Exact solution of the Schrodinger equation with the spin-boson Hamiltonian

Details Exact solution of the Schrodinger equation with the spin-boson Hamiltonian Exact solution of the Schrodinger equation with the spin-boson Hamiltonian

2011-03-22

arxiv.org/abs/1103.4383v1

J. Phys. A: Math. Theor. 44 (2011) 195301

Physics

Quantum Physics

9 pages, LaTeX, to appear in Journal of Physics A: Mathematical and Theoretical

Scientific paper

10.1088/1751-8113/44/19/195301

We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.

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