Abstract : This paper is devoted to the analysis of an abstract formula describing quantum adiabatic charge pumping in a general context. We consider closed systems characterized by a slowly varying time-dependent Hamiltonian depending on an external parameter $\alpha$. The current operator, defined as the derivative of the Hamiltonian with respect to $\alpha$, once integrated over some time interval, gives rise to a charge pumped through the system over that time span. We determine the first two leading terms in the adiabatic parameter of this pumped charge under the usual gap hypothesis. In particular, in case the Hamiltonian is time periodic and has discrete non-degenerate spectrum, the charge pumped over a period is given to leading order by the derivative with respect to $\alpha$ of the corresponding dynamical and geometric phases.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00464797
Contributor : Alain Joye <>
Submitted on : Thursday, March 18, 2010 - 7:08:53 AM
Last modification on : Friday, February 22, 2019 - 4:54:02 PM

### Identifiers

• HAL Id : hal-00464797, version 1
• ARXIV : 1002.1223

### Citation

Alain Joye, Valentina Brosco, Frank. W. J. Hekking. Abstract adiabatic charge pumping. Confluentes Mathematici, Institut Camille Jordan et Unité de Mathématiques Pures et Appliquées, 2010, 2, pp.159-180. ⟨hal-00464797⟩

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