Feshbach projection formalism for open quantum systems

Abstract

We provide a new approach to open quantum systems which is based on the Feshbach projection method in an appropriate Hilbert space. Instead of looking for a master equation for the dynamical map acting in the space of density operators we provide the corresponding equation for the evolution in the Hilbert space of the system. Its solution enables one to construct a legitimate quantum evolution (completely positive and trace preserving). The big advantage of this approach is the ability of performing a consistent approximation which creates notorious problems in the standard Nakajima-Zwanzig approach. The new scheme is illustrated by well known spin-boson model beyond rotating wave approximation.

5 pages; minor corrections

References in corpus (4)

• Assessing non-Markovian dynamics
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Master Equation and Control of an Open Quantum System with Leakage
• Feshbach Projection Operator Partitioning for Quantum Open Systems: Stochastic Approach

Cited by in corpus (19)

• On the degree of non-Markovianity of quantum evolution
• Perturbative approach to Markovian open quantum systems
• Non-Markovianity degree for random unitary evolution
• All-optical non-Markovian stroboscopic quantum simulator
• Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables
• Emergent non-Hermitian models
• Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems
• Witnessing non-Markovianity of quantum evolution
• Fano feature induced by a bound state in the continuum via resonant state expansion
• Density-operator evolution: Complete positivity and the Keldysh real-time expansion
• Non-Markovian evolution of multi-level system interacting with several reservoirs. Exact and approximate
• Exploring the halo character and dipole response in the dripline nucleus ${}^{31}$F
• Multiple-scale analysis of open quantum systems
• Non-equilibrium thermodynamics approach to open quantum systems
• Solomon equations for qubit and two-level systems: Insights into non-Poissonian quantum jumps
• Continued-fraction representation of the Kraus map for non-Markovian reservoir damping
• Minimalistic analytical approach to non-Markovian open quantum systems
• Fermionic duality: General symmetry of open systems with strong dissipation and memory
• Evolution of open quantum systems: time scales, stochastic and continuous processes