Rydberg Electrons in Crossed Fields: A Paradigm for Nonlinear Dynamics Beyond Two Degrees of Freedom

Uzer, T.

doi:10.1238/physica.topical.090a00176

Cited by 6 publications

(12 citation statements)

References 79 publications

(113 reference statements)

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“…In all cases in figure 13 we choose the initial cell so that the vector u 1 is vertical, i.e., along axis h, and u 2 is nearly horizontal. The vector u 1 does not change while u 2 changes so that u 2 = u 2 + ku 1 where k is the same as in (10).…”

Section: Quantum Monodromymentioning

confidence: 99%

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Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields

Efstathiou

Lukina

Sadovskiı́

2009

J. Phys. A: Math. Theor.

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We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields in near-orthogonal configurations. Normalization of the Keplerian symmetry reveals that in the parameter space such systems belong in a 'zone' of systems close to the 1:1 resonance, the latter corresponding to the exactly orthogonal configuration. Integrable approximations obtained from second normalization of systems in the 1:1 zone are classified into several different qualitative types, many of which possess nontrivial monodromy. We compute monodromy of the complete threedimensional energy-momentum map, compare the joint quantum spectrum to classical bifurcation diagrams, and show the effect of second normalization to the joint spectrum.

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Section: Quantum Monodromymentioning

confidence: 99%

“…Namely, systems near the Zeeman and Stark limits similar to those studied in [2,3], and systems with monodromy. There has been a significant number of studies of this problem from different points of view [5][6][7][8][9][10]. Here we mention only the most directly related work.…”

Section: Introductionmentioning

confidence: 99%

Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields

Efstathiou

Lukina

Sadovskiı́

2009

J. Phys. A: Math. Theor.

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“…The electron motion in a hydrogen atom exposed to an electric field F in the x direction and a magnetic field B in the z direction is governed by the Hamiltonian, 10) in atomic units,…”

Section: §1 Introductionmentioning

confidence: 99%

“…Superimposed over the level lines of the potential energy are the FPOs in the x and y direction for E = 1 (thick lines) and the rotated coordinate system(10). Both FPOs intersect the surface of section v = 0 (which coincides with the u-axis) at u = 0.…”

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confidence: 99%

Gluing Torus Families across a Singularity: The Lens Space for the Hydrogen Atom in Crossed Fields

Bartsch

Gekle

Main

et al. 2007

Prog. Theor. Phys. Suppl.

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We demonstrate that topological information that can be extracted from periodic orbits in a near-integrable system can lead to a complete topological characterization of families of invariant 2-tori in terms of lens spaces. This approach ties in with the techniques we developed for classifying the tori in systems with more than two degrees of freedom. It therefore offers a general way to investigate families of invariant 2-tori in higher-dimensional Hamiltonian systems. §1. IntroductionPeriodic orbits are the simplest invariant objects in the phase space of a dynamical system. 1) Because they form the fundamental building blocks of the dynamics and because they are much simpler to calculate numerically than any more complicated structures, they are widely used as a tool to study the geometrical and dynamical structure of a multidimensional phase space. 2), 3) In a near-integrable system, the phase-space structure is dominated by a hierarchy of invariant tori of various dimensions. As we showed in a recent series of publications, 4) the existence of such a hierarchy, about which no detailed knowledge is required, can be used to impose an ordering principle upon the periodic orbits, and conversely, this ordering of periodic orbits allows one to obtain information about the higher-dimensional invariant tori that are not easily accessible through direct numerical methods.In the present paper we will demonstrate how the results of our earlier work can be extended into a complete topological characterization of families of invariant tori. Since we found the familiar Poincaré surface of section plots a somewhat unreliable tool to this end, we will analyze the singularities of Poincaré maps that lead to this failure, and we will show how the nature of the singularities is related to the topology of the family of tori under consideration.Because the present paper is focused on the topology of families of 2-tori, which exist in systems with two or more degrees of freedom, and on their representation in Poincaré plots, which are available only in two degrees of freedom, we will largely restrict our discussion to this case. Nevertheless, we will also show how these results can be generalized to higher-dimensional systems.

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“…Consequently for more than a quarter century (up to the present) experimentalists and theorists have been investigating atomic Rydberg spectra in external fields, including in particular the interesting case of crossed static electric and magnetic fields [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. These latter investigations for the crossed field case include studies of motional Stark effects on Rydberg atom spectra in a magnetic field [2], of novel, highly excited resonance states [3,6,7,8,10,12,14,17,24], of circular Rydberg states [9], of Rydberg wave packets in crossed fields ...…”

Section: Introductionmentioning

confidence: 99%

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

2006

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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.

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Rydberg Electrons in Crossed Fields: A Paradigm for Nonlinear Dynamics Beyond Two Degrees of Freedom

Cited by 6 publications

References 79 publications

Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields

Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields

Gluing Torus Families across a Singularity: The Lens Space for the Hydrogen Atom in Crossed Fields

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

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