Transport and localization amongst coupled substructures

The dynamics of the transport of the mean-square diffuse wave amplitude among coupled substructures is examined. Applications include coupled quantum dots, reverberation rooms, and chaotic billiards. A self-consistent theory is found to predict classical diffusive behavior at strong coupling, but to predict localization when coupling times are comparable to or greater than Heisenberg times. Predictions are compared to an exact result, to the Vollhardt-Wolfle self-consistent theory for multiply scattering continua, and to direct numerical simulations.

Figure 1

Contour for the integral (32).

Figure 2

Flow dynamics between two equal-sized rooms at various values of dimensionless coupling $\kappa$. Time is in units of modal density $c$.

Figure 3

Comparison of the theory of [5] with the hydrodynamical self-consistent theory (36). All curves are for the weak coupling limit $\kappa ⪡1$.

Figure 4

For the case of two equal-sized rooms, the fraction of the total energy present in room No. 2 is plotted versus dimensionless time $t∕c$. Smooth lines are the prediction of theory for the indicated values of $\kappa$. The jagged lines are the results of six distinct ensemble averages of direct numerical simulations.

Figure 5

For the case of three equal-sized rooms, the fraction of the total energy present in rooms Nos. 2 and 3 is plotted versus dimensionless time $t∕c$. Smooth lines are the prediction of theory for the indicated values of $\kappa$. The jagged lines are the result of three distinct ensemble averages of direct numerical simulations. (a) For springs of stiffness 0.05, (b) for a more strongly coupled system with springs of stiffness 0.15.

Figure 6

The three-room structure. The points represent randomly positioned springs coupling adjacent rooms.