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This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

The paper has been withdrawn due to a crucial error in section 3.

This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.

This paper has been withdrawn by the author due to an error

This paper has been withdrawn by the author due to incomplete interpretation for the results.

The Hall conductivity given by the Kubo formula is a linear response of the quantum transverse transport to a weak electric field. It has been intensively studied for a quantum system without decoherence, but it is barely explored for…

This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.

This paper has been withdrawn by the authors due to essential errors in Theorem 5.6.

This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).

This paper has been withdrawn by the authors due to new experimental results.

This paper has been withdrawn by the author due to some mistakes

This paper has been withdrawn by the author(s), due a crucial error in the data.

This paper has been withdrawn by the authors due to an incorrect analysis.

This paper has been withdrawn by the author due to a crucial error in the submission action.

This paper has been withdrawn due to a error in Theorem 3.1.

This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

This paper has been withdrawn by the authors, due a oversimplified decoherence model. It will be substituted by a new work.

This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .

This paper has been withdrawn because it is a duplicate of [math/0609208].

This paper has been withdrawn by the author due to a crucial error in equation.