This book provides an introduction to topics in non-equilibrium
quantum statistical physics for both mathematicians and theoretical
physicists. The first part introduces a kinetic equation, of
Kolmogorov type, which is needed to describe an isolated atom
(actually, in experiments, an ion) under the effect of a classical
pumping electromagnetic field which keeps the atom in its excited
state(s) together with the random emission of fluorescence photons
which put it back into its ground state. The quantum kinetic theory
developed in the second part is an extension of Boltzmann's
classical (non-quantum) kinetic theory of a dilute gas of quantum
bosons. This is the source of many interesting fundamental
questions, particularly because, if the temperature is low enough,
such a gas is known to have at equilibrium a transition, the
Bose-Einstein transition, where a finite portion of the particles
stay in the quantum ground state. An important question considered
is how a Bose gas condensate develops in time if its energy is
initially low enough.
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