Magneto-Dynamics of a Double Quantum Dot System

We have examined the microscopic dynamics of a double quantum dot system modeled by a potential having two three-dimensional Dirac delta functions of generally unequal strengths separated in position by$\vec {a}$: \[ V(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over {r}} )=-\alpha _1 \delta ^{(3)}(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over {r}} -\raise0.7ex\hbox{${\vec {a}}$} \!\mathord{\left/ {\vphantom {{\vec {a}} 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$})-\alpha _2 \delta ^{(3)}(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over {r}} +\raise0.7ex\hbox{${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over {a}} }$} \!\mathord{\left/ {\vphantom {{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over {a}} } 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}). \] While these delta function potentials individually support a single energy level, the introduction of a strong magnetic field gives rise to Landau quantization and a plethora of energy levels. The relative magnitude of $\raise0.7ex\hbox{${\alpha _1 }$} \!\mathord{\left/ {\vphantom {{\alpha _1 } {\alpha _2 }}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${\alpha _2 }$}$affects the bonding/antibonding character of the states, as well as the multiplicity of levels induced by magnetic quantization.