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Application of the Mathematical Methods of the Braid Group Theory to Quantization of Many-Particle Systems

100%

Jacak D., Jacak L., Wieczorek K.

Acta Physica Polonica A

1994

vol. 85

issue 3

483-496

The problem of the non-standard statistics for one-, two- and three-dimensional systems of N identical particles on various manifolds is reviewed in terms of the braid group theory. The braid groups together with their unitary representations are studied for the line, circle, plane, sphere, torus and the three-dimensional Euclidean space. Nonequivalent quantizations of several physical systems are presented.

Model of Qubit in Multi-Electron Quantum Dot

88%

Jacak L., Krasnyj J., Jacak D., Salejda W., Mituś A.

Acta Physica Polonica A

2001

vol. 99

issue 2

277-292

The discussion of qubit for quantum computation in quantum dots technology is presented. The state-of-the-art structure of multi-electron dot is considered and the appropriate quasi-two-level system is suggested employing the singlet-triplet transition in the presence of magnetic field. The methods of qubit rotation (the write procedure) as well as two-qubit operations, as controlled-NOT, in vertically stacked dots system are analysed.

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2 Acta Physica Polonica A

1 2001

1 1994

2 Jacak D.

2 Jacak L.

1 Krasnyj J.

1 Mituś A.

1 Salejda W.

1 Wieczorek K.

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Application of the Mathematical Methods of the Braid Group Theory to Quantization of Many-Particle Systems

Model of Qubit in Multi-Electron Quantum Dot