Mecânica quântica no espaço de fase não-comutativo e aplicações em termodinâmica
Fecha
2016-08-26Autor
Santos, Jonas Floriano Gomes dos
Metadatos
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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.