Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative
arXiv:1501.06289 · doi:10.1103/PhysRevA.92.022119
Abstract
Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.
5 pages, 2 figures
References in corpus (10)
- Non-Markovian effects on the dynamics of entanglement
- Genuine quantum trajectories for non-Markovian processes
- Open system dynamics with non-Markovian quantum jumps
- Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach
- Pure-state quantum trajectories for general non-Markovian systems do not exist
- General Non-Markovian structure of Gaussian Master and Stochastic Schrödinger Equations
- Non-Markovian continuous quantum measurement of retarded observables
- Crossover Between Non-Markovian and Markovian Dynamics Induced by a Hierarchical Environment
- Fermionic Stochastic Schrödinger Equation and Master Equation: An Open System Model
- Approach to solving spin-boson dynamics via non-Markovian quantum trajectories
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