The Time-Convolutionless Projection Operator Technique in the Quantum Theory of Dissipation and Decoherence

Breuer, Heinz‐Peter; Kappler, Bernd; Petruccione, Francesco

doi:10.1006/aphy.2001.6152

Cited by 156 publications

(158 citation statements)

References 34 publications

Supporting

Mentioning

156

Contrasting

Order By: Relevance

“…Such a Master Equation, obtained by using the time-convolutionless projection operator technique [19,20], is the superoperatorial version of the Hu-Paz-Zhang Master Equation [9]. Let us note, first of all, that the Master Equation (2) is local in time, even if non-Markovian.…”

Section: Exact Dynamicsmentioning

confidence: 99%

Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator

Maniscalco¹,

Intravaia²,

Piilo³

et al. 2004

J. Opt. B: Quantum Semiclass. Opt.

View full text Add to dashboard Cite

show abstract

Section: Exact Dynamicsmentioning

confidence: 99%

Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator

Maniscalco¹,

Intravaia²,

Piilo³

et al. 2004

J. Opt. B: Quantum Semiclass. Opt.

View full text Add to dashboard Cite

show abstract

“…Formally exact dynamics for the system is described by the Nakajima-Zwanzig equation with time convolution 5,6 and the time-convolutionless ͑TCL͒ equations. [7][8][9][10][11] The first is equivalent to the chronological ordering prescription while the second corresponds to a partial ordering prescription of the time ordering in a system-bath cumulant expansion. 7,12,13 Under certain conditions, the convolution kernel can be transformed into the TCL kernel by including the appropriate backward propagation for the density matrix.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian quantum jumps in excitonic energy transfer

Rebentrost

Chakraborty

Aspuru‐Guzik

2009

The Journal of Chemical Physics

130

166

View full text Add to dashboard Cite

We utilize the novel non-Markovian quantum jump ͑NMQJ͒ approach to stochastically simulate exciton dynamics derived from a time-convolutionless master equation. For relevant parameters and time scales, the time-dependent, oscillatory decoherence rates can have negative regions, a signature of non-Markovian behavior and of the revival of coherences. This can lead to non-Markovian population beatings for a dimer system at room temperature. We show that strong exciton-phonon coupling to low frequency modes can considerably modify transport properties. We observe increased exciton transport, which can be seen as an extension of recent environment-assisted quantum transport concepts to the non-Markovian regime. Within the NMQJ method, the FennaMatthew-Olson protein is investigated as a prototype for larger photosynthetic complexes.

show abstract

“…Several tentatives have been made to provide a non-Markovian master equation for the spin-boson model, exploiting e.g. the noninteracting-blip approximation [3], the time convolution-less technique (TCL) [1,6], or the stochastic approach [7]. However, only approximated results were obtained.…”

mentioning

confidence: 99%

Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models

Ferialdi

2017

Phys. Rev. A

View full text Add to dashboard Cite

We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model. In order to describe these systems one needs to consider a non-static bath, i.e. a bath that keeps track of the interaction with the TLS. Accordingly, some memory effects build up and the dynamics is non-Markovian. Several tentatives have been made to provide a non-Markovian master equation for the spin-boson model, exploiting e.g. the noninteracting-blip approximation [3], the time convolution-less technique (TCL) [1,6], or the stochastic approach [7]. However, only approximated results were obtained. The lack of an exact analytical description lead to investigate the problem by means of numerical techniques, among which we mention hierarchical equations of motion [8], * Electronic address: ferialdi@fmf.uni-lj.si arXiv:1609.00645v3 [quant-ph]

show abstract

The Time-Convolutionless Projection Operator Technique in the Quantum Theory of Dissipation and Decoherence

Cited by 156 publications

References 34 publications

Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator

Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator

Non-Markovian quantum jumps in excitonic energy transfer

Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models

Contact Info

Product

Resources

About