Mixedness timescale in non-Hermitian quantum systems

Pires, Diego Paiva; Macrì, Tommaso

doi:10.1103/physreva.107.022202

Cited by 1 publication

(3 citation statements)

References 114 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The former two were derived from, respectively, Equations ( 5) and ( 9), whereas the latter is the one with a conserved norm. These equations belong to the same equivalence class as (20); therefore, the choice between them for a specific model is a matter of physical relevance, cf. the remarks at the end of Section 2.…”

Section: Dephasing and State-vector Reductionmentioning

confidence: 99%

“…which can be easily derived from Equation (20); it is, thus, sufficient to study a case of a normalized state vector |Ψ⟩, as mentioned before.…”

Section: Generic Nh-driven Evolutionmentioning

confidence: 99%

“…In the eigenbasis of the operator â, solutions to the other generalized Schrödinger Equations ( 12) and ( 13) are related via the transformations in (20):…”

Section: Nh-gksl Evolution and Cancellation Of Dissipationsmentioning

confidence: 99%

See 2 more Smart Citations

Generalization of the Schrödinger Equation for Open Systems Based on the Quantum-Statistical Approach

Zloshchastiev

2024

Universe

View full text Add to dashboard Cite

Within the framework of the quantum-statistical approach, utilizing both non-Hermitian Hamiltonian and Lindblad’s jump operators, one can derive various generalizations of the von Neumann equation for reduced density operators, also known as hybrid master equations. If one considers the evolution of pure states only, i.e., disregarding the coherence between states and spontaneous transitions from pure to mixed states, then one can resort to quantum-mechanical equations of the Schrödinger type. We derive them from the hybrid master equations and study their main properties, which indicate that our equations have a larger range of applicability compared to other generalized Schrödinger equations proposed hitherto. Among other features, they can describe not only systems which remain in the stationary eigenstates of the Hamiltonian as time passes, but also those which evolve from those eigenstates. As an example, we consider a simple but important model, a quantum harmonic oscillator driven by both Hamiltonian and non-Hamiltonian terms, and derive its classical limit, which turns out to be the damped harmonic oscillator. Using this model, we demonstrate that the effects of dissipative environments of different types can cancel each other, thus resulting in an effectively dissipation-free classical system. Another discussed phenomenon is whether a non-trivial quantum system can reduce to a classical system in free motion, i.e., without experiencing any classical Newtonian forces. This uncovers a large class of quantum-mechanical non-Hamiltonian systems whose dynamics are not determined by conventional mechanics’ potentials and forces, but rather come about through quantum statistical effects caused by the system’s environment.

show abstract

Section: Dephasing and State-vector Reductionmentioning

confidence: 99%

“…which can be easily derived from Equation (20); it is, thus, sufficient to study a case of a normalized state vector |Ψ⟩, as mentioned before.…”

Section: Generic Nh-driven Evolutionmentioning

confidence: 99%