Quantum fluctuation theorem for dissipative cyclotron motion

We examine the fluctuation theorems which traditionally have been studied for classical systems and enquire if they can be extended to the quantum domain, especially at low temperatures. The example chosen is that of a problem which has proven to be of great interest in the context of Landau diamagnetism viz. the quantized motion of an electron in a magnetic field and in a dissipative environment. It is established from first principles that the quantum work operator W has a Gaussian distribution even though the system under consideration has a four dimensional phase space. The parameter $\alpha$ in the fluctuation theorem $p(W )/p(-W) = exp(\alpha W)$ depends on the system dynamics and has characteristic quantum features, especially at low temperatures. Certain unique low temperature signatures are also discussed.