Semilinear Response

Abstract

We discuss the response of a quantum system to a time-dependent perturbation with spectrum Φ(ω). This is characterised by a rate constant D describing the diffusion of occupation probability between levels. We calculate the transition rates by first-order perturbation theory, so that multiplying Φ(ω) by a constant λchanges the diffusion constant to λD. However, we discuss circumstances where this linearity does notextend to the function space of intensities, so that if intensities Φ_i(ω) yield diffusion constants D_i, then the intensity \sum_i Φ_i(ω) does not result in a diffusion constant \sum_i D_i. This `semilinear' response can occur in the absorption of radiation by small metal particles.

7 pages, 1 figure

Cited by in corpus (12)

• Rate of energy absorption by a closed ballistic ring
• Semilinear response for the heating rate of cold atoms in vibrating traps
• The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture
• Random-matrix modeling of semi-linear response, the generalized variable range hopping picture, and the conductance of mesoscopic rings
• The conductance of a multi-mode ballistic ring: beyond Landauer and Kubo
• Quantum response of weakly chaotic systems
• Non-equilibrium steady state of sparse systems
• Energy absorption by "sparse" systems: beyond linear response theory
• From the Kubo formula to variable range hopping
• "Weak Quantum Chaos" and its resistor network modeling
• Quantum transport in a driven disordered potential: onset of directed current and noise-induced current reversal
• Quantum anomalies and linear response theory