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\nIn the second part of my ta lk\, I investigate the geometric phase induced on the spin states duri ng the adiabatic movement of the III-V semiconductor quantum dots in t he plane of two-dimensional electron gas under the influence of applie d gate potential along the lateral direction. Here\, I present the spi n-flip probabilities during the adiabatic evolution in the presence of the Rashba and the Dresselhaus linear spin-orbit interactions. I use the Feynman disentanglement technique to determine the non-Abelian Ber ry phase and find exact analytical expressions for three special cases : (a) the pure Rashba spin-orbit coupling\, (b) the pure Dresselhause linear spin-orbit coupling\, and (c) the mixture of the Rashba and Dre sselhaus spin-orbit couplings with equal strength. For a mixture of th e Rashba and the Dresselhaus spin-orbit couplings with unequal strengt hs\, I obtain numerical results by solving the Riccati equation origin ating from the disentangling procedure. I find that the spin-flip prob ability in the presence of the mixed spin-orbit couplings is generally larger than those for the pure Rashba case and for the pure Dresselha us case\, and that the complete spin-flip takes place only when the Ra shba and the Dresselhaus spin-orbit couplings are mixed symmetrically.

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\nReferences:

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\nGate control of a quantum dot single-electron spin in realistic confining potentials: Anisotropy ef fects\; Sanjay Prabhakar and James Raynolds\, phys. Rev. B 79\, 195307 (2009).

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\nManipulation of single electron spin in a GaAs quantum dot through the application of geometric phases: The Feynman disentangling technique\; Sanjay Prabhakar\, James E Raynolds\, Akira Inomata and Roderick Melnik\, Phys. Rev. B 82\, 195306 (2010).

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\nManipulation of the Lande g-factor in InAs quantum dots throug h the application of anisotropic gate potentials\; Sanjay Prabhakar\, James E Raynolds and Roderick Melnik\, Phys. Rev. B 84\, 155208 (2011) .

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\nThe influence of anisotropic gate potentials on the p honon induced spin-flip rate in GaAs quantum dots\; Sanjay Prabhakar\, Roderick Melnik and Luis L Bonilla\, Applied Physics Letters 100\, 02 3108 (2012).

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