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… 
View PDF on arXiv
75 Citations
Highly Influential Citations
2
Background Citations
13
Methods Citations
8

Figures from this paper

75 Citations

Quantum entropy of systems described by non-Hermitian Hamiltonians
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann…
Embedding quantum systems with a non-conserved probability in classical environments
  • A. Sergi
  • Physics, Mathematics
    Theoretical Chemistry Accounts
  • 2015
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be…
Linear Quantum Entropy and Non-Hermitian Hamiltonians
TLDR
This work considers the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians and studies novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics.
A comparative study on the reliability of non-Hermitian effective Hamiltonian approach for modeling open quantum systems
Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay
The Wigner–Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a…
Non-Hermitian Hamiltonians and stability of pure states
We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the…
A comparative study on different non-Hermitian approaches for modeling open quantum systems
Protecting coherence in the non-Hermitian two-level system
We have constructed a non-Hermitian two-level system (a PT -symmetric system) in dissipative environments, and investigated the quantum coherence in the non-Hermitian two-level system. Our results…
Nonadiabatic dynamics of a dissipative spin chain in a transverse magnetic field
The density matrix in the non-Hermitian approach to open quantum system dynamics
In this paper we review an approach to the dynamics of open quantum systems based of non-Hermitian Hamiltonians. Non-Hermitian Hamiltonians arise naturally when one wish to study a subsystem…
...
...

References

SHOWING 1-10 OF 114 REFERENCES
A non-Hermitian Hamilton operator and the physics of open quantum systems
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.
  • Holyst, Turski
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
TLDR
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
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
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
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…
Quantum mechanics of nonconservative systems
Time-dependent theory of non-Hermitian Schrödinger equation: application to multiphoton-induced ionisation decay of atoms
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
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
DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS
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…
...
...