Sentence examples for reduced master equation from inspiring English sources
We then use these values of (lbracealpha_{k,j}(t) rbrace) to formulate the time-dependent reduced master equation (Eq. (55)), and use an order-1.5 stochastic Runge-Kutta method [25] to integrate it.
Here, we provide a simplified derivation of the reduced master equation.
The most economical equation for simulating the desired homodyne measurement is a reduced master equation acting only on the qubit register.
As we have shown in the Results section, under conditions of timescale separation and for small intrinsic noise, there always exists a reduced linear Langevin description of monostable stochastic reaction networks (the ssLNA) but there is generally not a physically meaningful reduced master equation description.
These results are in line with those of Mastny et al.[ 54] which show that for the Michaelis-Menten reaction without substrate input, the sQSPA method, a rigorous singular-perturbation approach, leads to a reduced master equation whenever the free enzyme or complex concentrations are very small (see Table II of Ref. [ 54]).
We reduce the master equation to a corresponding neural Langevin equation and show that both intrinsic and extrinsic noise sources lead to multiplicative white noise terms in the Langevin equation.
In the limit (taurightarrow0), (2.5) reduces to the neural master equation of Buice et al. [17, 20].
Here, we discuss the fundamental theory behind the SE and note that it may be justified through a master equation when reduced to its continuum limit.
After some algebraic calculation, the master equation ofthe reduce density operation of the SQDs' subsystem can be written as ∂ t ρ S Q D = − i [ H e f f, ρ S Q D ] + ς ′ S Q D. (5).
In accordance with standard procedure [25 28], we can obtain the Born-Markovian master equation of the reduced density matrix of the coupled system, ρ (t), through tracing out the environmental degrees of freedom as d ρ d t = - i ℏ [ H, ρ ] + A { [ S -, [ S +, ρ ] ] + h.
The measured reaction rate constants follow a pressure dependence trend close to the theoretical results by Zhang et al. (2011) [10] based on transition state theory master equation analysis, and reducing their theoretical results by ∼40% leads to a close match with the current data.
