Quantum Dynamics via a Hidden Liouville Space  

作　　者：Gombojav O. Ariunbold Gombojav O. Ariunbold(Department of Physics and Astronomy, Mississippi State University, Starkville, MS, USA)

机构地区：[1]Department of Physics and Astronomy, Mississippi State University, Starkville, MS, USA

出　　处：《Journal of Applied Mathematics and Physics》2023年第7期1871-1880,共10页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Liouville Space S-Operator Time-Ordered Exponentials Quantum Oscillators SQUEEZING Husimi Q-Function 

分 类 号：O17[理学—数学]