Quantum Manifestations of Bifurcations of Classical Orbits: An Exactly Solvable Model

Peters, Aaron D.; Jaffé, Charles; Delos, J. B.

doi:10.1103/physrevlett.73.2825

Cited by 72 publications

(57 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This formula is very similar to that obtained for the case of parallel static electric and magnetic fields [59,60], in which the largest oscillation amplitude of the cross section corresponds to classical orbits for which for an electron is ejected along the static field direction and reflected by the static electric field such that its return time satisfies T ret = jT B . In the parallel fields case, the motion in the plane perpendicular to the magnetic field is simply cyclotron motion with period T B .…”

Section: Fromsupporting

confidence: 81%

Photodetachment ofH−by a short laser pulse in crossed static electric and magnetic fields

2006

View full text Add to dashboard Cite

We present a detailed quantum mechanical treatment of the photodetachment of H − by a short laser pulse in the presence of crossed static electric and magnetic fields.An exact analytic formula is presented for the final state electron wave function (describing an electron in both static electric and magnetic fields and a short laser pulse of arbitrary intensity). In the limit of a weak laser pulse, final state electron wave packet motion is examined and related to the closed classical electron orbits in crossed static fields predicted by Peters and Delos [Phys. Rev. A 47, 3020 (1993)].Owing to these closed orbit trajectories, we show that the detachment probability can be modulated, depending on the time delay between two laser pulses and their relative phase, thereby providing a means to partially control the photodetachment process. In the limit of a long, weak pulse (i.e., a monochromatic radiation field) our results reduce to those of others; however, for this case we analyze the photodetachment cross section numerically over a much larger range of electron kinetic energy (i.e., up to 500 cm −1 ) than in previous studies and relate the detailed structures both analytically and numerically to the above-mentioned, closed classical periodic orbits.

show abstract

Section: Fromsupporting

confidence: 81%

Photodetachment ofH−by a short laser pulse in crossed static electric and magnetic fields

2006

View full text Add to dashboard Cite

show abstract

“…Clearly, k = 0 does not satisfy either (5) or (6). Suppose that there exists k 1 > 0 that achieves (5), then…”

Section: Mathematical Preliminariesmentioning

confidence: 93%

“…Bifurcations appear in a wide variety of nonlinear dynamical systems in biology [1], [2], [3], fluid flow [4], [5], and quantum mechanics [6], [7] as well as in engineering applications such as power systems [8], acoustics [9], chemical processes [10], and aircraft dynamics [11]. In engineering design, it is often important to avoid bifurcations because of their intimate connection to the system's stability properties and behavior.…”

Section: Introductionmentioning

confidence: 99%

Non-existence conditions of local bifurcations for rational systems with structured uncertainties

Kishida

Braatz

2014

2014 American Control Conference

View full text Add to dashboard Cite

Sufficient conditions are presented for the avoidance of bifurcations for uncertain rational systems. A necessary condition for a steady-state bifurcation to occur is that the system's Jacobian has a zero eigenvalue, and a necessary condition for a Hopf bifurcation to occur is that the system's Jacobian has a pair of pure imaginary eigenvalues. Based on the structured singular value µ and skewed structured singular value ν, this paper derives guaranteed non-existence conditions for a zero eigenvalue and pure imaginary eigenvalues of the system's Jacobian. Conditions for systems with mixed parametric and dynamic uncertainties to maintain stability/instability are also derived. An example illustrates the determination of regions guaranteed to have no bifurcations.

show abstract

“…Actually, the photodetachment properties of H − in external fields are investigated quite intensively in past decade, such as in a motional field electric field, 21 a gradient electric field, 22 cross electric and magnetic fields, 23,24 and parallel electric and magnetic fields. 25,26 Besides the external fields, surface and/or interface have significant influence to the physical and chemical properties of atoms and molecules adsorbed on or near them. For example, the electronic structure of chemisorbed alkali atoms on noble metals is modified and new resonances emerge from the mixing of the Rydberg orbitals of the atoms interacting with the surface.…”

Section: Introductionmentioning

confidence: 99%

Quantum coherence and electric field control of the photodetached electron on elastic surface

Wang

Ran

et al. 2009

The Journal of Chemical Physics

View full text Add to dashboard Cite

The quantum dynamics of the photodetached electron of H(-) in electric field near a surface are studied in the time domain. The evolution of wave packet for different manifold eigenstates with limited lifetimes is obtain analytically. It is found that the quantum coherence and temporal evolution of surface electronic wave packet can be controlled by the laser central energy and electric field. The correspondence between classical and quantum mechanics is shown explicitly in the system. Numerical simulation shows that the temporal evolution of photodetached electronic wave packet on elastic surface exhibits some similar properties of time-resolved two-photon photoemission signal of surface electron.

show abstract

Quantum Manifestations of Bifurcations of Classical Orbits: An Exactly Solvable Model

Cited by 72 publications

References 10 publications

Photodetachment ofH−by a short laser pulse in crossed static electric and magnetic fields

Photodetachment ofH−by a short laser pulse in crossed static electric and magnetic fields

Non-existence conditions of local bifurcations for rational systems with structured uncertainties

Quantum coherence and electric field control of the photodetached electron on elastic surface

Contact Info

Product

Resources

About