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http://hdl.handle.net/1843/51529| Type: | Tese |
| Title: | Relation between Lyapunov exponents and decoherence for real scalar fields in De Sitter spacetime |
| Authors: | Gustavo Henrique Costa de Souza |
| First Advisor: | Marcos Donizeti Rodrigues Sampaio |
| First Co-advisor: | Karen Milena Fonseca Romero |
| First Referee: | Pablo Lima Saldanha |
| Second Referee: | George Emanuel Avraam Matsas |
| Third Referee: | Sérgio Eduardo de Carvalho Eyer Jorás |
| metadata.dc.contributor.referee4: | Giancarlo Queiroz Pellegrino |
| Abstract: | We investigate the relationship between orbital instability and decoherence in de Sitter (dS) spacetime. We consider a simple quadratic toy model proposed by Brandenberger, Laflamme and Mijic of two interacting scalar fields in a dS background. It admits a modewise separation, with each mode consisting of a pair of nonautonomous coupled harmonic oscillators. We show that the (classical) maximal Lyapunov exponent of every mode equals the asymptotic rate of (quantum) von Neumann entropy production of each oscillator, assuming an initial vacuum. This allows us to establish a logarithmic divergence of the entropy modulated by the spacetime inflation rate, and to calculate the late times superhorizon relationship between entropy generation of an oscillator and the system's exponential orbit separation rate. The connection between orbital instability and the decoherence of an oscillator's state is also examined from the point of view of the nonclassical depth, a quantity that is related to the existence of a phase-space representation for it interpretable as a classical stochastic distribution. We prove that its superhorizon behavior is determined by the balance between single-mode squeezing and entropy. In this regime, the entropy of a mode and the system's exponential orbit separation rate increase significantly as one moves from the weak- to the strong-coupling limit. If this increase is large enough for the entropy of an oscillator to grow more rapidly than squeezing, for example in the strong-coupling limit for not too high frequencies, the noise of every quadrature of the asymptotic state will be larger than the vacuum noise (zero nonclassical depth). The results suggest the possibility that simple, nonlinear interacting physical processes with unstable or chaotic classical counterparts may provide an important contribution to the effectiveness of the classicalization of cosmological scalar fields during a dS stage of spacetime expansion. |
| Subject: | Decoerência Sistemas quânticos abertos |
| language: | eng |
| metadata.dc.publisher.country: | Brasil |
| Publisher: | Universidade Federal de Minas Gerais |
| Publisher Initials: | UFMG |
| metadata.dc.publisher.department: | ICX - DEPARTAMENTO DE FÍSICA |
| metadata.dc.publisher.program: | Programa de Pós-Graduação em Física |
| Rights: | Acesso Aberto |
| URI: | http://hdl.handle.net/1843/51529 |
| Issue Date: | 3-Mar-2015 |
| Appears in Collections: | Teses de Doutorado |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| De_Sitter.pdf | 1.82 MB | Adobe PDF | View/Open |
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