Measurement, decoherence and chaos in quantum pinball

Dewdney, C.; Malik, Z.

doi:10.1016/0375-9601(96)00533-6

Cited by 21 publications

(19 citation statements)

References 7 publications

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“…In recent years several authors (Dürr et al 1992;Faisal and Schwengelbeck 1995;Parmenter and Valentine 1995;de Polavieja 1996;Dewdney and Malik 1996;Iacomelli and Pettini 1996;Frisk 1997;Konkel and Makowski 1998;Wu and Sprung 1999;Makowski et al 2000;Cushing 2000;Falsaperla and Fonte 2003;de Sales and Florencio 2003;Wisniacki and Pujals 2005;Valentini and Westman 2005;Efthymiopoulos and Contopoulos 2006;Efthymiopoulos et al 2007) presented a consistent approach to the problem of chaos in quantum-mechanical systems that does not rely on the classical properties of the same systems. This is the Bohmian (or 'pilot wave') approach (de Broglie 1926;Bohm 1952a,b, etc), that considers deterministic quantum orbits.…”

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confidence: 98%

Ordered and chaotic Bohmian trajectories

Contopoulos

Efthymiopoulos

2008

Celest Mech Dyn Astr

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We discuss the issue of ordered and chaotic trajectories in the Bohmian approach of Quantum Mechanics from points of view relevant to the methods of Celestial Mechanics. The Bohmian approach gives the same results as the orthodox (Copenhagen) approach, but it considers also underlying trajectories guided by the wave. The Bohmian trajectories are rather different from the corresponding classical trajectories. We give examples of a classical chaotic system that is ordered quantum-mechanically and of a classically ordered system that is mostly chaotic quantum mechanically. Then we consider quantum periodic orbits and ordered orbits, that can be represented by formal series of the "third integral" type, and we study their asymptotic properties leading to estimates of exponential stability. Such orbits do not approach the "nodal points" where the wavefunction ψ vanishes. On the other hand, when an orbit comes close to a nodal point, chaos is generated in the neighborhood of a hyperbolic point (called X-point). The generation of chaos is maximum when the X-point is close to the nodal point. Finally we remark that high order periodic orbits may behave as "effectively ordered" or "effectively chaotic" for long times before reaching the period.

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confidence: 98%

Ordered and chaotic Bohmian trajectories

Contopoulos

Efthymiopoulos

2008

Celest Mech Dyn Astr

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“…(16)(17)(18)(19)22,23,45) A physical realization of the standard map, and an archetype of many chaotic systems, the rotator not only illustrates subtleties of the Bohmian classical limit, it also confronts us with a major obstacle to achieving that limit. Our discussion of the rotator will be limited to features relevant to our purposes.…”

Section: Kicked Rotatormentioning

confidence: 99%

“…(3,4,16,23,38,39) In what follows, we argue that the usual means of seeking the classical limit of Bohmian mechanics is flawed. We hope to make a compelling case that the correct route must combine mixed states, narrow wave packets, and decoherence.…”

Section: Introductionmentioning

confidence: 99%

On the Classical Limit in Bohm?s Theory

Bowman

2005

Found Phys

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“…For the classically chaotic cases (b and c), H increases abruptly and has large positive values as compared to the integrable cases. Hence, we can say that two initially nearby trajectories remain close to each other in the integrable case but separate The quantum cat map, [94,95] the parabolic barrier, [96,97] hydrogen atom in an oscillating electromagnetic field, [98] and also the quantum pinball monitored by measuring devices [99] are some examples of the physical systems where quantum chaos has been studied. Konkel and Makowski [100] showed that the Bohmian trajectories generated by the combination of two suitably chosen stationary state wave functions generated chaos.…”

Section: Some Chaotic Anharmonic Oscillatorsmentioning

confidence: 99%

Density dynamics in some quantum systems

Khatua

Chakraborty

Chattaraj

2013

Int J of Quantum Chemistry

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The quantum domain behavior of classical nonintegrable systems is well-understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov-Arnold-Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field-induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories.Quantum fluid density functional theory may be used to understand different time-dependent processes like ion-atom/ molecule collisions, atom-field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained.

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Measurement, decoherence and chaos in quantum pinball

Cited by 21 publications

References 7 publications

Ordered and chaotic Bohmian trajectories

Ordered and chaotic Bohmian trajectories

On the Classical Limit in Bohm?s Theory

Density dynamics in some quantum systems

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