Dynamics and thermodynamics of linear quantum open systems
I will present general results concerning the evolution and the emergence of the laws of thermodynamics for arbitrary networks of quantum oscillators coupled with arbitrary reservoirs. For such systems, I will show that the quantum state of the network always satisfies a local master equation with a simple analytical solution. Then, I will use this to demonstrate the emergence of the laws of thermodynamics in the long time regime.
Finally, I will apply these results to
study properties crystals formed by cold trapped ions. As it is well known, depending on the number of ions and on the trapping fields, this system undergoes a series of phase transitions where the structure of the ion crystal changes from 1D to 3D.
For all these cases, I will analyze the
conduction of heat through the crystal and discuss the (non)--recovery of Fourier's law.