The Bloch equation models the evolution of the state of electrons in matter described by a Hamiltonian. To model more physical phenomena we have to introduce phenomenological relaxation terms. The introduction of these terms has to conserve some positiveness properties. The aim of this paper is to review possible relaxation models and to provide insight into how to discretize them properly in view of numerical computations.
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We consider the propagation of a high intensity, strongly focused laser pulse in transparent dielectrics. These are the materials with a large band-gap energy W i ӷប 0 , where 0 is the laser frequency; therefore, the absorption coefficient at low intensities is negligibly small. Following the experimen-PHYSICAL REVIEW B 76, 024101 ͑2007͒
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