TITLE:
Quantum Dynamics via a Hidden Liouville Space
AUTHORS:
Gombojav O. Ariunbold
KEYWORDS:
Liouville Space, S-Operator, Time-Ordered Exponentials, Quantum Oscillators, Squeezing, Husimi Q-Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.7,
July
19,
2023
ABSTRACT: 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.