Quantal trajectories and geometric phase

University dissertation from Uppsala : Acta Universitatis Upsaliensis

Abstract: This thesis concerns the following topics: geometric phase in the context of Galilean invariance and quantum measurements, Rydberg states of hydrogen atoms, vibronic coupling in the <I>E Ä e Jahn-Teller system and realism in quantum computations. In the analyses the de Broglie-Bohm pilot-wave formulation of quantummechanics is mainly used.It is shown that geometric phase is not Galilean invariant. Experimental implications are discussed and it is found that the experiments performed to date are frame independent. An experiment which is in principle able to detect the noninvariance is sketched. By adopting the measurement theory of the pilot-wave formulation it is shown how the measurement induced geometric phase continuously emerges. The Samuel-Bhandari geometric phase is identified as the nonrandom part of the total geometric phase induced in the measurement.Ensembles of particles for a circular Rydberg wave packet are studied. The trajectories of pilot-wave particles are shown to accurately imitate the behaviour of the wave packet in the high quantum number limit. The nonclassical features of the wave packet are intuitively explained by the nonvanishing quantum potential.Vibronic coupling in the Longuet-Higgins model of the <I>E Ä e Jahn-Teller system is investigated by means of quantal trajectories. The pilot-wave picture provides an intuitive tool for discussing time-scales. An argument based on ergodicity leads to an understanding of the averaging procedure over the electronic motion which provides the approximate nuclear motion.The existence of efficient quantum algorithms triggers questions on Natures ability of storing and processing information during quantum computations. The role of elements of reality in quantum computations is addressed using quantal trajectories. It is found that there is a many-to-one relationship between quantal trajectories and performed computations when quantum parallelism is utilized.

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