Axiomatic open quantum physics
Pp. 93-108 (16)
This chapter is devoted to Lindblad master equation, obtained by a generalization of
the quantum dynamic group to a time dependent semigroup. For this equation, we present
a demonstration of Alicki and Lendi, obtained by a linear approximation of the openness
operator, which describes the time evolution of a system of interest in an environment. We
re-obtain this equation by taking the total dynamic equation with a bilinear dissipative
potential in system and environment operators, and tracing over the environment states.
In this way, we get physical expressions of the dissipation coefficients, as functions of the
system operators. We present the quantum theory of Sandulescu and Scutaru, where the
dissipative dynamics is described by friction and diffusion processes, with coefficients which
satisfy fundamental constraints.
Hilbert space, Banach space, evolution operator, dynamic map, dynamic
group, dynamic semigroup, superoperator, openness operator, Born-Markov approximation,
Lindblad’s generator, dissipative dynamics, dissipation coefficient, hermiticity, positivity,
convexity, normalization, Gibbs distribution, friction, diffusion, fundamental constraint.
Center of Advanced Studies in Physics of the Romanian Academy, Bucharest Romania.