Hence, this work includes all the results of both [4] (no power source) and [6] (no resistances) as special cases. The fluctuations and uncertainty product in the DN and in the DSN are plotted in Figure 5. We can adjust the uncertainty (or fluctuation) of a quadrature to be small at the expense of broadening that

of another quadrature, or vice versa. The uncertainty in the case of this figure is larger than , while is smaller than due to the squeezing effect. Therefore, it is relatively difficult for us to know the precise value of charge q 1, while we can find out the conjugate current p 1 more precisely. However, the relevant uncertainty product in the DSN is nearly unaltered from see more that in the DN. Figure 5 Fluctuations. This inset shows fluctuations (dashed line) and (thick solid line) (a), and (dashed line) and (thick solid line) (b), and uncertainty product (dashed line) and (thick solid line)

(c) as a function of t where n 1=n 2=0, , R 0 = R 1 = R 2 = 0.1, L 0 = L 1 = L 2 = 1, C 1 = 1, and C 2 = 1.2. The values of squeezing parameters for the DSN are r 1 = 0.1, r 2 = 0.3, ϕ 1 = 1.2, and ϕ 2 = 0.6. Conclusions In summary, the time evolution of the DSN for the two-dimensional electronic circuit composed of nanoscale elements and driven Caspase inhibitor by a power source is investigated using unitary transformation method. Two steps of the unitary transformation are executed: We removed the cross term involving in the original Hamiltonian from the first step, and the linear terms represented in terms of in the firstly transformed Hamiltonian are eliminated by second unitary transformation.

We can see from Equation 6 that the original Hamiltonian is time-dependent. When treating a time-dependent Hamiltonian system dynamically, one usually employs classical solutions of the equation of motion for a given system (or for a system similar to a given system) [6, 7]. We also introduced such classical solutions in Equations 19 to 20 and in Equations 47 to 48. Among them, particular solutions q j p and p j p are important in developing quantum theory of the system involving most external power source since they are crucial factors that lead the transformed Hamiltonian to be simple so that we can easily treat it. Since the transformed system is just the same as the one that consists of two independent simple harmonic oscillators, provided that we can neglect the trivial terms in the transformed Hamiltonian, we easily identified the complete quantum solutions in the DSN in the transformed system. We also obtained the wave functions of the DSN in the original system via the technique of inverse transformation, as shown in Equation 50. If we regard the fact that the probability does not reflect the phase of a wave function, the overall phase of these states is relatively unimportant for many cases.