Relaxamento para o equilíbrio quântico em osciladores harmônicos acoplados

Abstract

In this thesis we approach the problem of the interpretation of quantum phenomenathrough the Pilot Wave Theory, initially developed by Louis de Broglie and consolidated by David Bohm. Initially the paradoxes of the Copenhagen Interpretation and thediscussions around the hidden variables question are presented. The historical development of the Pilot Wave Theory is described, demonstrating how the theory solves the measurement problem without violating the conditions imposed by experimental results. The complete formulation of the theory and it’s applications are also presented. In the context of the Pilot Wave Theory the Born rule is not postulated and to explain it’s validity an statistical argument, analogous to the classical H theorem was developed to describe the equality between the distribution and the square module of the wave functionas an equilibrium state. The development of the classical version of the theorem is briefly described to introduce the construction of the quantum H theorem. It is demonstrated how, for systems that violate the Born rule - out of quantum equilibrium -, the Heisenberg inequalities do not hold and the instantaneous sending of signals becomes possible. The decay to equilibrium is analysed through numerical simulations made for simple system sinitially out of equilibrium. The central objective of this thesis is to analyse the decay to equilibrium of a quantum system composed by two one-dimensional oscillators coupled by a time-dependent potential. Through the realization numerical simulations effects of the variation of the coupling constant, the number of modes and the phases of the initial on the decay time wave function were discussed. Finally, some cosmological scenarios where non-equilibrium may have existed and the possible ways it can be found experimentallyare described.