| 1. |
- Carlsen, Henrik
(författare)
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Quantal trajectories and geometric phase
- 1998
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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 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 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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| 2. |
- Carlsen, Henrik, et al.
(författare)
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Quantal trajectories for adiabatic and nonadiabatic regimes of vibronic systems
- 1999
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Ingår i: International Journal of Quantum Chemistry. - 0020-7608 .- 1097-461X. ; 75:4-5, s. 409-416
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Tidskriftsartikel (refereegranskat)abstract
- Exact and averaged nuclear pseudorotational quantal trajectories are compared for Various adiabatic and vibronic states of the Longuet-Higgins E x epsilon Jahn-Teller model. It is argued that the usual averaging over the electronic motion could be understood as being a consequence of ergodicity. The failure of the Born-Oppenheimer factorization to obey the ergodic hypothesis was examined. A quantitative separation of the electronic and nuclear time-scales is, nevertheless, achieved for all regimes. It is shown that the short-time deviations from the global "drift" of the electronic and nuclear motions are perfectly correlated.
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| 3. |
- Sjöqvist, Erik, et al.
(författare)
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Berry's phase in pilot-wave theory
- 1998
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Ingår i: Foundations of physics letters. - 0894-9875 .- 1572-9524. ; 11:2, s. 179-188
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Tidskriftsartikel (refereegranskat)abstract
- The projective-geometric derivation of Berry's adiabatic geometric phase for a single trajectory in the de Broglie-Bohm pilot-wave theory is given. The relation between this phase and the first order nature of pilot-wave theory is discussed. It is shown, in the case where the electromagnetic vector potential is a gradient, that the phase can be given in a locally phase invariant form. The appearance of the Berry connection is justified and its physical significance in pilot-wave theory is discussed.
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| 4. |
- Sjöqvist, Erik, et al.
(författare)
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Fractional statistics in Bohm's theory
- 1995
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Ingår i: Physics Letters A. - 0375-9601 .- 1873-2429. ; 202:2-3, s. 160-166
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Tidskriftsartikel (refereegranskat)abstract
- We introduce fractional statistics in Bohm's formulation of quantum mechanics.
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| 5. |
- Sjöqvist, Erik, et al.
(författare)
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Galilean noninvariance of geometric phase
- 1997
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Ingår i: Physics Letters A. - 0375-9601 .- 1873-2429. ; 229:5, s. 273-278
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that generally geometric phase in nonrelativistic quantum mechanics is not Galilean invariant. It appears, however, that in none of the actual experiments performed to date on geometric phase is the measured phase frame dependent.
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| 6. |
- Sjöqvist, Erik, et al.
(författare)
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Geometric phase, quantum measurements, and the de Broglie-Bohm model
- 1997
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 56:2, s. 1638-1641
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Tidskriftsartikel (refereegranskat)abstract
- An approach to the measurement induced geometric phase based on the de Broglie-Bohm hidden-variable model is developed. The analysis involves an evolving geometric phase connecting the initial and final states of an individual experimental run. As an illustration the geometric phase produced by a cyclic sequence of spin-1/2 filtering experiments is considered. It is argued, in this case, that the geometric phase can be made close to the Samuel-Bhandari phase.
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