Recent Developments

Alicki, Robert; Lendi, K.

doi:10.1007/3-540-70861-8_3

Cited by 307 publications

(703 citation statements)

References 73 publications

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“…Following this latter approach, one derives that the evolution over a finite time ∆t must be of the form (Stinespring theorem, Ref. [14])…”

Section: Lindblad From Kraus-stinespringmentioning

confidence: 99%

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Laser theory in manifest Lindblad form

Henkel

2007

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We discuss the laser theory for a single-mode laser with nonlinear gain. We focus in particular on a micromaser which is pumped with a dilute beam of excited atoms crossing the laser cavity. In the weak-coupling regime, an expansion in the coupling strength is developed that preserves the Lindblad form of the master equation, securing the positivity of the density matrix. This expansion breaks rapidly down above threshold. This can be improved with an alternative approach, not restricted to weak coupling: the Lindblad operators are expanded in orthogonal polynomials adapted to the probability distribution for the atom-laser interaction time. Results for the photon statistics and the laser linewidth illustrate the theory.

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“…Following this latter approach, one derives that the evolution over a finite time ∆t must be of the form (Stinespring theorem, Ref. [14])…”

Section: Lindblad From Kraus-stinespringmentioning

confidence: 99%

“…Consider a polynomial approximation of order N to the cos and sinc functions in Eqs. (14,17). The operator C † C is then of order 2N in gτ and the operator S † S of order 2N + 2 [cf.…”

Section: Consistency Of the Expansionmentioning

confidence: 99%

Laser theory in manifest Lindblad form

Henkel

2007

J. Phys. B: At. Mol. Opt. Phys.

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“…The semigroup Λ t should satisfy the following conditions Λ t Λ s = Λ t+s − semigroup property (7) lim t→+0 Λ t σ = σ − continuity (8) for σ ≥ 0 , Λ t σ ≥ 0 − positivity (9) for any σ ∈ T (H) , Tr (Λ t σ) = Tr σ − trace preservation .…”

Section: Axiomatic Approachmentioning

confidence: 99%

“…which is a sum of "pure" transition maps ρ → V j ρV * j corresponding to elementary irreversible processes [7]. The following expansion for Λ t = exp(tL) involving only sums (or integrals) and compositions of manifestly completely positive maps Φ (15) and W t…”

Section: B Completely Positive Dynamical Semigroupsmentioning

confidence: 99%

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Invitation to Quantum Dynamical Semigroups

Alicki

2002

Dynamics of Dissipation

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The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general mathematical structures is discussed. Then basic derivation schemes of the constructive approach including singular coupling, weak coupling and low density limits are presented in their higly simplified versions. Two-level system coupled to a heat bath, damped harmonic oscillator, models of decoherence, quantum Brownian particle and Bloch-Boltzmann equations are used as illustrations of the general theory. Physical and mathematical limitations of the quantum open system theory, the validity of Markovian approximation and alternative approaches are discussed also.

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Compression of Quantum Information

Horodecki

2001

Fortschr. Phys.

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Recent Developments

Cited by 307 publications

References 73 publications

Laser theory in manifest Lindblad form

Laser theory in manifest Lindblad form

Invitation to Quantum Dynamical Semigroups

Compression of Quantum Information

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