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The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic…
Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation.…
This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.
An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.
The paper has been temporarily withdrawn by the authors.
This paper has been withdrawn by the author due to an error.
This is an addendum to a previous article, which aims to provide the proofs of some results in that paper (Theorem 7.5 and Proposition 9.15) which were removed from its final version. The reason for such omission is that these proofs follow…
This paper has been withdrawn by the author due to unspecified problems.
This paper has been withdrawn by the authors, due an error involving the weak* convergence argument in section 2
The paper has been withdrawn due to very low reproducibility. About 100 samples have been made, only 3 samples show the superconducting-like behavior. We think it may be an unlikely result.
We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We…
This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2080.
We extend the main vanishing theorem in a paper of de Fernex and Ein to singular varieties without assuming locally complete intersection.
This paper has been withdrawn by the author due to extremely unscientific errors.
This paper has been withdrawn by the author(s), because it contains erroneous conclusion. Some part of the contents of the paper may be used in a future communication.
This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.
We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.
This paper has been withdrawn by the author: it was a too preliminary version.
This paper has been withdrawn by the author due to a mistake in one of the main lemmas.
This paper has been withdrawn Abstract: This paper has been withdrawn by the author due to the publication.