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Computer Physics Communications

Many-body quantum dynamics by adiabatic path-integral molecular dynamics: Disordered Frenkel Kontorova models

Florian R. Krajewski, Martin H. Müser

Published Apr 11, 2005• 1 citation
Publisher
DOI
10.1016/j.cpc.2005.03.094

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The phonon dispersion relation of the commensurate quantum Frenkel–Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.
We demonstrate a microfabricated surface-electrode ion trap that is applicable as a nanofriction emulator and studies of many-body dynamics of interacting systems. The trap enables both single-well and double-well trapping potentials in the radial direction, where the distance between the two potential wells can be adjusted by the applied RF voltage. In the double-well configuration, parallel ion strings can be formed, which is a suitable system for the emulation of the Frenkel-Kontorova (FK) model. We derive the condition under which the trap functions as an FK model emulator. The trap is designed so that the Coulomb interaction between two ion strings becomes significant. We report on the microfabrication process for such downsized trap electrodes and experimental results of single-well and double-well operation with calcium ions. With the trap demonstrated in this work we can create atomically accessible, self-assembled Coulomb systems with a wide tuning range of the corrugation parameter in the FK model. This makes it a promising system for quantum simulations, but also for the study of nanofriction in one and higher dimensional systems.