Applications of DECIDE Quantum-Classical Dynamics: Proton Transfer and Quantum Battery Models

• Author / Creator

  Liu, Zhe

• The quantum-classical Liouville equation (QCLE) provides a foundation for simulating the dynamics of quantum systems coupled to classical environments. Many processes including proton-transfer reactions, electron-transfer reactions, and heat transport in molecular junctions, for example, take place in such mixed quantum-classical systems. The most accurate algorithms for solving the QCLE require very large ensembles of trajectories to obtain converged results, which is computationally prohibitive for many systems. The recently developed "Deterministic evolution of coordinates with initial decoupled equations" (DECIDE) method has demonstrated promise in solving the QCLE with high accuracy and low computational cost for several model systems; however, its broad scale applicability is still under investigation.
  Previously, the applications of DECIDE relied on subsystem and adiabatic energy basis representations. While these representations are convenient for certain systems, the position representation is convenient for many other systems, including systems undergoing proton- and electron-transfer reactions. Thus, as a starting point, we cast the DECIDE equations of motion for a simple one-dimensional proton-transfer model in a finite quantum harmonic oscillator position basis. After solving the DECIDE equations of motion in this basis, we showed that it is possible to generate trajectories that conserve the total energy of the system and we calculated various quantities of interest. Next, we considered a two-dimensional proton-transfer model. In this case, it was not possible to generate trajectories that conserve energy out to arbitrary times. Our analysis revealed that the finite nature of the position basis and the order of the Hamiltonian are responsible for the accumulation of numerical errors that ultimately lead to a breakdown of energy conservation.
  
  In a recent study, our group proposed a novel platform for an open excitonic quantum battery (EQB), which takes advantage of a symmetry-protected dark state residing in a decoherence-free subspace. While in this dark state, the EQB can store an exciton for an indefinite period of time without any environment-induced population losses (known as the storage phase). When a symmetry-breaking perturbation is connected to the EQB, the battery begins to discharge the exciton (known as the discharge phase). In this thesis, we demonstrated that the quantum battery is not only loss-free with respect to exciton population during the storage phase, but also with respect to the battery energy. We then went on to explore the population and energy dynamics of the battery during the discharge phase over a wide range of parameter regimes – site energies, bath temperatures, and bath reorganization energies. Our results shed light on how to control the rate/amount of population and/or energy from the battery.

• Subjects / Keywords

  • Mixed Quantum-Classical Dynamics
  • Proton Transfer
  • Quantum Battery

• Graduation date

  Spring 2022

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-zw4q-k557

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.