Nontrivial eigenvalues of the Liouvillian of an open quantum system
arXiv:1010.5302 · doi:10.1007/s10773-010-0606-9
Abstract
We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state and the ket state. We also introduce the integral equations equivalent to the original eigenvalue problem.
5 pages, 2 figures, proceedings
References in corpus (1)
Cited by in corpus (12)
- Multiple quantum Mpemba effect: exceptional points and oscillations
- Time-reversal symmetric resolution of unity without background integrals in open quantum systems
- Efficient determination of the Markovian time-evolution towards a steady-state of a complex open quantum system
- Current correlations for the transport of interacting electrons through parallel quantum dots in a photon cavity
- Regimes of radiative and nonradiative transitions in transport through an electronic system in a photon cavity reaching a steady state
- Electroluminescence caused by the transport of interacting electrons through parallel quantum dots in a photon cavity
- Time-dependent current into and through multilevel parallel quantum dots in a photon cavity
- Oscillations in electron transport caused by multiple resonances in a quantum dot-QED system in the steady-state regime
- Generalized Master Equation Approach to Time-Dependent Many-Body Transport
- Cavity-photon induced high order transitions between ground states of quantum dots
- Tutorial: projector approach to master equations for open quantum systems
- Self-induction and magnetic effects in electron transport through a photon cavity