A dynamic model of interactions between conscious and unconscious

This paper advocates that some limits of the rational agent hypothesis result from the improper assumption that one individual should be modeled as a single rational agent. We model an individual composed of two autonomous and interacting structures, conscious and unconscious. Each agent utility form depends both on external signals and other structures' actions. The perception of the signal depends on its recipient and its grid of interpretation. We study both the static and dynamic version of this interaction mechanism. We show that the dynamics may display instability, depending on the structures interactions'strength. However, if unconscious has a strategic advantage, greater stability is reached. By manipulating other structures�goals, the strategic agent can lead the whole system to an equilibrium closer to its own optimum. This result shows that some switch in the conscious�objective can appear. Behaviors that can't be explained with a single utility can thus be rational if we add a rational unconscious agent. Our results justify our hypothesis of a rational interacting unconscious. It supports the widening of the notion of rationality to multi-rationnality in interaction.dual agent; conscious and unconscious; rationality; multi-rationality; emotions; choices and preferences; multi-agent model; consistency;

Dirac Particles in a Gravitational Field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in comparison to previous works on the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings which contribute to the breaking of the particle - antiparticle symmetry

Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order $\hbar$ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.Comment: 15 page