No description available.

No description available.

No description available.

No description available.

No description available.

Neste trabalho apresentamos um estudo da dinâmica de subsistemas quânticos dando ênfase ao fenômeno da decoerência. Em particular, estudamos os efeitos da decoerência num sistema de dois níveis acoplado a um outro sistema cujo espectro de energia é um contínuo no contexto do fenômeno quântico de tunelamento. Investigamos também aspectos da relação entre a descrição do sistema de dois níveis e a descrição do modelo linear na aproximação de onda girante em termos de uma equação mestra na aproximação de Born-Markov e a dinâmica exata destes dois subsistemas. Estudamos também o experimento proposto por L. Davidovich e colaboradores para medir a decoerência de superposições mesoscópicas de estados coerentes dentro do contexto da computação quântica. Este experimento pode ser re interpretado como um computador quântico capaz de solucionar o problema de Deutsch. O grande problema deste experimento, do ponto de vista da computação quântica, é a presença da decoerência. Esta decoerência provoca o aparecimento de erros no resultado final. Assim, nós mostramos uma maneira de reduzi-la, diminuindo assim os eventuais erros que possam aparecer. Finalmente, mostramos através de dois exemplos a relação entre o efeito Zeno e a decoerência. / We study the quantum decoherence process in different contexts. In particular, we study decoherence effects in the dynamics of a two-level system coupled to another system which has a continuous energy spectrum. We also investigate when the master equation description, in a Born Markov approximation reproduces the exact solution. We extend this investigation to the model which describes the interaction between a harmonic oscillator and a thermal bath of harmonic oscillators in the rotating wave approximation. We also study the two atom correlation scheme originally proposed by Davidovich, Brune, Raimond and Haroche for measuring the decoherence of a mesoscopic superposition of coherent states of a QED cavity in the context of quantum computation. We show that this experiment is equivalent to a quantum computer solving Deutsch\'s problem. We find a way to reduce the errors due to decoherence. Finally, we show how the Zeno effect is related to the decoherence process.

Neste trabalho apresentamos um estudo da dinâmica de subsistemas quânticos dando ênfase ao fenômeno da decoerência. Em particular, estudamos os efeitos da decoerência num sistema de dois níveis acoplado a um outro sistema cujo espectro de energia é um contínuo no contexto do fenômeno quântico de tunelamento. Investigamos também aspectos da relação entre a descrição do sistema de dois níveis e a descrição do modelo linear na aproximação de onda girante em termos de uma equação mestra na aproximação de Born-Markov e a dinâmica exata destes dois subsistemas. Estudamos também o experimento proposto por L. Davidovich e colaboradores para medir a decoerência de superposições mesoscópicas de estados coerentes dentro do contexto da computação quântica. Este experimento pode ser re interpretado como um computador quântico capaz de solucionar o problema de Deutsch. O grande problema deste experimento, do ponto de vista da computação quântica, é a presença da decoerência. Esta decoerência provoca o aparecimento de erros no resultado final. Assim, nós mostramos uma maneira de reduzi-la, diminuindo assim os eventuais erros que possam aparecer. Finalmente, mostramos através de dois exemplos a relação entre o efeito Zeno e a decoerência. / We study the quantum decoherence process in different contexts. In particular, we study decoherence effects in the dynamics of a two-level system coupled to another system which has a continuous energy spectrum. We also investigate when the master equation description, in a Born Markov approximation reproduces the exact solution. We extend this investigation to the model which describes the interaction between a harmonic oscillator and a thermal bath of harmonic oscillators in the rotating wave approximation. We also study the two atom correlation scheme originally proposed by Davidovich, Brune, Raimond and Haroche for measuring the decoherence of a mesoscopic superposition of coherent states of a QED cavity in the context of quantum computation. We show that this experiment is equivalent to a quantum computer solving Deutsch\'s problem. We find a way to reduce the errors due to decoherence. Finally, we show how the Zeno effect is related to the decoherence process.

