Effects of the rotating-wave and secular approximations on non-Markovianity

Mäkelä, Harri; Möttönen, Mikko

doi:10.1103/physreva.88.052111

Cited by 39 publications

(43 citation statements)

References 37 publications

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“…We make a further reasonable assumption of the independence of the pumping source and the phonon reservoir, which yields After a straightforward derivation in the framework of the secular approximation [56], we find…”

Section: Appendix C: Master Equation For Polaritonsmentioning

confidence: 99%

Quantum treatment of the Bose-Einstein condensation in nonequilibrium systems

et al. 2015

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We develop a fully quantum-mechanical approach, based on stochastic trajectories, for an incoherently pumped system of interacting bosons in contact with a thermal reservoir. It enables a complete characterization of coherence in such a multimode system. We apply our model to microcavity exciton polaritons interacting with acoustic phonons and observe the formation of a macroscopic occupation in the lowest-energy mode accompanied by the simultaneous establishment of temporal and spatial coherence. We describe the transition from thermal to coherent statistics together with the expected emergence of an off-diagonal long-range order.

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Section: Appendix C: Master Equation For Polaritonsmentioning

confidence: 99%

Quantum treatment of the Bose-Einstein condensation in nonequilibrium systems

et al. 2015

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“…Now we apply our method to a spin-boson model with [20][21][22][23] assuming an initial system state of σ z = 1 with the bath at zero temperature. In the following calculations, all coupling strengths and frequencies are in units of ω.…”

Section: Results On a Spin-boson Modelmentioning

confidence: 99%

Approach to solving spin-boson dynamics via non-Markovian quantum trajectories

Yip

Deng

et al. 2014

Phys. Rev. A

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We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equation for an open quantum system that can be strongly coupled to an environment. As an important application, we consider a real-time simulation of a spin-boson model in a strong coupling regime that is difficult to deal with using conventional methods. We show that the non-Markovian stochastic Schrödinger equation can be efficiently implemented as a real-time simulation for this model, so as to give an accurate description of spin-boson dynamics beyond the rotating-wave approximation.

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“…On the other hand, it is known that these approximations, for instance in the case of the spin-boson model, fail to detect the non-Markovianity of the dynamics [15]. Since a properly defined quantifier of non-Markovianity would allow to assess whether and to what extent these approximations describe the time evolution correctly, it is important to investigate the exact dynamics of Gaussian channels in the general case, making no approximations except the weak coupling limit assumption that preserves the form of the master equation for the dynamical map.…”

Section: Introductionmentioning

confidence: 99%

Exact non-Markovian dynamics of Gaussian quantum channels: Finite-time and asymptotic regimes

Torre

Illuminati

2018

Phys. Rev. A

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We investigate the Markovian and non-Markovian dynamics of Gaussian quantum channels, exploiting a recently introduced necessary and sufficient criterion and the ensuing measure of non-Markovianity based on the violation of the divisibility property of the dynamical map. We compare the paradigmatic instances of Quantum Brownian motion (QBM) and Pure Damping (PD) channels, and for the former we find that the exact dynamical evolution is always non-Markovian in the finite-time as well as in the asymptotic regimes, for any nonvanishing value of the non-Markovianity parameter. If one resorts to the rotating wave approximated (RWA) form of the QBM, that neglects the anomalous diffusion contribution to the system dynamics, we show that such approximation fails to detect the non-Markovian nature of the dynamics. Finally, for the exact dynamics of the QBM in the asymptotic regime, we show that the quantifiers of non-Markovianity based on the distinguishability between quantum states fail to detect the non-Markovian nature of the dynamics.

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Effects of the rotating-wave and secular approximations on non-Markovianity

Cited by 39 publications

References 37 publications

Quantum treatment of the Bose-Einstein condensation in nonequilibrium systems

Quantum treatment of the Bose-Einstein condensation in nonequilibrium systems

Approach to solving spin-boson dynamics via non-Markovian quantum trajectories

Exact non-Markovian dynamics of Gaussian quantum channels: Finite-time and asymptotic regimes

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