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| Author(s): |
Tiago Barbin Batalhão
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT) |
| Defense date: | 2012-07-26 |
| Examining board members: |
Miled Hassan Youssef Moussa;
Eduardo Ribeiro de Azevêdo;
Marcel Novaes
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| Advisor: | Miled Hassan Youssef Moussa |
| Abstract | |
We present a comprehensive treatment of the interaction of a quantum system with an environment modeled as a set of harmonic oscillators. We start from a previous treatment of a network of quantum dissipative harmonic oscillators. Using the characteristic function, we transform the von Neumann equation in a differential equation, and exploring its linearity, this is transformed in a vector equation, whose solution is computationally efficient. Our method, whose origin lies on a network not necessarily divided into system and reservoir, allows us to circumvent the necessity of the sudden-coupling approximation for the exact treatment of the system evolution. After this, we show that this dynamics can always be described by a master equation in standard Lindblad form, although its coefficients may be functions of time. This opens new possibilities for the system dynamics, and lead to effects that may be called non-Markovian, even if they are described by a completely local-in-time master equation. It should be emphasized that, as it is based on an exact solution, the method may be applied for any strength of the system-reservoir interaction, and it is considerably simpler than other available methods, such as those based on path integrals. Finally, we employ computer simulations to investigate the validity of the rotating-wave and Born-Markov approximations, and the phenomena that migth be observed in regimes in which they fail to be valid. (AU) | |
| FAPESP's process: | 10/13672-9 - Quantum trajectories, atomic lithography, interaction of matter with Casimir radiation and quantum dissipation |
| Grantee: | Tiago Barbin Batalhão |
| Support Opportunities: | Scholarships in Brazil - Master |