A comparative study on different non-Hermitian approaches for modeling open quantum systems

Abstract

In this paper, we test and compare the performance of two different theoretical methods that use anti-Hermitian terms for modeling open quantum systems. It is, the non-Hermitian quantum mechanics method (NHQM) and the recent methodology known as corrected non-Hermitian effective Hamiltonian (corrected NHEH) approach. In particular, we provide a comprehensive analysis of the performance of these two theoretical approaches by describing the dynamics of the pumped-dissipative Jaynes-Cummings model. Our results demonstrate that whereas the NHQM method fails for describing correctly the time evolution of the density matrix elements as well as the quantum fidelity measure. The corrected NHEH approach shows an excellent agreement with simulations based on the Lindblad master equation formalism.

Adiabatic elimination and subspace evolution of open quantum systems

“…1 , we provide a rigorous connection between non-Hermitian Hamiltonian decay dynamics (Γ (1) 1 /γ 11 → 0) and fully trace preserving dissipative dynamics (Γ (1) 1 /γ 11 → ∞) thanks to the nonlinear term of the form − z z+Γ . This connection is not restricted to the single discrete level-system but is a general feature of discrete levels coupled to a manifold of continua where the evolution presents a transition from non-Hermitian decay Hamiltonians to trace preserving generators, when the dissipation rate from the continuum is varied, and which could provide insight into comparisons of both approaches [53,54].…”

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

“…Such effective dynamical equation is extensively applied in the non-Hermitian quantum mechanics [32]. The reliability of the non-Hermitian Hamiltonian approach has been already tested in the dynamics of the pumped-dissipative JC model [33]. As our numerical method expands the initial state in Fock space, it is directly applicable to systems of dissipations.…”

Kondo effect in a non-Hermitian, $\mathcal{PT}$-symmetric Anderson model with Rashba spin-orbit coupling

“…These states preserve the norm and form a complete set which also allows for an unambiguous definition of expectation of physical observables. Physically, non-Hermitian models represent open quantum systems [3][4][5] . These models can exhibit eigenvalue degeneracies at certain values of non-Hermitian parameters, called exceptional points (EPs), which correspond to quantum phase transitions of the level-crossing type.…”