This master’s thesis investigates the relationship between supersymmetry and integrability in quantum mechanics. This is done by finding a suitable way to systematically add more supersymmetry to the system. Adding more super- symmetry will give constraints on the potential which will lead to an integrable system. A possible way to explore the integrability of supersymmetric quantum mechanics was introduced in a paper by Crombrugghe and Rittenberg in 1983, their method has been used as well as another approach based on expanding a N = 1 system by introducing complex structures. N = 3 or more supersymmetry is shown to give an integrable system.

The central aim of this thesis is to present a new kind of realism that is driven not from the traditional realism/anti-realism debate but from the practice of physicists. The usual debate focuses on discussions about the truth of theories and how they relate with nature, while the real practices of the scientists are forgotten. The position I shall defend is called "phenomenological realism". The realist doctrine was recently undermined by the argument from pessimistic meta-induction, also known as the argument from scientific revolutions. I argue that phenomenological realism is a new kind of scientific realism that can overcome the problem generated by the pessimistic meta-induction, and which reflects scientific practice. The realist has tried to overcome the pessimistic meta-induction by suggesting various types of theory dichotomy. I claim that the different types of dichotomy normally presented by realists do not overcome the problem, for these dichotomies cut through theory vertically. I argue for a different kind of dichotomy, one that cuts horizontally, between high-level and low-level theoretical representations. I claim that theoretical forms in physics have two distinct types depending on the way they are built. These are theoretical models that are built depending on a top-down approach and phenomenological models that are built depending on a bottom-up approach. I argue that for the most part only phenomenological models are the vehicles of accurate representation. I present two case studies. The first case study is from superconductivity, where I contrast the BCS model of superconductivity with the phenomenological model of Landau and Ginzburg. The other case study is a fresh look at the Bohr-Einstein debate.

The theory of classical chaos is reviewed. From the definition of integrable systems using the Hamilton-Jacobi equation, the theory of perturbed systems is developed and the Kolmogorov-Arnold-Moser (KAM) theorem is explained. It is shown how chaotic motion in Hamiltonian systems is governed by the in tricate connections of stable and unstable invariant manifolds, and how it can be catagorised by algorithmic complexity and symbolic dynamics, giving chaotic measures such as Lyapunov exponents and Kolmogorov entropy. Also reviewed is Gutzwiller's semiclassical trace formula for strongly chaotic systems, torus quantisation for integrable systems, the asymptotic level density for stationary billiards, and random matrix theories for describing spectral fluctuation properties. The classical theory is applied to rotating billiards, particularly the free motion of a particle in a circular billiard rotating uniformly in its own plane about a point on its edge. Numerically, it is shown that the system's classical behaviour ranges from fully chaotic at intermediate energies, to completely integrable at very low and very high energies. It is shown that the strong chaos is due to discontinuities in the Poincare map, caused by trajectories which just glance the boundary-an effect of the curvature of trajectories. Weaker chaos exists due to the usual folding and stretching of the Hamiltonian flow. Approximate invariant curves for integrable motion are found, valid far from the presence of glancing trajectories. The major structures of phase space are investigated: a fixed point and its bifurcation into a two-cycle, and their stabilities. Lyapunov exponents for trajectories are calculated and the chaotic volume for a wide range of energies is measured. Quantum mechanically, the energy spectrum of the system is found numerically. It is shown that at the energies where the classical system is completely integrable the levels do not repel, and at those energies where it is completely chaotic there is strong level repulsion. The nearest neighbour level spacing distributions for various ranges of energy and values of Planck's constant are found. In the semiclassical limit, it is shown that, for energies where the classical system is completely chaotic, the level spacing statistics are Wigner, and where it is completely integrable, the level spacing statistics are Poisson. A model is described for the spacing distributions where the levels can be either Wigner or Poisson, which is useful for showing the transition from one to the other, and ad equately describes the statistics. Theoretically, the asymptotic level density for rotating billiards is calculated, and this is compared with the numerical results with good agreement, after modification of the method to include all levels.