We develop quantum mechanical Dirac ket-bra operator’s integration theory in Q-ordering or P-ordering to multimode case,where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the l...We develop quantum mechanical Dirac ket-bra operator’s integration theory in Q-ordering or P-ordering to multimode case,where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the left of all Qs.As their applications,we derive Q-ordered and P-ordered expansion formulas of multimode exponential operator e iPlΛlkQk.Application of the new formula in finding new general squeezing operators is demonstrated.The general exponential operator for coordinate representation transformation q1q2→A B C D q1q2is also derived.In this way,much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.展开更多
A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable ...A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its （q-order and 2q-order） time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its （q-order and 2q-order） time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.展开更多
In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identiti...In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q-P ordering and P-Q ordering is introduced.The Q-P ordered and P-Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q-P or P-Q ordering much more convenient.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 11175113)
文摘We develop quantum mechanical Dirac ket-bra operator’s integration theory in Q-ordering or P-ordering to multimode case,where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the left of all Qs.As their applications,we derive Q-ordered and P-ordered expansion formulas of multimode exponential operator e iPlΛlkQk.Application of the new formula in finding new general squeezing operators is demonstrated.The general exponential operator for coordinate representation transformation q1q2→A B C D q1q2is also derived.In this way,much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.
文摘A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its （q-order and 2q-order） time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its （q-order and 2q-order） time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.
基金supported by the National Natural Science Foundation of China (Grant No.11175113)
文摘In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q-P ordering and P-Q ordering is introduced.The Q-P ordered and P-Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q-P or P-Q ordering much more convenient.
