# Semilinear Response

@inproceedings{Wilkinson2005SemilinearR, title={Semilinear Response}, author={Michael Wilkinson and Bernhard Mehlig and Doron Cohen}, year={2005} }

. – 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 λ changes the diﬀusion constant to λD . However, we discuss circumstances where this linearity does not extend to the function space of intensities, so that if intensities Φ i…

## 6 Citations

### Rate of energy absorption by a closed ballistic ring

- Physics
- 2006

We make a distinction between the spectroscopic and the mesoscopic conductance of a closed ring. We show that the latter is not simply related to the Landauer conductance of the corresponding open…

### Quantum anomalies and linear response theory

- Physics
- 2010

The analysis of diffusive energy spreading in quantized chaotic driven systems leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation, a driven chaotic…

### Random-matrix modeling of semilinear response, the generalized variable-range hopping picture, and the conductance of mesoscopic rings

- Physics
- 2010

Semi-linear response theory determines the absorption coefficient of a driven system using a resistor network calculation: Each unperturbed energy level of a particle in a vibrating trap, or of an…

### 2 2 A pr 2 00 6 The conductance of a closed mesoscopic system

- Physics
- 2006

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…

### Quantum transport in a driven disordered potential: onset of directed current and noise-induced current reversal

- Physics
- 2014

Abstract
We study motion of a quantum wavepacket in a one-dimensional potential with correlated
disorder. Presence of long-range potential correlations allows for existence of both
localized and…

### The mesoscopic conductance of disordered rings, its random matrix theory and the generalized variable range hopping picture

- Biology
- 2007

It is argued that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime is studied.

## References

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- Mathematics
- 2005

The elementary properties of random matrices are reviewed and widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles are discussed.

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### cond-mat/0505295 (2005)

- J. Phys. A 39, 11755
- 2006