Time-dependent behavior of
mesoscopic Wigner crystals
Here we present molecular dynamics results for small electron clusters.
They show the electron fluctuations around their stable locations on the
cluster shells.
The equilibrium configuration, including quantum effects, can be seen
here
For the theoretical background, please, check our
publications
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Temperature: During the simulations, electron velocities are rescaled in order to maintain the
chosen temperature T. T is in units of 1/Gamma, with Gamma=U_coul/E_kin, the
ratio of Coulomb repulsion energy to kinetic energy.
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Energy conservation: During the simulations, total energy is practically
conserved (the initial period where correlations are being built up is skipped).
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Initial conditions: The MD simulations are performed starting from electrons
being close to their equilibrium locations. Initial velocities are chosen
to reproduce the given kinetic energy (temperature T).
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Pinninng: Due to the trap symmetry, the whole cluster can freely rotate. To
avoid this, in some cases, one electron of the outer shell will be pinned.
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Zero initial rotation: In some cases, initially zero total angular momentum is
chosen. Since angular momentum is conserved, rotation of one shell leads to counter-rotation
of the other (if there is no pinning).
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Melting: The MD simulations confirm the melting behavior predicted by the
Monte Carlo simulations, click here and then go to
higher temperatures.
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Shell rotation: To study collective rotation of all electrons on one shell
relative to the other shell(s), and its dependence on T and N is one of the main
goals of this analysis. In particular, we study the effect of addition/removal
of one single electron on intershell rotation.
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Single-electron control: Choosing T inbetween the orientational melting temperature
of the clusters with N (19, for example) and N+1 (20), intershell rotation can be
initiated or stopped by adding/removing a single electron. This is particularly
striking for N=19 ("magic" cluster) vs. N=20, since the orientational melting
temperatures differ by 9 (!) orders of magnitude.
See our paper on this idea
The MD simulations have been performed by Vova Golubnychiy who also produced
the animated gif files.
Note, each animation starts over a second time (see the time step on top of the
figure). To rerun it, click the reload button.
To see the animations, start here
In case the simulations are running too slow, you may choose to
download the animated gif files
19 Electrons, Gamma=500 |
20 Electrons, Gamma=500 |
19 vs 20 Electrons, Gamma=500
19 Electrons, 1 pinned, Gamma=500 |
19 Electrons, 1 pinned, Gamma=160 |
19 Electrons, Gamma=100, 1 pinned
19 (1 pinned ) vs 20 Electrons, Gamma=500 |
19 Electrons free vs. pinned, Gamma=500
19 Electrons (1 pinned), Gamma=500 vs. 160
19 Electrons, Gamma=500, zero initial rotation |
20 Electrons, Gamma=500, zero initial rotation |
20 Electrons, Gamma=100, zero initial rotation