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The wave function in a ring satisfies the relation (Formula presented) we therefore have (Formula presented) according to the Bloch theorem. As a result, (Formula presented) for (Formula presented) if ever (Formula presented) which is satisfied in the models addressed in the present paper.
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The wave function in a ring satisfies the relation (Formula presented) we therefore have (Formula presented) according to the Bloch theorem. As a result, (Formula presented) for (Formula presented) if ever (Formula presented) which is satisfied in the models addressed in the present paper.
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21144467387
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The necessary and sufficient condition for the existence of cyclic evolution for an arbitrary state in a closed system is that the spectrum of the system can be represented as (Formula presented) where (Formula presented) is an integer, (Formula presented) and (Formula presented) is real. See A.N. Seleanyova, J. Phys. A 26, 981 (1993).
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Some specific states superposed linearly by no more than two eigenstates may follow a cyclic evolution regardless of the spectrum.
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Some specific states superposed linearly by no more than two eigenstates may follow a cyclic evolution regardless of the spectrum.
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In the case of (Formula presented) the energy Eq. (14) can be written as (Formula presented)It is clear that (Formula presented) Meanwhile Eq. (15) becomes (Formula presented)Therefore the currents carried by electrons in the completely filled levels (Formula presented) and (Formula presented) should be canceled.
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In the case of (Formula presented) the energy Eq. (14) can be written as (Formula presented)It is clear that (Formula presented) Meanwhile Eq. (15) becomes (Formula presented)Therefore the currents carried by electrons in the completely filled levels (Formula presented) and (Formula presented) should be canceled.
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