Numerical test of Born–Oppenheimer approximation in chaotic systems

Shim, Jeong-Bo; Hussein, M. S.; Hentschel, Martina

doi:10.1016/j.physleta.2009.07.080

Cited by 3 publications

(5 citation statements)

References 21 publications

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“…In previous studies, either or both subsystems-i.e., particle and wall-were treated either classically or quantum mechanically [4][5][6]. TISE solutions were presumed for the quantum subsystems, as will be the case here as well.…”

Section: Additional Backgroundmentioning

confidence: 99%

“…Hussein, a nuclear physicist, realized that a very similar model could be used to exploit energy loss in quantum systems. This would then lead to a microscopic, albeit simplified, derivation of what may be called the "quantum friction force" [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…With collaborators from this institution, he studied the same particle-wall system, but now with the wall subjected to an external (harmonic) force. This makes the system chaotic, and an interesting mean emerges in the study of the quantum validation of the BO approximation in this case [6].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Trajectory Description of the Time-Independent (Inverse) Fermi Accelerator

Hussein

Poirier

2020

Braz J Phys

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We reexamine the (inverse) Fermi accelerator problem by resorting to a quantum trajectory description of the dynamics. Quantum trajectories are generated from the time-independent Schrödinger equation solutions, using a unipolar treatment for the (light) confined particle and a bipolar treatment for the (heavy) movable wall. Analytic results are presented for the exact coupled two-dimensional problem, as well as for the adiabatic and mixed quantum-classical approximations.

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Section: Additional Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Trajectory Description of the Time-Independent (Inverse) Fermi Accelerator

Hussein

Poirier

2020

Braz J Phys

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“…The adiabatic feature of the mode can be also understood with the effective radial potential in figure 2(a). As the rotational symmetry is broken by the deformation, the effective radial potential is not constant during the rotation anymore, but supposed to be modulated [34]. This modulation of course is caused by the nonlinear coupling between the radial motion and the rotational motion, and the period of the modulation is the same as that of the rotational motion.…”

Section: Evolution Of Modes With Deformationmentioning

confidence: 99%

Adiabatic formation of high-Qmodes by suppression of chaotic diffusion in deformed microdiscs

2013

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Resonant modes with high-Q factors in a two-dimensional deformed microdisc cavity are analyzed by using a dynamical and semiclassical approach. The analysis focuses particularly on the ultra-small cavity regime, where the scale of a resonant free-space wavelength is comparable with that of the microdisc size. Although the deformed microcavity has strongly chaotic internal ray dynamics, modes with high-Q factors in this regime show unexpectedly regular distributions in configuration space and adiabatic features in phase space. By tracing the evolution process of such high-Q modes through the deformation from a circular cavity, it is uncovered that the high-Q modes are formed adiabatically on cantori. Due to the openness of microcavities, such adiabatic formation of high-Q modes around cantori is enabled, in spite of strong chaos in ray dynamics. Since the cantori are in close contact with short periodic orbits, their influence on the modes, such as localization patterns in phase space, can be also clarified. In order to quantitatively analyze the spectral range where high-Q modes appear, the phase space section of the deformed microcavity is partitioned by partial barriers of short periodic orbits, and the semiclassical quantization scheme is applied to the partitioned areas and their action fluxes. The derived spectral ranges for the high-Q modes show a good agreement with a numerically observed spectrum. In the course of semiclassical quantization, it is shown that the chaotic diffusion in the system that we investigate can be resolved by the scale of a quarter effective Planck's constant, and the topological structure of the manifolds in phase space allows for this resolution higher than a Planck constant scale. By analyzing flux Farey trees, the role of short periodic orbits in chaotic diffusion and their connection to cantori are verified. Contents

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“…Thus the total wave function can be factorized into a product of two wave functions corresponding to the fast and slow variables. This method has been widely used in physics and quantum chemistry and has become a fundamental tool in these fields [10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach

Huang

Wang

2010

Phys. Rev. A

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Using the quantum trajectory approach, we extend the Born-Oppenheimer (BO) approximation from closed to open quantum systems, where the open quantum system is described by a master equation in Lindblad form. The BO approximation is defined and the validity condition is derived. We find that the dissipation in fast variables improves the BO approximation, unlike the dissipation in slow variables. A detailed comparison is presented between this extension and our previous approximation based on the effective Hamiltonian approach [X. L. Huang and X. X. Yi, Phys. Rev. A 80, 032108 (2009)]. Several additional features and advantages are analyzed, which show that the two approximations are complementary to each other. Two examples are described to illustrate our method.

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Numerical test of Born–Oppenheimer approximation in chaotic systems

Abstract: We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space.

Cited by 3 publications

References 21 publications

Quantum Trajectory Description of the Time-Independent (Inverse) Fermi Accelerator

Quantum Trajectory Description of the Time-Independent (Inverse) Fermi Accelerator

Adiabatic formation of high-Qmodes by suppression of chaotic diffusion in deformed microdiscs

Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach

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