Rate of energy absorption by a closed ballistic ring

TL;DR

This paper distinguishes between spectroscopic and mesoscopic conductance in closed quantum systems, revealing that non-universal matrix structures can create bottlenecks affecting energy absorption rates, with implications for ballistic device dissipation.

Contribution

It introduces a new perspective on conductance in closed systems, highlighting the role of matrix structure and its impact on energy absorption, differing from open system conductance models.

Findings

Mesoscopic conductance can increase as Landauer conductance decreases.

Non-universal matrix structures can suppress energy diffusion.

Differences between spectroscopic and mesoscopic conductance are significant in closed systems.

Abstract

We make a distinction between the spectroscopic and the mesoscopic conductance of closed systems. We show that the latter is not simply related to the Landauer conductance of the corresponding open system. A new ingredient in the theory is related to the non-universal structure of the perturbation matrix which is generic for quantum chaotic systems. These structures may created bottlenecks that suppress the diffusion in energy space, and hence the rate of energy absorption. The resulting effect is not merely quantitative: For a ring-dot system we find that a smaller Landauer conductance implies a smaller spectroscopic conductance, while the mesoscopic conductance increases. Our considerations open the way towards a realistic theory of dissipation in closed mesoscopic ballistic devices.