The finite quantum grand canonical ensemble and temperature from singleelectron statistics for a mesoscopic device
Abstract
I present a theoretical model of a quantum statistical ensemble for which, unlike in conventional physics, the total number of particles is extremely small. The thermodynamical quantities are calculated by taking a small N by virtue of the orthodicity of the canonical ensemble. The finite quantum grand partition function of a FermiDirac system is calculated. The model is applied to a quantum dot coupled with a small twodimensional electron system. Such a system consists of an alternatively singly and doubly occupied electron system confined in a quantum dot, which exchanges one electron with a small N twodimensional electron reservoir. The analytic determination of the temperature of a (1\leftrightarrow 2) electron system and the role of ergodicity are discussed. The generalized temperature expression in the small N regime recovers the usual temperature expression form on taking the limit of N\rightarrow \infty for the electron bath.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 January 2010
 DOI:
 10.1088/17425468/2010/01/P01003
 arXiv:
 arXiv:1001.2342
 Bibcode:
 2010JSMTE..01..003P
 Keywords:

 Quantum Physics
 EPrint:
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