Corrente quântica na representação de estados coerentes

Author(s)

Matheus Veronez

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2015-12-16

Examining board members

Marcus Aloizio Martinez de Aguiar; Ricardo Luís Doretto; Silvio Antonio Sachetto Vitiello; Marcel Novaes; Alfredo Miguel Ozório de Almeida

• Advisor: Marcus Aloizio Martinez de Aguiar

Abstract

Phase space representations are widely used tools to study and simulate the quantum dynamics of systems, mainly due to its natural classical appeal. In both classical and quantum mechanics, corresponding but not equivalent structures, such as probability densities, can be defined and explored to compare both dynamical regimes. In this work, we constructed from first principles the quantum phase space current for a quantum system in the canonical coherent states representation. We determined the quantum current for systems evolving under a general Hamiltonian, and we showed that the current can be expanded as a power series in $hbar$, whose lowest order term is the classsical current. We also calculated analytically the quantum current for simple one-dimensional systems. The quantum current presents non-classical features, such as momentum inversion and emergence of new stagnation points which appear in pairs during the dynamics. We showed that the pairs are composed by a saddle point, which is a zero of the phase space probability density and bears a topological charge -1, and a vortex, with charge +1. Both points constitute what we named a topological dipole. We analysed the role the dipoles play in the scattering of a particle by a gaussian barrier, and we showed that the location of the dipoles in relation to the classical energy surfaces and the quantum probability density maxima is a fingerprint of quantum tunneling (AU)

• FAPESP's process: 13/02248-0 - Quantum flow on the phase space
• Grantee: Matheus Veronez
• Support Opportunities: Scholarships in Brazil - Doctorate