Quantum master equations for a fast particle in a gas
- URL: http://arxiv.org/abs/2209.02056v2
- Date: Sun, 18 Dec 2022 19:43:01 GMT
- Title: Quantum master equations for a fast particle in a gas
- Authors: David Gaspard
- Abstract summary: The propagation of a fast particle in a low-density gas at thermal equilibrium is studied in the context of quantum mechanics.
A quantum master equation in the Redfield form governing the reduced density matrix of the particle is derived explicitly from first principles.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The propagation of a fast particle in a low-density gas at thermal
equilibrium is studied in the context of quantum mechanics. A quantum master
equation in the Redfield form governing the reduced density matrix of the
particle is derived explicitly from first principles. Under some
approximations, this equation reduces to the linear Boltzmann equation. The
issue of the positivity of the time evolution is also discussed by means of a
Lindblad form. The Born and Markov assumptions underlying these equations, as
well as other approximations regarding the bath correlation function, are
discussed in details. Furthermore, all these master equations are shown to be
equivalent with each other if the density matrix of the particle is diagonal in
the momentum basis, or if the collision rate is independent of the particle
momentum.
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