Statistical properties of spectra in harmonically trapped spin-orbit coupled systems

We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit a...

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Bibliographic Details
Published in:Journal of physics. B, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2014-10, Vol.47 (19), p.195303-11
Main Authors: Marchukov, O V, Volosniev, A G, Fedorov, D V, Jensen, A S, Zinner, N T
Format: Article
Language:English
Subjects:
Approximation
chaotic behavior
cold atoms
Coupling (molecular)
Deformation
Exact sciences and technology
Mathematical analysis
Nonlinear dynamics and nonlinear dynamical systems
Physics
Reproduction
Spectra
spin-orbit coupling
Statistical physics, thermodynamics, and nonlinear dynamical systems
Strength
Wigner distribution
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Summary:We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choice of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding the Zeeman field we can reproduce a Brody distribution, which is known to describe a transition between the Poisson and linear Wigner distributions.
ISSN:0953-4075
1361-6455
DOI:10.1088/0953-4075/47/19/195303