The Simplest Quantum Model Supporting the Kibble-Zurek Mechanism of Topological Defect Production: Landau-Zener Transitions from a New Perspective

It can be shown that the dynamics of the Landau-Zener model can be accurately described in terms of the Kibble-Zurek theory of the topological defect production in nonequilibrium phase transitions. The simplest quantum model exhibiting the Kibble-Zurek mechanism is presented. A new intuitive description of Landau-Zener dynamics is found.

Figure 1

Plot (a): relaxation time scale $\tau$ from the KZ theory. Plot (b): inverse of the gap in the LZ model (1). Lower plot: energy levels of the Hamiltonian (1); dotted line: ${\omega }_0=0$ case.

Figure 2

Density of defects for the system whose evolution starts at the anticrossing center. Solid line—prediction (10), dots—numerical data. The parameter $\alpha =0.77$ was found from a fit of (10) to numerics.

Figure 3

Density of defects. Solid lines—numerics, dashed lines—Eq. (11) with $\alpha$ determined from the fit. Upper (lower) curves correspond to ${\theta }_0=0.6\pi$, $\alpha =1.06$ ${\theta }_0=0.4\pi$, $\alpha =0.58$).