We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-Hermitian Hamiltonian ${H}_{\mathrm{eff}}$ , in accord with the Wigner-Weisskopf approximation, and an additional term of the Lindblad form, the so-called dissipator. We show that, after enlarging the original Hilbert space by states which represent the decay products of the unstable states, the non-Hermitian part of ${H}_{\mathrm{eff}}$ ---the ``particle decay''---can be incorporated into the dissipator of the enlarged space via a specific Lindblad operator. Thus the formulation of the time evolution on the enlarged space has a Hermitian Hamiltonian and is probability conserving. The equivalence of the formulation with the original one demonstrates that the time evolution which is governed by a non-Hermitian Hamiltonian and a dissipator of the Lindblad form is nevertheless completely positive, just as systems with Hermitian Hamiltonians.We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-Hermitian Hamiltonian ${H}_{\mathrm{eff}}$, in accord with the Wigner-Weisskopf approximation, and an additional term of the Lindblad form, the so-called dissipator. We show that, after enlarging the original Hilbert space by states which represent the decay products of the unstable states, the non-Hermitian part of ${H}_{\mathrm{eff}}$---the ``particle decay''---can be incorporated into the dissipator of the enlarged space via a specific Lindblad operator. Thus the formulation of the time evolution on the enlarged space has a Hermitian Hamiltonian and is probability conserving. The equivalence of the formulation with the original one demonstrates that the time evolution which is governed by a non-Hermitian Hamiltonian and a dissipator of the Lindblad form is nevertheless completely positive, just as systems with Hermitian Hamiltonians.

arXiv:quant-ph/0602116Physical Review AMay 1, 200695 citations

a Study of Decay Processes in Quantum Mechanics.

Mark S. Hillery

Mar 1, 19800 citations

Role of quantum statistics in multi-particle decay dynamics

Avi Marchewka, Er’el Granot

Annals of PhysicsFeb 23, 201511 citations

On the Relation between a Non-Hermitian Hamiltonian and a Stochastic Differential Equation in the Theory of Open Systems

Ashat M. Basharov

Abstract We show that a number of particle decay problems, which are described by the non-Hermitian Hamiltonian (correspondingly, the nonunitary dynamics is spoken of), can be correctly and consistently reformulated in terms of stochastic differential equations upon application of the algebraic perturbation theory. In this formulation, kinetic equations are obtained in the standard scheme of the theory of open quantum systems. The parameters of the kinetic equation coincide with similar parameters describing the decay of a particle when the decay is considered on the basis of the non-Hermitian Hamiltonian.Abstract We show that a number of particle decay problems, which are described by the non-Hermitian Hamiltonian (correspondingly, the nonunitary dynamics is spoken of), can be correctly and consistently reformulated in terms of stochastic differential equations upon application of the algebraic perturbation theory. In this formulation, kinetic equations are obtained in the standard scheme of the theory of open quantum systems. The parameters of the kinetic equation coincide with similar parameters describing the decay of a particle when the decay is considered on the basis of the non-Hermitian Hamiltonian.

Optics and SpectroscopyFeb 1, 20206 citations

Neutral kaons as an open quantum system in a second quantization approach

Kordian A. Smoliński

We have shown that it is possible to formulate the consistent and probability-preserving description of the $\mathit{CP}$ -symmetry-violating evolution of a system of decaying particles. This has been done within the framework of quantum mechanics of open systems. This approach allows the description of both the exponential decay and flavor oscillations. We have solved explicitly the Kossakowski-Lindblad master equation for a system of particles with violated $\mathit{CP}$ symmetry and found the evolution of any observable bilinear in creation and annihilation operators. The choice of a concrete observable can be done by the proper choice of initial conditions for the system of differential equations. We have calculated the evolution as well as mean values of the observables most interesting from the physical point of view, and we have found their lowest order difference with the $\mathit{CP}$ -preserved values.We have shown that it is possible to formulate the consistent and probability-preserving description of the $\mathit{CP}$-symmetry-violating evolution of a system of decaying particles. This has been done within the framework of quantum mechanics of open systems. This approach allows the description of both the exponential decay and flavor oscillations. We have solved explicitly the Kossakowski-Lindblad master equation for a system of particles with violated $\mathit{CP}$ symmetry and found the evolution of any observable bilinear in creation and annihilation operators. The choice of a concrete observable can be done by the proper choice of initial conditions for the system of differential equations. We have calculated the evolution as well as mean values of the observables most interesting from the physical point of view, and we have found their lowest order difference with the $\mathit{CP}$-preserved values.

arXiv:1509.07681Physical Review ASep 24, 20155 citations

We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-Hermitian Hamiltonian

{H}_{\mathrm{eff}}

, in accord with the Wigner-Weisskopf approximation, and an additional term of the Lindblad form, the so-called dissipator. We show that, after enlarging the original Hilbert space by states which represent the decay products of the unstable states, the non-Hermitian part of

{H}_{\mathrm{eff}}

---the ``particle decay''---can be incorporated into the dissipator of the enlarged space via a specific Lindblad operator. Thus the formulation of the time evolution on the enlarged space has a Hermitian Hamiltonian and is probability conserving. The equivalence of the formulation with the original one demonstrates that the time evolution which is governed by a non-Hermitian Hamiltonian and a dissipator of the Lindblad form is nevertheless completely positive, just as systems with Hermitian Hamiltonians.

We have shown that it is possible to formulate the consistent and probability-preserving description of the

\mathit{CP}

-symmetry-violating evolution of a system of decaying particles. This has been done within the framework of quantum mechanics of open systems. This approach allows the description of both the exponential decay and flavor oscillations. We have solved explicitly the Kossakowski-Lindblad master equation for a system of particles with violated

\mathit{CP}

symmetry and found the evolution of any observable bilinear in creation and annihilation operators. The choice of a concrete observable can be done by the proper choice of initial conditions for the system of differential equations. We have calculated the evolution as well as mean values of the observables most interesting from the physical point of view, and we have found their lowest order difference with the

\mathit{CP}

-preserved values.