arXiv subjects

Dongmei Wei

Publications and source records attributed to Dongmei Wei.

3 recordsLinked to original sources

arXiv2026

Simulation of Non-Markovian Quantum Accelerated Dynamics via Time-Fractional Schrödinger Equation

The Time-Fractional Schrödinger Equation (TFSE) is an effective tool for simulating the dynamics of non-Markovian quantum systems. The Quantum Speed Limit (QSL) time characterizes the minimum time required for the evolution of a non-Markovian quantum system. In this paper, Wei's TFSE is employed to simulate the non-Markovian quantum accelerated evolution process in the Resonant Dissipative Jaynes-Cummings (RDJC) model. By solving the QSL time of a time-fractional single-qubit open system, the enhancement mechanism of the system evolution speed induced by the non-Markovian memory effects of the environment is revealed. Further studies show that the optimized acceleration of the system evolution can be achieved by jointly regulating the fractional order, coupling strength, and photon number. Comparative analyses indicate that Wei's TFSE can accurately capture the non-Markovian accelerated dynamical features of the system over the entire fractional order range, whereas Naber's TFSE is applicable only within a limited fractional order interval. In addition, the comparisons of the average simulation time for calculating the dynamical trajectory of the excited-state probability demonstrate that Wei's TFSE has a significant simulation advantage in computational efficiency. Therefore, Wei's TFSE is more accurate and efficient for simulating the accelerated dynamics of non-Markovian quantum systems.

quant-ph↗

arXiv2023

Non-Markovian Dynamics of Time-Fractional Open Quantum Systems

Applications of Time-Fractional Schrodinger Equations (TFSEs) to quantum processes are instructive for understanding and describing the time behavior of real physical systems. By applying three popular TFSEs, namely Naber's TFSE I, Naber's TFSE II, and XGF's TFSE, to a basic open system model of a two-level system (qubit) coupled resonantly to a dissipative environment, we solve exactly for Time-Fractional Single Qubit Open Systems (TFSQOSs). However, the three TFSEs perform badly for the following reasons. On the other hand, in the respective frameworks of the three TFSEs, the total probability for obtaining the system in a single-qubit state is not equal to one with time at fractional order, implying that time-fractional quantum mechanics violates quantum mechanical probability conservation. On the other hand, the latter two TFSEs are not capable of describing the non-Markovian dynamics of the system at all fractional order, only at some fractional order. To address this, we introduce a well-performed TFSE by constructing a new analytic continuation of time combined with the conformable fractional derivative, in which for all fractional order, not only does the total probability for the system equal one at all times but also the non-Markovian features can be observed throughout the time evolution of the system. Furthermore, we study the performances of the four TFSEs applying to an open system model of two isolated qubits each locally interacting with its dissipative environment. By deriving the exact solutions for time-fractional two qubits open systems, we show that our TFSE still possesses the above two advantages compared with the other three TFSEs.

quant-ph↗

arXiv2023

Quantum Speed Limit for Time-Fractional Open Systems

The Time-Fractional Schrödinger Equation (TFSE) is well-adjusted to study a quantum system interacting with its dissipative environment. The Quantum Speed Limit (QSL) time captures the shortest time required for a quantum system to evolve between two states, which is significant for evaluating the maximum speed in quantum processes. In this work, we solve exactly for a generic time-fractional single qubit open system by applying the TFSE to a basic open quantum system model, namely the resonant dissipative Jaynes-Cummings (JC) model, and investigate the QSL time for the system. It is shown that the non-Markovian memory effects of the environment can accelerate the time-fractional quantum evolution, thus resulting in a smaller QSL time. Additionally, the condition for the acceleration evolution of the time-fractional open quantum system at a given driving time, i.e., a tradeoff among the fractional order, coupling strength, and photon number, is brought to light. In particular, a method to manipulate the non-Markovian dissipative dynamics of a time-fractional open quantum system by adjusting the fractional order for a long driving time is presented.

quant-ph↗