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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: It is shown that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution, and the third law imposes constraints on the low frequency behavior of the environmental spectral densities.
Abstract: We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.
92 citations
TL;DR: In this article, a comparison between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states has been made, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of deterministic equations.
Abstract: A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of O ( N 0 ) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is O (e N ). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.
92 citations
TL;DR: In this article, the authors derived the Kraus operators from the point of view of the quantum channel and proved the normalization conditions of the corresponding Kraus operator from the perspective of the phase sensitive process.
Abstract: We solve various master equations to obtain density operators' infinite operator-sum representation via a new approach, i.e., by virtue of the thermo-entangled state representation that has a fictitious mode as a counterpart mode of the system mode. The corresponding Kraus operators from the point of view of quantum channel are derived, whose normalization conditions are proved. Miscellaneous characters possessed by different quantum channels, such as decoherence, phase diffusion, damping, and amplification, can be shown explicitly in the entangled state representation of the density operators. Squeezing transformation is applied to the density operator for decoherence to generate a master equation for describing the phase sensitive process. Partial trace method for deriving new density operators is also introduced. Throughout our discussion, the technique of integration within an ordered product (IWOP) of operators is fully used.
92 citations
TL;DR: In this article, the quantum dynamics of an exciton boser or laser were analyzed and it was shown that the line width reduction obtained in a boser is limited by the strength of the exciton-exciton interactions.
92 citations
TL;DR: In this paper, a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation, is provided.
Abstract: Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born-Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.
92 citations