Quantum correction to the Kubo formula in closed mesoscopic systems

TL;DR

This paper investigates quantum corrections to the classical Kubo formula for energy dissipation in mesoscopic systems, highlighting how spectral discreteness influences dissipation rates under different symmetry conditions.

Contribution

It provides the first calculation of quantum corrections to the Kubo formula in mesoscopic systems with a parametric random-matrix Hamiltonian, revealing spectrum discreteness effects.

Findings

Quantum correction scales as v^{-2/3} in the orthogonal case.

Quantum correction vanishes in the unitary case.

Dissipation rate approaches the Kubo formula for fast perturbations.

Abstract

We study the energy dissipation rate in a mesoscopic system described by the parametrically-driven random-matrix Hamiltonian H[\phi(t)] for the case of linear bias \phi=vt. Evolution of the field \phi(t) causes interlevel transitions leading to energy pumping, and also smears the discrete spectrum of the Hamiltonian. For sufficiently fast perturbation this smearing exceeds the mean level spacing and the dissipation rate is given by the Kubo formula. We calculate the quantum correction to the Kubo result that reveals the original discreteness of the energy spectrum. The first correction to the system viscosity scales proportional to v^{-2/3} in the orthogonal case and vanishes in the unitary case.