Quantum Dissipative Harmonic Systems: a Study of the Specific Heat

We start this work by briefly introducing the reader to the theory of quantum dissipation in open quantum systems, using the Caldeira-Leggett model, with our focus being obtaining the thermodynamic properties of these systems. We show that the specific heat can become negative, which can be better understood when it is interpreted as the change of the environment specific heat when we attach an extra degree of freedom [G.- L. Ingold et al, Phys. Rev. E 79, 061105 (2009)]. We proceed introducing the problem which was our original motivation: for a model also composed of harmonic oscillators [H. Hasegawa, J. Math. Phys. 52, 123301 (2011)], it is possible to obtain negative specific heat in contradiction with the findings of [G.-L. Ingold et al.], where only for the free particle potential we could obtain such result. We obtain that because of the different potential renormalizations, each system describes a different physical reality, ensuring that there is in fact no contradiction. The last chapter is dedicated to analyse the influence of the system internal interaction in its thermodynamic proprieties.