Quantum mechanics

Gaussian

Pure mathematics

Equivalence (formal languages)

Statistics

Markov process

Computer science

Statistical physics

Physics

Quantum dynamics

Mathematics

Political science

Unitary state

Quantum

Time evolution

Physical Review Letters

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments---one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.

Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems