Physics – Quantum Physics
Scientific paper
2011-10-10
Physics
Quantum Physics
10 pages
Scientific paper
We present a deduction of the Lindblad equation that is accessible to students with a basic background on quantum mechanics. We consider a specific case, corresponding to a very simple situation, where a primary system interacts with a bath of harmonic oscillators at zero temperature, with an interaction Hamiltonian that resembles the Jaynes-Cummings format. We start with the Born-Markov equation and, tracing out the bath degrees of freedom, we obtain an equation in the Lindblad form. The speci?c situation is very instructive, for it makes it easy to realize that the Lindblads represent the e?ect on the main system caused by the interaction with the bath, and that the Markov approximation is a fundamental condition for the emergence of the Lindbladian operator. The formal derivation of the Lindblad equation for a more general case requires broader considerations regarding the environment, the temperature, and the use of quantum dynamical semi-groups than we have considered in the particular case treated here.
Brasil Carlos Alexandre
Fanchini Felipe Fernandes
Jesus Napolitano Reginaldo de
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