# NON-HERMITIAN QUANTUM DYNAMICS OF A TWO-LEVEL SYSTEM AND MODELS OF DISSIPATIVE ENVIRONMENTS

@article{Sergi2013NONHERMITIANQD, title={NON-HERMITIAN QUANTUM DYNAMICS OF A TWO-LEVEL SYSTEM AND MODELS OF DISSIPATIVE ENVIRONMENTS}, author={Alessandro Sergi and Konstantin G. Zloshchastiev}, journal={International Journal of Modern Physics B}, year={2013}, volume={27}, pages={1350163} }

We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system (TLS) coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling TLS. The time evolution is formulated and derived in terms of the normalized density operator of the model, different types of decays are revealed and analyzed. In particular, the population…

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## References

SHOWING 1-10 OF 114 REFERENCES

A non-Hermitian Hamilton operator and the physics of open quantum systems

- Physics
- 2009

The Hamiltonian Heff of an open quantum system consists formally of a first-order interaction term describing the closed (isolated) system with discrete states and a second-order term caused by the…

Dissipative dynamics of quantum spin systems.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1992

The quantum version of the Landau-Lifshitz equation for damped spin motion is analyzed using a properly tailored Gisin approach to the dissipative quantum mechanics and is shown to be equivalent to the conventional description.

Matrix Algebras in Non-Hermitian Quantum Mechanics

- Mathematics, Physics
- 2010

In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schrodinger's picture of quantum dynamics. Here it is shown in both…

Classical limit of non-Hermitian quantum dynamics—a generalized canonical structure

- Physics, Mathematics
- 2010

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by…

Wave-packet evolution in non-Hermitian quantum systems

- Physics
- 2011

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit ({h_bar}/2{pi}){yields}0 this yields the…

Time-dependent theory of non-Hermitian Schrödinger equation: application to multiphoton-induced ionisation decay of atoms

- Physics
- 1981

A rigorous and practical time-dependent formulation of quantum decay processes is obtained by converting the Hermitian Schrodinger problem into an equivalent non-Hermitian Schrodinger equation. The…

A simple nonlinear dissipative quantum evolution equation

- Physics
- 1981

The author has considered a nonlinear dissipative evolution equation that generalises the Schrodinger equation. In the corresponding evolution all the stationary states of the usual Schrodinger…

Microscopic derivation of a class of non-linear dissipative schrödinger-like equations

- Mathematics
- 1982

DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS

- Physics
- 2013

Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because…