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The evolution of a spin 1/2 particle subjected to a general Hamiltonian in interaction with its environment is considered. Using a new method, the exact solution of the spin-boson model for a general Hamiltonian is applied to investigate the dynamics of the open system. Born-Markov master equation in Caldeira-Leggett regime is used to derive an exact form of the expectation values of spin Pauli operators for a double-well potential. Subsequently, a definite form of spin uncertainty relation is calculated under the influence of the environment effects. Then, we scrutinize that how non-Unitary character of the evolution of open quantum systems can affect the traditional form of the spin uncertainty relation.
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