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
The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique...The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique where the Liouville space is briefly expanded with an additional (virtual) space only within ultrashort subintervals. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically “hitchhiking” via virtual space in discrete ultrashort time duration, are the hallmark of our technique. We believe that this technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.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The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique where the Liouville space is briefly expanded with an additional (virtual) space only within ultrashort subintervals. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically “hitchhiking” via virtual space in discrete ultrashort time duration, are the hallmark of our technique. We believe that this technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.
