Quantum Hamilton dynamics in a quantum dot

Ciann-Dong Yang, Shih Ming Huang

Research output: Contribution to journalArticle

Abstract

The lack of equations of motion in quantum mechanics has prohibited the analysis of quantum dots from a viewpoint of nonlinear dynamics. For a complete description of the electronic motion in a quantum dot, we need a new method that can provide not only the particle behavior of an electron but also its wave behavior. In the present paper, quantum Hamilton mechanics is shown to possess the desired ability of manifesting the wave-particle duality of electrons moving in a quantum dot. Solutions of nonlinear Hamilton equations reveal the existence of electronic standing waves in a quantum dot. A commensurability condition is derived from the nonlinear Hamilton equations to characterize all the critical magnetic fields yielding standing waves, whose occurrence is found to be accompanied by a jump in the electronic resistance. The comparison with the experimental data shows that the predicted locations of the critical magnetic fields match closely with the peaks of the measured magneto-resistance.

Original languageEnglish
Pages (from-to)90-99
Number of pages10
JournalAdvanced Science Letters
Volume16
Issue number1
DOIs
Publication statusPublished - 2012 Sep 1

Fingerprint

Quantum Dots
quantum mechanics
Semiconductor quantum dots
standing wave
electronics
mechanic
Quantum theory
Standing Wave
Electronics
Magnetic Fields
Mechanics
Nonlinear equations
magnetic field
electron
Wave-particle duality
Magnetic Field
Electrons
Electron
Magnetic fields
Magnetoresistance

All Science Journal Classification (ASJC) codes

  • Education
  • Health(social science)
  • Mathematics(all)
  • Energy(all)
  • Computer Science(all)
  • Environmental Science(all)
  • Engineering(all)

Cite this

Yang, Ciann-Dong ; Huang, Shih Ming. / Quantum Hamilton dynamics in a quantum dot. In: Advanced Science Letters. 2012 ; Vol. 16, No. 1. pp. 90-99.
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Quantum Hamilton dynamics in a quantum dot. / Yang, Ciann-Dong; Huang, Shih Ming.

In: Advanced Science Letters, Vol. 16, No. 1, 01.09.2012, p. 90-99.

Research output: Contribution to journalArticle

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