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Relativistic diffusive motion in thermal electromagnetic fields

“…The approach of Kubo [8]- [9] approximates the random Liouville operator in the exponential (17) by the τ 2 term in the expansion (18)(we discuss this approximation in the next section).…”

“…A damping factor inG is necessary if the integral (31) is to exist (such a damping factor is present in the Planck distribution (47)). The approach of Kubo [8]- [9] approximates the random Liouville operator on the rhs of eq. (18) by the τ 2 term.…”

“…The integral (38) is proportional to the correlation time τ c . As discussed in [8]- [9] even if the correlations of the random fields are not decaying exponentially then nevertheless the behaviour of the particle dynamics in random fields described by the matrix α for times small in comparison to the correlation time determines the behaviour for times large in comparison with the correlation time. The large time behaviour is diffusive with the diffusion matrixα related to α in eq.…”

“…The diffusion approximation finds applications in heavy ion collisions [4] [5], plasma physics and in astrophysics [2] [3][6] [7]. A detailed discussion of the diffusion approximation can be found in [8] [9] [10] [11] [12].…”

“…Assuming that the correlation functions of the electromagnetic modes (Fourier components) are decaying fast for the time larger than the correlation time τ c we can apply the Markov approximation treating the particle's subsequent scatterings upon electromagnetic modes as independent. According to Kubo's theory [8]- [9] the second order differential operator arising in the small time expansion is the generator of the diffusion defining the evolution of the system also at times large in comparison to the correlation time τ c . We show that the form of this diffusion is determined uniquely by the assumptions of the Lorentz invariance ofG.…”