@article{(Open Science Index):https://publications.waset.org/pdf/9561,
	  title     = {Modelling of Electron States in Quantum -Wire Systems - Influence of Stochastic Effects on the Confining Potential},
	  author    = {Mikhail Vladimirovich Deryabin and  Morten Willatzen},
	  country	= {},
	  institution	= {},
	  abstract     = {In this work, we address theoretically the influence of red and white Gaussian noise for electronic energies and eigenstates of cylindrically shaped quantum dots. The stochastic effect can be imagined as resulting from crystal-growth statistical fluctuations in the quantum-dot material composition. In particular we obtain analytical expressions for the eigenvalue shifts and electronic envelope functions in the k . p formalism due to stochastic variations in the confining band-edge potential. It is shown that white noise in the band-edge potential leaves electronic properties almost unaffected while red noise may lead to changes in state energies and envelopefunction amplitudes of several percentages. In the latter case, the ensemble-averaged envelope function decays as a function of distance. It is also shown that, in a stochastic system, constant ensembleaveraged envelope functions are the only bounded solutions for the infinite quantum-wire problem and the energy spectrum is completely discrete. In other words, the infinite stochastic quantum wire behaves, ensemble-averaged, as an atom.
},
	    journal   = {International Journal of Nuclear and Quantum Engineering},
	  volume    = {2},
	  number    = {7},
	  year      = {2008},
	  pages     = {1448 - 1451},
	  ee        = {https://publications.waset.org/pdf/9561},
	  url   	= {https://publications.waset.org/vol/19},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 19, 2008},
	}