensional semiclassical chiral kinetic theory possessing a Coriolis force term. The particle number and current densities deduced from this transport equation satisfy the anomalous continuity equation and generate the magnetic and vortical effects correctly.
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum graphs is obtained. Band spectra of the periodic quantum graphs of different topologies are calculated. Universality of the probability to be in the spectrum for certain graph topologies is observed.
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.
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