Mecânica quântica no espaço de fase não-comutativo e aplicações em termodinâmica

Abstract

In this work we study theoretical aspects arising from the fact of considering a quantum theory with general relations of noncommutativity. Through the quantum mechanics in phase-space formalism in the Wigner-Weyl prescription, we obtained the Wigner function describing the state of the system and the respective eigenvalues. By using the Seiberg-Witten map to describe noncommutative quantum systems in the standard Hilbert space, it was possible to write NC effects as potential terms in the Hamiltonian operator, where it was verified that they act in general like an effective external magnetic field on the system. We quantify the impact of this deformed Weyl-Heisenberg algebra in some relevant quantum systems through the tools of information theory. Finally, we investigate noncommutative effects in quantum heat engines and quantify them by using the thermodynamic eficiency for some specific cycles, the iso-magnetic and the iso-energetic ones. Also considering thermodynamics cycles, we investigated noncommutative effects in a Carnot cycle and one shows in this case that the e"ciency is not affected, reinforcing the validity of the second law of thermodynamics.