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Master equation

About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.


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TL;DR: In this article, a non-Lindblad master equation without Lindblad form was shown to violate the positivity of the density operator in the Ornstein Uhlenbeck process both at high and low temperatures.
Abstract: Master equations without Lindblad form can in principle violate the positivity of the density operator. However, when such a master equation arises through systematic adiabatic elimination of fast variables from underlying microscopic dynamics, the violation can at worst arise on time scales one has coarsegrained over when performing the adiabatic elimination and can thus simply be ignored. Examples of non-Lindblad master equations are shown to arise for the Ornstein Uhlenbeck process both at high and low temperatures and for a single-mode laser operated near threshold.

64 citations

Journal ArticleDOI
TL;DR: In this paper, it is demonstrated that in the case of integrable differential-difference equations similar to the well-known Volterra equation, there are many instances in which local master symmetries can be found.

64 citations

Journal ArticleDOI
H. Jirari1, W. Pötz1
TL;DR: In this paper, a Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism.
Abstract: A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the nonperturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum $Z$ gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significantly is a multicomponent low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.

64 citations

Journal ArticleDOI
TL;DR: In this article, the authors formalized the derivation of a generalized coarse-graining $n$-resolved master equation by introducing a virtual detector counting the number of transferred charges in single-electron transport.
Abstract: We formalize the derivation of a generalized coarse-graining $n$-resolved master equation by introducing a virtual detector counting the number of transferred charges in single-electron transport. Our approach enables the convenient inclusion of coherences and Lamb shift in counting statistics. As a Markovian example with Lindblad-type density matrices, we consider the Born-Markov-secular (BMS) approximation which is a special case of the non-Markovian dynamical coarse-graining approach. For illustration we consider transport through two interacting levels that are either serially or parallelly coupled to two leads held at different chemical potentials. It is shown that the coherences can strongly influence the (frequency-dependent) transport cumulants: in the serial case the neglect of coherences would lead to unphysical currents through disconnected conductors. Interference effects in the parallel setup can cause strong current suppression with giant Fano factors and telegraphlike distribution functions of transferred electrons, which is not found without coherences. We demonstrate that with finite coarse-graining times coherences are automatically included and, consequently, the shortcomings of the BMS approximation are resolved.

64 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the extracavity quantum vacuum radiation generated by a sudden switch on and off of the vacuum Rabi frequency of a single two-level system coupled to a single cavity mode in the strong and ultrastrong coupling regime.
Abstract: We study the extracavity quantum vacuum radiation generated by a sudden switch on and off of the vacuum Rabi frequency of a single two-level system coupled to a single cavity mode in the strong and ultrastrong coupling regime. Dissipation is described by including the qubit-resonator coupling in the derivation of the master equation. The output stream of photons and their second-order correlation functions are calculated by exploiting a recently developed input-output formulation of resonators valid for arbitrary light-matter couplings. The obtained output photon correlations provide direct information on the quantum correlations among the virtual excitations of the dressed vacuum.

64 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023140
2022344
2021431
2020460
2019420
2018427